IMPROVED MECHANISM FOR THE CONVERSION MODIFICATION, REGULATION AND TRANSMISSION OF MOTION
Year: 1885

page_text: Regulation, and Transmission of Motion.
I, WILLIAM GOLDING of Yarburgh Street, Moss Side, in the County of Lancaster,
Manufacturer, do hereby declare the nature of said Invention for IMPROVED
MECHANISM FOR THE CONVERSION MODIFICATION, REGULATION AND TRANSMISSION
OF MOTION, or described more fully A Complete Scientific System of Practical
Mechanics, effectuated by means of a new Mechanical Power to be called "Claviger"
for Receiving, Controlling and applying Force in Motion.
1. Means of utilizing Natural Forces, Wave impact, falling and running water
and tidal motion, explosive forces, muscular energy; and for fully utilizing the
expansive force of Steam.
2. Means of Collecting, Transmitting and Distributing Power over large areas.
3. For Driving Stationary and Marine Engines; for Driving Restraining and
Stopping Locomotive Engines and Trains; for propelling Boats and Ships; for
operating, Steering and Restraining "Cycles" of every description; for Rotating,
Dynamos and for Receiving Motion therefrom.
4. For Lifting, Weighing and Compressing Apparatus.
5. For perfectly Converting and Transmitting Motion in machines, and from
one machine to another by direct motion; for Modifying Motion in machines, in
forin, direction, velocity, extent, number and uniformity, so as to exactly adapt it
to every requirement.
6. For Regulating and Governing Motors, Machines and Clocks.
7. For Philosophical Instruments, to be as follows:-
The principle upon which this system of practical mechanics is founded is that
of the Parallelogram of Forces, and the mechanical power called "Claviger" which
is employed to carry it into effect is an exact practical counterpart of the theories
which have been established in connection with that principle.
By varying the proportion and adjustment of its parts and by combining two
or more clavigers, force in motion of any kind, acting in any direction, can be

page_text: unfection and at any desired distance,
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constraint upon the part to which the motion is referred, except tr
upon it of the the force applied in the direction of the motion desired.
straint
The proportion of speed and power as between the force and the work can be
varied by it to any extent, either in length or number.
The character of the velocity can also be changed by it, as uniform velocity into
uniformly accelerated or uniformly retarded or into irregular velocity, and vice
versa,
The movements hereinafter described are for convenience divided into two classes,
namely class A and class B.
The movements belonging to class A deal with conversion, transmission and
modulation of motion by means of this mechanical power in its simplest form;
namely, that of rigid rods, operating from centres.
Most of the movements of conversion and all those of transmission are mathe-
matically exact, while those which are not exactly so approach so nearly to it, that
in practice the difference is not important, being in most instances so
to be observable.
small as not
In all cases the motion is smooth, noiseless and precise, with continuous full
impulse, not needing the assistance of inertia.
Under Class B this mechanical power is dealt with in its perfect form, which
consists, in most of the movements, of more parts than in Class A.
By means of this form, force in motion is perfectly converted, varied, regulated
governed and transmitted exactly as required.
When a movement is explained belonging to Class A if it is not a perfect
movement it will be stated in what respects it falls short of perfection.
When explaining a movement belonging to Class B it will be described as a
perfect movement.
By a perfect movement, whether of conversion, transmission or modulation, or all
combined, is meant a transferrence of the force with full and continuous equal
impulse, delivered throughout to the receiving part of the machinery to be moved
in a direction exactly conterminous with its notion, however long complicated and
varied the desired resulting motion may be. An exact constant uniformity of
velocity between the power and the operating ends; or the velocity multiplied or
reduced, retaining a constant ratio between them; or the velocity exactly varied
in any manner to suit the requirements of the machine. The lines of movement
to be mathematically exact, that is supposing rectilinear motion to be changed into
circular, the power end of the claviger will move in an exact straight line while
the operative end will describe an exact circle without forcible constraint.
friction to be between parallel surfaces only, that is a hollow cylinder rotating on a
cylinder, or vice versa, as in pivots, fixed axes, or circular bearings, or that of
blocks moving along a straight or circular slide, and the friction to be the least
possible consistent with the movement.
The
In addition to the perfect transferrence of the motion, these mechanical move-
ments are simple in their construction and capable of application to the most
delicate machinery, such as that of watches and clocks, while they can be
constructed of enormous strength for any class of machinery, with less material
and weight than that now required for the same purpose.
In addition to the description of the simple movements a few examples of their
practical application in machinery are given, in order to show how variations inay
be made in the normal forms for particular purposes, and also of some of its
movements requiring the addition of subsidiary parts for particular purposes, in
order to indicate the scope of its application in machinery generally.
This description is divided into articles numbered for convenience of reference,
so as to avoid undue verbal repetition.

page_text: 1. In order. now to explain the principle of the movement and its practical
operation, reference is first made to Plate 1. Fig. 1. A B, B C, Sx and Sy
represent four rigid rods.
The rods A B and B. C are equal in length to each other. The rods S and Sy
are also equal to each other and are each half the length of the rod A B or B C.
The two rods A. B and B. C are pivoted together at their ends at B, and the two
rods SxSy are pivoted together at their ends at S, and are each pivoted at their
other ends to the centres of the rods A B and B. C respectively.
The rods are free to turn upon the pivots. A stud or a bearing hole is made at
the ends A and C for supplying means of attachment to the connecting machinery
If the centres of the pivots A, x, B, y, C and S are now supposed to be connected
by straight lines the four rods form a parallelogram, with two of its contiguous
sides extended to twice their length and the points A S and C are in a straight
line. Now if these rods are moved upon their pivots this combination will be
found to possess certain qualities of mobility and rigidity which will be now.
explained. Whatever motion may be given to the rods the points A S and C are
always in a straight line, and the angles A. S B and C S. B are always right
angles.
The point S is also always in the centre of a straight line joining the
points A and C. .As a result of these qualities, if force in motion in any
direction be independently impressed upon the points A and C, the point S
will remain fixed if the two forces are equal in magnitude and opposite in.
direction, or it will move along a line which is the resultant of the two forces
impressed upon A and C.
If the same two forces which are applied at the points A and C be applied to a
particle and represented in direction and magnitude by two straight lines drawn
from the point of application and a parallelogram be described on these straight
lines as adjacent sides, the particle will move along the diagonal of the parallelogram
which passes through the point.
The point S moves exactly in the same direction but its line of movement is
half the length of the diagonal of the parallelogram.
If the diagonal of the parallelogram be divided into four equal parts, the line,
described by the point S'will be, in most cases, represented by the two parts of the
diagonal adjacent to the centre.
In the case of the movement of the particle, the diagonal of the parallelogram
represents the magnitude of the resultant. With respect however to the movement
of the combination of rods just described the intensity of the resulting force is
inversely as the length of the line of motion described by S to the line of motion.
described by A plus the line of motion described by C.
That is the magnitude of the force of the resultant is equal to the magnitude of
the forces of the components.
2. If pressure be exerted independently upon the points A and C, during a
certain interval of time, and the intensity and direction of the pressure be varied
during the interval so as to cause the points A and C to describe regular or
irregular figures of any kind and similar or dissimilar to each other, the point S
will describe a figure which is the resultant of the two figures described by the .
points A and C. If it be supposed that the same forces which have operated upon
the points A and C so as to compel them to describe any such figures be made to
act upon a particle, such particle will move along a course or figure of exactly the
same shape as that described by the point S. but of twice the extent.
3. Let the pivot at S be fixed, still leaving the rods free to move upon it. Let
any movement be described by the point A. The point C will describe a similar.
movement but opposite in direction.
In Plate 1. Fig. 2. the ends A and C are shewn connected with two cranks.
If the crank at A be moved from 0 to 1 the crank at C will be moved by the rods
also from 0 to 1 but the direction is directly opposite.

page_text: If the crank A be moved from figure to figure consecutively, round the crank
pin circle, the crank C will move in the same order round its circle and thus the
crank C will be rotated in the same direction as the crank A. If the crank at C.
be taken away the point C will still describe a perfect circle of the same diameter
as that described by A. When the point A is moved away from or towards the
fixed point, S by the motion of the crank the point C. is correspondingly moved
away from or towards the point S,. to the same extent. When the point A is
depressed by the action of the crank, the point C is correspondingly raised to the
saine extent; when the point A is raised the point C is depressed to the same
extent. The motion of the crank A is thus perfectly transmitted to the crank C.
This transmission is effected by means of the rods acting through leverage and by
direct thrust and pull combined in the exact proportion necessary. The method
of this action will be more clearly understood when considering the conversion of
rectilinear motion into continuous circular motion. The point. S bisects a line
joining the centres of the two crank shafts, it also bisects every line drawn from
any part of the circumference of the crank pin circle of A to a corresponding part
of the circumference of the crank pin circle of C measuring the points from zero
in each, in the same direction.
4. Plate 1. Fig. 3 represents rectilinear motion transmitted along the same
straight line, but reversed in direction. The pivot S is fixed. The pivots A and C
are supplied with wheels or rollers. A guide F. G. is fixed in position so as to
allow the rollers A and C to run along its lower surface. The rollers cannot be
moved away from the guide. If motion be given to the point A towards or away
from S the point C moves to the same extent in an opposite direction.
5. Plate 1. Fig. 4. represents a similar movement but the lines of motion are
parallel. The motions of A and C are directed by the fixed guides F. G and HK,
one guide is between one roller and the fixed point S and the other guide is outside
the other roller. This arrangement gives a reciprocal restraint, allowing the
rollers freedom to run along the guides but preventing the possibility of moving
them away from their line of motion, without breaking the parts.
1
6. In the foregoing examples the lines of motion of the points A and C are
equal, and the point S, the centre of force, is midway between them.
The contained parallelogram Sx By in these examples is a rhombus. Fig. 5,
represents a method of transferring any of the motions previously described and at
the same time shortening or lengthening the line of motion.
In this arrangement of the rods, the contained parallelogram is a rhomboid and
two of its sides are produced to A and C, the three points A. S. C. being in a
straight line.
+
The necessary restraint is here represented by a bearing the connecting rod L.
If the point A be moved towards M, the point C will move in a parallel and
opposite direction, the length of its line of inotion bearing the same ratio to the
length of the line of motion of A that the line S. C. bears to the line S A. If both
ends A and C are left free to move in any direction and the point A be made to
describe any figure, the point C will describe the same figure inverted, and reduced
in size in the ratio of S. C. to S. A.
If each of these figures be divided into the same number of equal parts and the
corresponding division in each be connected by a straight line all these straight
lines (which are of different lengths) will pass through the point S, and it will
divide each line into two parts which bear the same ratio to each other that the
line A. S. bears to the line S. C.
7. In the examples given in Plate 1 Figs 2. 3. 4 and 5 the point S is fixed,
because the centre of force is a point, and the forces necessary to move the points A
and C along their line of motion are for the same interval of time equal in
magnitude and opposite in direction. A different condition is represented by
Plate 1. Fig. 6. The pivots A. S and C are fixed to blocks which are placed in and

page_text: :
are free to move along slides D. E. N M and F. D. The centre of the slide N M
from 0 to 14 is in length and direction represented by half the diagonal of the
parallelogram of which the centre of the slides F. D. and D. E from 0 to 14
represent two adjacent sides. If the centre of the block A be placed over the
point marked 0 the block S and the block C. each take up their positions over the
point 0 in their respective slides. If the point A be now moved along the slide
towards E the points S and C move along their respective slides, passing the
corresponding figures in each at the same instant. If power be applied at A in
the direction of the arrow it will raise a weight at C, the virtual velocity being
the same for both weight and power.
If the weight or the work be attached at S the virtual velocity will be
P's Vel: W's Vel:: DE: NM: W: P.
The position and extent of M N may be found, whatever the direction of F D
and D. E, by dividing the lines of motion along F D and D E into the same
number of indefinately small equal parts. The commencement of each line of
motion is then taken as zero and the divisions numbered consecutively in the
direction of the motion. The centre point in a straight line joining each corre-
sponding point in the two lines is then marked, and the locus of these centre
points is the line along which the centre pivot at S is to move. This line is
hereinafter designated the centre locus. It is always a mean, in respect to
direction and form, between the two lines of motion described by the power and
weight ends A and C.
8. Plate 1. Fig. 7, represents the application of the principle described in the
previous article to the conversion of continuous circular motion to reciprocal
rectilinear or vice versa. The end A is here attached to a crank. The end C is
provided with a block placed in and free to move along the straight slide E. F.
The centre point of the block C moves from the point 0 to 0.
The length
between these two points is equal to the circumference of the crank pin circle.
This line and each half of the crank pin circle is divided into the same number of
equal parts and the centre locus found as described in the previous article. This
centre locus consists of two halves of common cycloids reversed. The centre pivot S
is provided with a roller. A fixed guide M. is placed in position. The profile of
its inner surface is parallel to the centre locus and is distant therefrom a space
equal to the radius of the roller on the centre pivot S. When the crank is rotated
in the direction of the arrow the centre pivot S rolls along the guide while the
point C moves along the straight line in the sense of the arrow with the same
velocity as A until A has reached its lowest point 0. Immediately the crank has
passed 0 the point C returns along the straight line in the opposite direction.
Also the power may be applied at C but in that case the crank must be started
to rotate in the opposite direction to that indicated by the arrow. Reciprocal
rectilinear motion is thus converted into continuous circular.
9. It may be stated generally that whatever conversion, transmission or modu-
lation of motion is required the centre locus between the two complete lines of
motion should be found. The two ends of the rods A and C should be constrained
to move along the two lines of motion and the centre pivot along the centre locus.
This statement exhibits the application of this system in its crudest form. It is
frequently the case that a guide cannot be shaped parallel to the centre locus
without part of its bearing edges being cut away. In many cases also the direction
of the motion given by the power to the ends A or C is unsuitable to maintaining
and moving the centre pivot S along the centre locus. These difficulties are
completely overcome, as will be explained in detail when considering the different
movements, by firstly, a system of reciprocal restraint applicable to every movement,
the application of which to rectilinear motion is illustrated in Plate 1. Figs. 3
and 4, and described in articles 4 and 5; and secondly, by application of a second.
arrangement of rods similar to those represented in Plate 1. Fig. 1 (which in all'

page_text: cases will have a fixed pivot either at the centre or at one end), whose office is to
hold the centre pivot and move it directly along its centre locus. In many cases
the centre locus is so nearly an arc of a circle that by slightly varying the velocity
of the power or weight end of the rods the centre locus may be made so. In that
case there is no need for fixed guides for the centre locus, as it is moved and
controlled by a link supported by a fixed pivot or stud.
It is on this principle the movements in class A are designed.
10. In order to facilitate the description of the movements to follow, names are
given to the different rods and their combinations. Plate 1, Fig. 8, represents a
claviger. The rod A B is called the clavis rod; the link or arm x S is called the
restraining arm. S is a fixed stud supporting the restraining arm and is called the
fixed axis. The pivot x is called the pivot and is either a stud rigidly attached to
either A. B or x S with the other free to revolve upon it or it is a pin not attached
to either, and both are free to revolve upon it. The line described by the power
end of the clavis rod is called the traverse. When the pivot x is at the centre of
the clavis rod and the restraining arın x S is half the length of A Bit is then a right
claviger. When the dimensions are different it is called an irregular claviger.
When two clavigers are pivoted together at one end of the clavis rods while the
fixed axes of the two restraining arms are in different positions it forms a claviger
pair. If the two clavigers are right clavigers and the distance between the two
fixed axes S S is equal to the length of one of the clavis rods then it is a right
claviger pair, see Plate 1. Fig. 9. Three or more clavigers so combined form a
claviger chain. When it is so arranged that lines joining the fixed axes form
right angles and all the clavis rods can be placed so that each shall make an angle
of 45° with such lines, it is a right claviger chain. This is represented in
Plate 1. Fig. 10. Two right clavigers pivoted together at the ends of the clavis
rods and at the ends of the restraining arms form a right claviger couple with
equal limbs, represented in Plate 1. Figs. 1, 2, 3, 4, 6 and 7.j
When two irregular clavigers are coupled together so as to form a rhomboid with
two sides produced so that the points A, S, C, see Plate 1 Fig. 5 are in a straight
line and Sy is equal to yC and Sx to Ax, it is a right claviger couple with
unequal limbs. The claviger couple in its simplest form is a parallelogram with
one side extended, formed by four rods pivotted together. A point is then taken
on one rod which lies between any two points taken on two other rods so that the
three points shall be in a straight line. This point is the centre pivot or centre of
force, see S Plate 1. Fig. 11. Whatever motion is given to the rods these three
points are always in a straight line and the centre point maintains the same relative
position with respect to the other two. Any number of additional rods may be added
for strength, forming additional parallelograms, without affecting the movement.
Plate 1. Figs. 12. 13. 14. and 15 are examples of irregular claviger couples with
equal limbs..
Plate 1. Figs. 16 and 17 represent irregular claviger couples with unequal limbs.
Plate 1. Fig. 18 represents four parallelograms formed by six equal rods
pivotted at their centres and ends, this is a double claviger couple.
11. The rods of which the clavigers are composed are. inflexible and may be
composed of steel or any other elastic metal, solid or hollow, and shaped propor-
tionately to withstand the strains to which they are to be subjected, so as to
economise material and lessen the weight.
In some cases the rods may be replaced by arms built up of various parts,
properly stayed, and bolted or otherwise rigidly fixed together.
In the drawings, straight rods are shewn in all cases, so as to clearly represent
the movements; supporting framework is only rarely shewn, the fixed axes and
guides being indicated by a small cross.
The pivots, joints and cranks are treated somewhat conventionally, and small
details of construction are not represented, such as bolts, washers, crank-keys, &c.

page_text: Instead. of cranks, single and double and crank shafts as represented, crank
wrists attached to revolving or oscillating discs, wheels or. rods are employed where
-more convenient.
12. Rectilinear Motion Converted to Circular Motion and vice versa.-In article 8
it has been shewn that the centre locus of a circle and a straight line of equal
lengths, consists of two halves of a common cycloid reversed. This is the case
whatever the relative positions of the circle and straight line may be. The cycloid
is generated by a rolling circle of half the circumference of the circle, the directrix
being half the length of the straight line. The generating point is taken at
starting on the perpendicular line drawn on the directrix through its point of
contact with the rolling circle. If two points be taken midway between the ends
of the straight line and the centre of the circle, the line joining these two points is
the line along which the axis of the generating circle moves. The directrix is
situated on opposite sides of this line for each half cycloid. If the straight line
be longer or shorter in length than the circumference of the circle, the half cycloids
are generated by a generating circle of half the circumference of the circle invariably
connected with a rolling circle whose circumference is half the length of the straight
line. The positions of the circle, straight line and cycloid are also interchangeable.
Thus when a cycloid is found which is the centre locus of a given circle and a
given straight line, the circle is also a centre locus between the cycloid and the
straight line, and the straight line is a centre locus between the circle and the
cycloid. Each of them is however of half its dimensions when it is in position as
centre locus.
Plate 2, Figs. 1. 2 and 3 shew a series wherein the straight line is the centre
locus, and Figs. 4. 5 and 3 shew a series having a circle for the centre locus.
In each series the centre figure is the resultant of the two outer figures which are
the components.
If any length be taken in Figs..1 and 3 say from 0 to 1, and it is supposed to be
sufficiently short in each, to be regarded as a straight line, these two lengths will
represent in direction and magnitude the two adjacent sides of a parallelogram of
which the corresponding length in the straight line Fig. 2 will represent in direction
the diagonal, but of half its magnitude. This is also the case with the series Figs. 4.
5 and 6, and is true of any two figures whatever and their centre locus. By this
means curves representing the movements of bodies as the result of regular forces
can be analyzed and resolved into their elements.
13. Reference is now made to Plate 2, Fig. 6. C. D. is a straight line, and for
clearness of explanation it may be given a length in numerals say 37 inches. It is
divided into 15 equal parts by the points, marked from a to 8, each part being 2
inches in length. From point g as a centre with the length of one part as radius
the circle shewn in the figure is described. At point la straight line A. B. is drawn
perpendicular to the line CD. The circumference of the circle is divided into any
number of equal parts; it is here divided into 16, commencing zero at the point
nearest the straight line. Through the divisions 0, 4, 8, 12 and 0 straight lines are
drawn equal in length to C. D, and divided in the same manner. Each line cuts
the line A, B at its tenth division, marked l. The points in the straight line A. D
through which the five lines so drawn pass are marked with the same numerals as
the circle. Each of the four parts of the line straight A. B from 0 to 4, 4 to 8 8 to 12
and 12 to 16 is equal in length to the diameter of the circle.
The line A. B. is divided into the same number of equal parts as the circle, and
the straight lines joining the corresponding numerals in each are divided by points
into the same number of equal parts as the corresponding part of the line C. D, and
these points are. extended outwards into 15 equal divisions along straight lines
corresponding with the five straight lines previously drawn, but they are not
exactly of the same length. The loci of these points are cycloids, and they will
be used for converting rectilinear into circular motion, with rigid rods composing.

page_text: Intermediate divisions or further divisions obtained by prolonging the lines in
either direction continue the same sequence.
If a locus be taken between the straight line A B and the circle by dividing each
straight line joining the corresponding numerals in each into two parts, bearing to
each other the same ratio that the straight line bears to the circumference, the
shortest distance being next the circle, such locus is a common cycloid. Also if a
centre locus be taken between the straight line and the circumference, it is a
contracted cycloid, described by a generating circle of 21 inches diameter invariably
connected with a rolling circle of 10 inches circumference. Each half of this curve
is very nearly identical with an arc of a circle having a radius of 6 inches and
this fact is the foundation of the first movement to be described.
14. Plate 3, Fig. 4 represents a right claviger attached to a crank. A. B, the
clavis rod is five times the length of the crank. Sx the directing arm is half the
length of A B'and is pivotted to it at its centre. S is the fixed axis upon which
the restraining arm Sx is free to, turn. OB is the crank. R is the fixed bearing
of the crank shaft. The fixed axis S is distant from O, the centre of the crank
shaft, twice the length of the crank, and along a line drawn from O parallel
to D A.
When pressure is exerted at A, through the connecting rod, in the direction of
the arrow, the traverse end of the clavis rod moves along the line A. D, while the
crank is rotated half a revolution in the sense of the arrow. The numerals indicate
the positions successively taken up by the various parts along the lines of move-
ment, during one revolution of the crank. The length from 1 to 5 and from 5
to 9 along the line A D are each equal to the diameter of the crank pin circle, and
the traverse for half a revolution is equal to two diameters.
The departure of the end C of the clavis rod during a small part of its traverse
from a straight line is so extremely small as to be practically of no moment.
The
crank can be rotated in either direction. When rotated in the direction shewn the
strain upon the directing arm is tensile. When the stroke commences at the
highest point and the crank is rotated in the opposite direction the strain upon
the directing arm is compressive. The forward stroke either way is along the

page_text: straight line A D and the return is along the outward curve shewn. The forward
stroke gives an impulse to the crank for about 11ths of a revolution. The return
takes place during the time the crank is making the remaining ths of the
revolution.
At the commencement of the stroke starting from the point in the crank pin
circle nearest to the traverse line, the force is for an indefinately short time
conveyed by thrust alone; the force conveyed by leverage then commences and
uniformly increases, while that due to thrust uniformly decreases, until at the
completion of a quadrant of revolution the two forces are equal. From this point
the force due to thrust diminishes, while the force due to leverage increases until
the second quadrant is completed, which for an indefinitely short movement at its
limit is effected by the leverage force alone. When the half revolution is com-
menced from the highest point the half of the force is transmitted by direct pull
instead of by direct thrust. When a whole revolution is effected at each stroke,
as in movements to be described, the same order is observed but during the third
and fourth quadrants the direction of the movements is reversed and direct pull
substituted for direct thrust. The proportion and direction at every point of the
two applications of the force are such that if they are regarded as being two
straight lines indefinately small, forming two adjacent sides of a parallelogram,
then the diagonals of all the parallelograms coincide with the circumference of the
crank pin circle.
It will thus be seen that the movement along the circumference is the resultant
of the two forces, but it is represented by the circumference in direction only not
in magnitude. This is owing to the two forces being in reality one, divided in
operating, so that the action of one division is complementary to that of the other.
If the traverse line be marked in a scale of equal parts representing the magnitude
of the force in units of weight, and the clavis rod moved over a certain number of
these parts, the crank end moving over a corresponding portion of the circum-
ference, but of less extent, exerts greater force; the intensity of the force varying
according to the inverse ratio of the lengths covered.
The virtual velocity of the claviger power, in all the movements in Class A for
converting rectilinear motion to continuous circular, is therefore: P's Vel: W's Vel::
4 dia : W: P, (where represents the ratio of the diameter to the circum-
ference of a circle). The right claviger described above, when attached to a crank
as represented in Plate 3 Fig. 1. is described as a hanger claviger. In all the
various forms of the banger claviger the normal proportion is for the clavis rod to
be five times the length of the crank. If any other proportion is employed the
motion of the crank is less uniform with that of the traverse end of the clavis rod,
When the hanger claviger has the proportions described above, the motion of the
crank is almost uniform with the motion of the traverse end A of the clavis rod,
and the force is transmitted throughout as a constant effort applied to the crank
pin tangentially to its circle. Half the force is transmitted through the rod by
direct thrust or pull and half by leverage upon the moveable fulcrum x, and these
two divisions of the original force are divided and re-combined automatically in
the exact proportion necessary. The size of the crank is not material and the
movement will operate an eccentric equally well.
If
The relative proportion of the parts of the hanger claviger may however be
varied to almost any extent. If the clavis rod be longer than five times the crank
tbe traverse line is longer than four diameters and the quadrant first described by
the crank, starting from the position nearest the traverse line as shewn in Plate 3.
Fig. 1, takes less than half the traverse and the second quadrant takes more.
the clavis rod be less than five times the length of the crank the reverse is the
case. The same results follow if the line of traverse slopes diagonally towards or
away from the circle. If the clavis rod be taken of any length relatively to the
size of crank and placed in position with the crank at the point nearest the
traverse line, and the traverse end A of the clavis rod be placed in position so that
the line A B shall be equal to the line C. D, see plate 3. Fig. 1. and the crank

page_text: turned half round in the direction of the arrow while the traverse end A of the
'clavis is moved along the line A. D, some one point in every clavis rod whatever
its length may be, will describe a curve which is almost identically the same as an
arc of a circle. This point when found is the position for the pivot x. It may be
found in all cases by means of the following formula :-
Let traverse for semicircle.
"
"
7" = length of the clavis rod.
x== distance to the pivot from the traverse end A of the clavis rod.
traverse for semi-circle of the normal length of clavis rod.
Then trt:- -T: x.
"
T
=
Having found and marked the position of the pivot as above place the clavis rod
and crank in its first position as represented in Plate 3. Fig. 1. and mark the
position of x on the plane of movement of the clavis rod, represented by the plane
of the paper. Next move the crank a quarter revolution forward so that it shall
be over the division marked 5 while the traverse end A. of the clavis rod has its
centre on the line A D; here again mark the position of a on the plane. Thirdly,
place the crank at 9, the completion of half a rotation, while the end A of the
clavis rod is on D and again mark the position of . Find the centre of a circle,
an are of which will pass through these three points. This centre will be the
position for S, the fixed axis.
The length of tlie restraining arm is the distance from S to x.
The normal form of hanger claviger is for converting alternate rectilinear motion
into continuous circular.
For steam engines two cylinders are employed giving alternate strokes in the
same direction to two cranks set, 180° apart or alternate strokes in opposite
directions to the same crank: Each forward stroke gives full impulse forward
. during gths of a revolution (or less if required).
The piston is nearly stationary during 1 th of a revolution at the commencement
and end of the stroke allowing time for lead. Thus one forward stroke may begin
immediately the other ceases giving half a revolution for each forward stroke or each
stroke can be lengthened and made to overlap the other, either at the commence-
iment or finish or both. As the movement gives a full tangential impulse, a uniform
.motion is obtained without a flywheel. This movement can also be employed for
converting reciprocal rectilinear motion into continuous circular by means of com-
pounds cylinders, the steam being used expansively for effecting the return stroke.
The amount of pressure required to overcome the same resistances during the
return stroke being less than in the forward stroke in the direct proportion of the
angular movements of the crank pin made in the forward and backward strokes.
The strain upon the crank web is transverse throughout and is the least possible
consistent with the load. There is no strain upon the crank or crank shaft or its
bearings as a result of the conversion of the motion as this is borne by the fixed
axis supporting the directing arm.
15. Continuous Circular Motion Converted into Reciprocal Rectilinear with
quick return. Class A.-Plate 3. Figs. 2. 3 and 4 illustrate adaptations of the
hanger claviger suitable for planing, slotting, shaping and other similar machines,
the tool being moved backward faster than while employed at work. The traverse
ends of the clavis rods are provided with rollers. There is a straight guide to
each, fixed parallel to the traverse line outward, and distant from it a length greater
than the radius of the roller. The stock of the tool is fixed directly to the end of
the clavis rod without the intervention of a connecting rod. In each instance the
cranks are rotated in the direction of the arrows. During the forward stroke
the strain upon the directing arms is tensile and all the parts remain in the same
relative positions as shewn in Plate 3. Fig. 1. At the commencement of the back-
ward movement the rollers touch the guide and owing to the action of the crank
roll back upon it into position for the next stroke. This backward movement
along the straight guide is permitted in three different ways as represented in the
figures. Fig. 2 has a slotted clavis rod. The pivot attaches the directing arm to

page_text: a block which moves downward along the slot during the return movement. In
Fig. 3 the stud supporting the directing arm is not fixed to the framework. It is
attached to a block which moves upwards along a fixed slide during the return'
movement. The effect is obtained in Fig. 4 by jointing the directing arm. These
movements are well adapted for planing irregular or curved work as the operative
end of the clavis rod yields to the variations of surface without losing force as the
power constantly tends to drive it back into the the traverse line.
16. Alternate or Reciprocal Rectilinear Motion Converted into Continuous
Circular, one revolution for each single stroke, Class A.-Reference is again made
to Plate 2. Fig. 6. Let E F represent a rigid rod, and let it be moved so that its
tenth division marked shall move along the line A B and its fifth division
marked shall describe the circle ff. The motions of the points land f now have
not exactly the same constant ratio of velocity, though they approximate very
closely to it. The locus of the points from f to s, along the line or rod E F during
the movement, are now slightly varied from the cycloids described in article 13.
The extent of the variation and the quality of the curves described by the points
marked along the rigid rod may be determined by testing them against a straight
line as centre locus. The cycloids represented in Plate 2. Fig. 6, are described by
a point on the circumference of a generating circle invariably attached to a rolling
circle, which rolls along a straight line, as previously described. The generating
point at the commencement of the cycloid, for those cycloids marked a to k, is in
the same relative position with respect to the centre of the generating circle as the
zero point is with respect to the centre of the circle ff, that is it is below, as it is
represented in the figure. At the commencement of the cycloids from m to s it
is in the contrary direction.
Now if a second point be taken in each case on the circumference of the
generating circle and on the same diameter as the generating point, it will describe
à cycloid exactly similar to that described by the generating point, but contrary in
direction. The line traversed by the common axis of the generating and rolling
circles is the centre locus between the two reversed cycloids, and the length of a
straight line joining corresponding divisions in the reversed cycloids is constant, as
it is the diameter of the generating circle.
When however the motion of translation of the axis of the generating circle and
the motion of rotation of the generating points have not a constant velocity ratio,
the two curves described by the two generating points (equidistant from the centre
and on the same diameter of the generating circle) are dissimilar.
Now taking the case of the rigid rod moved along the line A. B. the motion of
the point along A B may be uniform, or the motion of the point f along the
circumference of the circle ff may be uniform, or both may be irregular, without
affecting the curves described by the points from a to s, as the curves are the same
in any case.
If a point be taken along the rod midway between the points f and the curve
it describes during the movement is generated by a point on the circumference of a
generating circle of 24 inches diameter, whose centre moves along a straight line.
half the length of A. B, parallel to it, and midway between it and the centre of the
circle ff. The motion of translation of the centre of the circle is the same in
quality as the motion of the point along the line A. B. but it has only half the
velocity, and the angular motion of rotation of the generating point is the same as
the angular motion of the point f with respect to the centre of the circle ff. If
the curve described by the generating point, and the straight line traversed by the
centre of the generating circle be each divided into the same number of parts
representing the positions of the centre and of the generating point at the same
equal intervals of time during the movement, and the straight line be taken as
centre locus the other outer locus to the curve can be found, and the length of the
straight line joining the corresponding divisions of the two outer loci is constant.
The other outer locus is the arc of a circle with its centre at the centre of the

page_text: circle ff. The division just considered is the only one in which the other outer
locus of the curve is an arc of a circle.
In each of the other divisions, however, one point in the generating circle
describes an arc of a circle whose centre is at the centre of the circle ff. The
diameters of the generating circles are, for the length given to the line C D, the
same as noted in article 13. The straight lines traversed by the centres of the
generating circles are all parallel to the line A. B. and each passes through its
corresponding division in the line C. D. The limits of the lines traversed are
defined by two straight lines drawn from A and B respectively to the centre of the
circle ff. and produced in both directions. The point in each generating circle
from a to which describes the arc is on the same diameter as the generating point
and distant therefrom a length equal to the radius of the circle ff. If the radius of
the generating circle is longer than the radius of the circle ff the point describing
the arc is between the centre of the generating circle and the generating point.
In plate 2 Fig. 7, the line A B represents that part of the line E F in Fig. 6
which lies between the straight line and the circle. The line O B is the radius of
the circlo BF which corresponds to the circle ff in Fig. 6. The point x bisects
the line A B. The line Rx is the diameter of the generating circle. Its centre C
is on the straight line P N parallel to the line L M. The point R is connected
with O the centre of the circle B F. If the four lines A,B, BO, OR, R are
represented by rods pivotted together at the points BO and R they form a
claviger couple and the pivot at O is a fixed axis. The rod A B is five times
the length of the rod O B or R x and the rod RO is half the length of the
rod A B. If the point B be now moved round the circle B F with an uniform
velocity and the point A be constrained to move along the straight line L M,
the various points in the rods, during equal intervals of time pass over the
positions indicated by the numerals in the figure.-The point C moves along the
straight line P N and each length marked along the line P N is half the corre-
sponding length along the line L M. The centre point of the rod A B describes
the centre locus x zy. The point R describes the arc R P. The point B is
then rotated again round its centre in the same direction as before with an uniform
velocity, while the point A is constrained so that it cannot leave the line L M but
is free, to move along it. The positions taken up during the return movement are
also indicated by the figures. The point C moves both during the forward and
return movements along the line. P N. The whole of the curve described by the
point during the forward and return movements has the line P N as its centre
locus and the arc R P is the other outer locus. During the whole movement the
rod R is parallel to the rod O B, except at the instant they are crossing the
perpendicular line O D when they coincide in direction with it. The forward
movement of the point A along the straight L M from A to T corresponding to one
revolution of the point B is equal in length to four times the diameter of the
circle B F. The whole forward movement of the point A from L to M corresponds'
to a rotation of the point B from dead point to dead point in the circle it describes.
These dead points are marked x and y¹ on the circumference of the circle B F
and the distance from one to the other during the forward movement is 12.677
revolutions or 7.9653 times the length of radius; during the return movement the
distance from one dead point to the other is 7323 of a revolution or 4.601 times
the length of radius. The length of the traverse A to T for one revolution has the
ratio of 4 5 to the whole length of the traverse line L to M.
17. Plate 4. Figs. 1 and 2 represent the practical application of the principle and
movements just described. Fig. 1 represents an end view and Fig. 2 a front view
of the applied movement. The same letters indicate the same parts in each and
the same as they, indicated in Plate 2, Fig. 7 just described. O B is a double
crank in a crank shaft O B O, free to rotate in the fixed bearings W W. A B is
the clavis rod and x its centre point. RO is the arm centred at one end on the
crank shaft O and free to revolve round it. R x C is a double cranked U shaped
rod with one side half the length of the other. The shorter end C of this cranked-
·

page_text: piece passes through a block I. The longer end of it passes through a bearing in
the end of R of the arin R O. The centre of it passes through a bearing in the
clavis rod at x.
A fixed guide P N along which the block I is to slide is placed
in position so that a line along its centre corresponds in position with the line P N
in Plate 2 Fig. 7.
When pressure is applied at A along the traverse line the
crank is rotated one revolution at a stroke with full tangential impulse. The
centre point is carried and supported along the centre locus and the resistance
required by the leverage half of the force for its fulcrum at is supplied by the
arm RO and the fixed slide P N. The point A moves along a straight line
forward and back ward and cannot be moved away from it. The office of the block
and slide is to direct the force. If the point A be constrained to move in a straight
line the block and slide at C may be dispensed with. In the latter case however
if the joints in the rods are badly fitted or become worn the leverage half of the
force may not bite and the stress of it will be thrown upon the means used to
constrain A along the traverse line. It is preferable to constrain the point C to
move along a straight line and leave the end A of the clavis rod free as shewn.
Then, however the joints may be worn the only effect is a departure of the
point A from an exact straight line and a further variation in the velocity ratio,
The cranked rod R x C may be varied in shape from that described, as the
arm R O and the block and slide may be both on the same side of the clavis rod
or they may both be duplicated on each side. In some arrangements of the move-
ment the cranked piece may be dispensed with. The clavis rod at x has then
instead of a bearing hole two projecting studs. The block I and the arm RO
have corresponding studs. The studs in x are then connected to the studs in the
block and arm by rods with a bearing hole at each end, and are properly secured
in position by nuts. This movement may have the clavis rod and consequently
the traverse line any length relatively to the crank. The clavis rod A. B must in
all cases be equal in length to the line D F (see Plate 2 Fig. 7) perpendicular to
the traverse line and passing through the centre of the crank pin circle. Whatever
relative length of clavis rod is employed if the fulcrum is at the centre of the
clavis rod, the length of the line joining the points R and x is equal to the length
of the crank and the point C is at its centre. Any other point may be taken or
two or more points as fulcra may be taken in the same rod. The shape and
dimensions of the cranked piece R Cx and the relative positions of the points R C
and for any relative length of clavis rod with fulcra in any part of its length
are determined by the diameter of the generating circle which is the same for the
corresponding equal divisions in the clavis rod whatever its relative length may be
and they are in the same ratio to the length of crank as set forth in articles 13.
and 16 for this movement when its relative lengths were normal. If a fulcrum be
required on any part of the clavis rod corresponding to the divisions from 1 to 8
Plate 2, Fig. 6, the point on the cranked rod to be connected by the arm to the
crank shaft is obtained by lengthening the line which represents the radius of the
generating circle for that division. The generating point is between the required
point and the centre of the generating circle. The length from the generating
point to the required point is equal to the length of the crank.
18. Plate 4, Fig. 3, represents the same movement illustrated in Fig. 1, with the
addition of a right claviger couple A M O, one end O is centred on the crank shaft.
In the drawing it is represented as centred on the crank shaft on the opposite side
of the crank to that upon which the arm RO is centred. The other end of the
right claviger couple is pivotted to A, the traverse end of the clavis rod. Its centre
pivot is the part C of the cranked rod R x C which passes through the block 1.
When pressure is exerted at A to rotate the crank a portion of the force, in the
exact proportion required, is taken by the right claviger couple and employed by
it to hold and move the block I along the slide P N at the precise velocity required
by the movement, thus transmitting a double impulse to the crank OB. The
arm R O, and the limb Rx of the cranked rod are not essential to this movement
and may be dispensed with.

page_text: 19. Plate 4, Fig. 4 represents another form of the movement where great
strength is required. The clavis rod A B E is of a length sufficient to reach
beyond the crank B so that B E is equal to half A B. A double arm R R¹ equal
in length to the part of the clavis rod from a to E is centred, at its centre point,
on the crank shaft O. An additional cranked rod CE R¹ of the dimensions
suited to its position, as previously described, is connected with the end E of the
clavis rod and the end R¹ of the arm. Its longer end is turned at right angles and
passes through the block I which moves along the fixed slide PN There is
thus a double guide and double leverage. A M N is a claviger couple with four
points A, C, O, and C in a straight line. The rod L M is centred at the point O
on the crank shaft. The rod N Q is centred at the point C on the part of the
cranked rod R x C which passes through the block I. The end C₁ of the rod
NLC is centred on the part C¹ of the cranked rod R¹ E C¹, which passes through
the block I. The end A of the rod A Q M is pivotted to the end A of the clavis
rod. This claviger couple during the movement holds and moves along their slides
the blocks I and I with just the velocity required. In this arrangement the force
is divided among the rods. Each conveys its share in a different manner and all
combine with the common object of turning the crank.
The rods of the claviger couples A M W in Fig. 3 and A M N in Fig. 4, are of
sufficient length so that when the claviger couples are at the points of longest span
the rods will not need to pass over each other and all lie over the same straight
line. This is the case with all the claviger couples to be represented unless the
contrary is stated.
20. Plate 4, Fig. 5, illustrates another method of carrying the pivot x along the
centre locus and of providing the necessary resistance for the leverage half of
the force acting upon it as a fulcrum. It is represented with two clavis rods for
alternate strokes or for reciprocal strokes with two cylinders. For the return
strokes, with compound cylinders the steam can be used at low pressure. The
shaft O has three double cranks of the same length in it, O B and O'B', parallel to
each other other.
Between them is the crank O D set at 180° angular distance, from the others.
The clavis rod A B is connected to the crank O B and the clavis rod A B¹ to the
crank O B¹.
The two directing arms xs and a¹s are centred at their ends s on two studs
projecting on opposite sides of the block I, which moves along the fixed slide D.
A right claviger couple D MS is centred at its end D on the crank O D; its other
end S is centred on the stud S between the two directing arms. Its centre pivot.
is a stud projecting from the block K which moves along the fixed slide P. The
centre of the slide P is midway between the centre of the traverse line and the
centre O. The direction of the slide coincides with the perpendicular line O D.
The centre pivot moves along the slide a distance equal to the radius of the crank
pin circle. The direction of the slide D is along the traverse line. Its centre
at D is the centre of the traverse line. The length of movement of the centre of
the stud S along the slide D is equal to the diameter of the crank pin circle. The
position represented in the figure is that of the parts after an angular advance
of 90° of the crank from the commencement of the movement. When the cranks
OB and O B¹ are rotated by pressure applied to the ends A. and A¹ of the clavis
rods, the circular movement given by the crank O D to the end D of the claviger
couple is resolved by it into two components acting at right angles, one along the
direction of the traverse line and one along the direction of the line O D. The
component acting in the direction of O D is eliminated by the movement of
the centre pivot along the slide P, so that the force received by D is transmitted
as rectilinear force to S and it moves S along the slide D. The quality of the
transmitted force is such that it holds and moves the pivot S so that a plane
passing through the points B and B' (the centre of the crank pins of the cranks
O B and O B¹) and through the point S is always parallel, or coincident with, a

page_text: plane passing through the axis of the crank shaft and through the point D the
centre of the traverse line. This movement carries the pivot exactly along its
centre locus and gives the resistance required by the leverage. One revolution
with full tangential impulse is effected for each single stroke.
21. Plate 5. Figs. 1, 2, 3, 4, and 5 represent the same or similar movements to
those described in articles 17, 18, and 19 but without the blocks and slides. In
place of these the means of directing the force along a straight line is obtained by
rollers running along straight guides giving a reciprocal restraint. After the
descriptions and explanations previously given the figures will be readily under-
stood without further description. The movement represented by Fig. 3 is a
particularly good one with few and simple parts. Figs. 4 and 5 are similar to
Plate 4 Fig. 4.
In all the movements described in articles 17, 18, 19, 20 and 21 the crank may
be rotated in either direction and the forward stroke is in either direction according
as the crank is rotated. The.clavigers described in articles 17, 18, 19 and 21 are
for convenience of reference called cranked clavigers.
22. Reciprocal Rectiliner Motion in two directions at right angles to each other
converted into Continuous Circular, or vice versa, Class A. Plate 6, Fig. 1.-Let the
two dotted lines L M and C P, in directions at right angles to each other, represent
the travel of the ends A and C of two pistons LA and N C. Take a point
midway between the centre of the lines L M and C P. It is at O the axis of a
shaft, cranked from O to S.
Place the point C at the commencement of its line of
travel and the point A at the centre of its line. Place the crank OS in position
so that the centre of its crank pin S shall be midway between the points C and A.
Connect the three points A, S and C together by a right claviger couple A B C, of
sufficient span for the movement. The end of one clavis rod of the couple is
pivotted to the piston at C, the end of the other clavis rod is pivotted to the other
piston at A and the centre pivot is the crank pin S. When pressure is exerted on
the pistons so as to force then to move along their lines of travel the crank is
rotated in either direction. The divisions marked along the lines CD and L M
and round the circumference of the crank pin circle are the positions taken up by
the respective parts which move along these lines, at equal intervals of time during
the movement. For every angular movement of the crank pin round its circle the
points C and A move a distance along their lines of travel, the one equal to the
sine and the other equal to the versed sine of the angle moved, the radius being
twice the length of the crank O.S. One piston is always half a stroke behind the
other thus one is always at its centre when the other is at the commencement and
end of its stroke. The motion of the crank pin S round its circle is the resultant
of the two forces acting along the lines L M and C S. These two forces are the
components; they are received by the arms of the claviger couple and composed at
its centré pivot into the continuous circular motion of the crank O S. It is not
necessary either that the force applied to each end A and C of the claviger couple
respectively should vary in intensity according to the sine and versed sine of the
angle, as the claviger couple by its reciprocally complementary action takes the sum
of the two forces and automatically divides and adjusts it between the two ends A
and C in the exact proportion required. In order to insure that the points A and C
shall travel exactly along the lines L M and C P both of the points are constrained.
The pivot which connects the clavis rod B C to the piston rod NC is elongated
upon it is centred a roller and also a right claviger C x¹ A¹ S'. The fixed axis S¹ of
this claviger is on the line C P extended. The other end A¹ of the clavis rod C A¹
is provided with a roller. A fixed guide I K Z in shape the same as two adjacent
sides of a square is placed in position. The side I K is parallel to the line C.P
and its inner edge is distant therefrom the length of the radius of the roller.
fixed axis S¹ is on the diagonal of the square. It is placed on one side so as not
to impede the movement of the roller at C. The end A is also constrained as
shewn. These arrangements give a reciprocal restraint and makes it impossible to
The
'

page_text: th
clavis rod slides along the slot. The proportions represented are the same as in
Fig. 5. The forward stroke corresponds to. of a revolution of which ths of a
revolution gives uniform motion to the end A of the clavis rod. It slows down at
each end during of a revolution. The return is during the time taken by the
crank to make a quarter of a revolution. During the return the end A describes
an outward curve. The forward stroke in either direction according to the direction
the crank is rotated is along the straight line. The stock which carries the cutting
tool is joined to the end Z of the connecting rod Z A. The positions occupied by
the different points, at equal intervals of time during the movement are represented
by the numerals.
.
The shorter the clavis rod is made in proportion to the crank, the quicker is the
return in proportion to the forward movement, though the motion of the forward
movement is then less uniform. With a clavis rod 5 times the length of the crank,
the forward stroke corresponds to ths of revolution, nearly uniform during of a
revolution, slowing down during of a revolution at each end, and returning
during th of a revolution. This movement is suitable for operating a pump or
other similar work. With a pedal attached to the end A it is a movement suitable
for operating a sewing or other machine to be worked by one foot.
1_th
Any ratio of velocity of the forward to the return strokes can be obtained with
the same crank and slider claviger by varying the position of the fulcrum S. If it
be moved nearer the crank the forward movement is lengthened and the return is
correspondingly hastened. If a large crank be used and the fulcrum S be moved
as near the crank pin circle as is possible after leaving sufficient clearance for the
crank pin, the time taken for return may be made to be a very small fraction of
the time taken for the forward movement. In this case the end A of the clavis
rod describes a curve during both forward and return strokes, but with a clavis
rod 8 times the length of crank, the variation of the end Z of the connecting rod
from uniform motion during the greater part of the forward stroke is slight. The
fulcrum S may be readily made adjustable along the line c d by using, in place of
a fixed stud, a short rod rigidly connected at each end to rectangular bushes which
slide along slotted supports placed parallel to the line c d and fixed securely to the
framework. The bushes are clamped in the position desired.
25. This movement may be adapted for operating hammers, also for ore stampers
or pulverizers and for shears for cutting metal plates &c. In these cases the clavis
rod is a solid rod provided with a bearing piece, screwed, clamped, shrunk or keyed
on it, which projects laterally and slides along the block supported by the fixed
stud during the forward or lifting stroke. The fixed stud and its supports are
placed so as not to intersect the plane of movement of the clavis rod. At a certain
point of the movement according as the bearing piece is arranged, it moves clear
of the block leaving the clavis rod free to fall. After falling it is in position for
the next forward stroke.
26. Reciprocal Rectilinear Motion converted into Continuous Circular, half a
revolution for each single stroke. Class A. Plate 3, Fig. 8, illustrates a fourth
form of claviger for this purpose, and it may be described as the roller claviger.
It has the fulcrum for the leverages, half of the force rigidly fixed to the clavis
rod in the form of a stud projecting from it at a right angle. This stud is
furnished with a wheel or roller. The bearing for the fulcrum is a fixed guide G
along which the roller travels during the movement. The profile of the bearing
surface of the guide is one of the cycloids described in article 13, modified as
described in article 16. The fixed guide not only supplies the bearing for the
fulcrum but guides the direction of the thrust and pull. The fulcrum of the
clavis rod has two distinct motions with reference to the bearing surface of the fixed
guide, during the movement. . One is a motion of translation due to the part of
the force acting by direct thrust or pull and a motion of partial rotation on its
axis due to the part of the force acting by leverage. In the figure the fulcrum
is represented at the centre of the clavis rod. The positions simultaneously
occupied by the traverse end of the clavis rod, the centre of the stud, and the

page_text: crank pin respectively, at equal intervals of time during the movement, when
the motion of the crank is uniform, are indicated by the numerals. The forward
and return strokes. are both along the straight line C D. The roller and guide
may be on one side of the clavis rod, as represented in the figure, or the roller and
guide may be duplicated, with the clavis rod between; or the clavis rod may be
double for part of its length near the fulcrum and carry the wheel between on an
axis rigidly fixed to the rod at each end, or the wheel and axis can turn together
with the bearings in the rod on either side; the double part of the rod encloses the
fixed guide. The fixed guide G represented in Fig. 8 is efficient for rotating the
crank in one direction only, that indicated by the arrow.
27. Alternate Rectilinear Motion converted into Continuous Circular, one revo-
lution for each single stroke. Class A. Plate 6, Fig. 2.-The two roller clavigers
A B and C B are attached to the same crank O B. The fulcra F, F' are repre-
sented the of the length of clavis rod from the crank ends. This position for the
fulera is taken because the same guides are used for both forward and return
movements and this position suits the return movement better than when the
fulcra are at the middle of the clavis rods. The guides are efficient for rotating
the crank in the direction of the arrow only. The forward stroke of one claviger
overlaps the other and they are represented in the figure in a position where both
are operating upon the crank at the same time. Both clavigers pass the vertical
line joining the centre of the crank shaft and the middle of the traverse line at the
same instant and move in opposite directions. The ends A and C of the clavis
rods describe during the return two outward curves touching the traverse line at
its middle point. The return movement is effected by the action of the crank
.running the rollers along the guide.
28. Continuous Circular Motion converted into Reciprocal or Alternate Recti-
linear.
The movements described in articles 26 and 27 are efficient for this purpose
when the cranks are rotated in the opposite direction to that indicated by the
arrows.
29. Continuous Circular Motion converted into Curvilinear.
The fixed fulcrum guides can be shaped to give any required curve to the traverse
of the operative end of the clavigers for shaping machines, for finishing up propeller
blades and such work. In these cases the stock of the tool is attached to the clavis
rod direct and the latter is made with an elbow joint to allow the tool to be
returned across the surface of the work.
30. With the roller claviger as with the other forms the ratio of the clavis rod
to the crank can be varied to any extent and the fulcrum can be placed at any
convenient part of the clavis rod, the guide being shaped accordingly. The position
and profile of the bearing surface of the guide can be readily determined in practice
by moving the traverse end of the clavis rod along the line of traverse, while the
other end of the clavis rod is being slowly rotated by the crank, and marking the
series of positions taken up consecutively by the centre of the stud during the
movement. The profile of the guide, is to be parallel to the locus so obtained and
distant from it a length equal to the radius of the roller.
31. Reciprocal Rectilinear Motion converted into Continuous Circular or vice
versa. Half a revolution for each stroke. Class B. Plate 6. Fig. 3.-The rod M A
is a piston or a connecting rod through which the rectilinear force acts. The
dotted line A D represents the lougth of stroke, which in the movement illustrated
is twice the diameter of the crank pin circle. O is the crauk shaft and O B the
crank. The force is delivered at an uniform velocity by the rod M. A. It is
required to rotate the crank so that it and the rod M A shall have a constant
velocity ratio. The traverse line A D is divided into any number of equal parts
and each division is numbered consecutively commencing zero at the commence-
ment of the forward stroke. The divisions are also numbered the reverse way
taking zero at the commencement of the backward stroke. The circumference of
the crank pin circle is divided into the same number of equal parts as the traverse

page_text: line. The zero points in it are 180 degrees apart. The traverse line in the figure
if produced passes through the centre of the crank shaft. It may however be in
any direction in the plane of the crank pin circle. Whatever may be its position
the zero points should be taken on the circumference of the crank pin circle in
such a position that the first indefinitely small movement of the crank pin at the
commencement of each forward and backward stroke shall be parallel in direction
to the traverse line; that is, at the commencement of the stroke the crank should
be in a direction perpendicular to the traverse line. The divisions in the circum-
ference of the crank pin circle are also numbered the reverse way. A centre
locus is found between one rotation of the crank, starting from zero, and a double
reciprocal stroke along the traverse line. It consists of two half cycloids reversed.
The points in the centre locus corresponding to the divisions in the traverse line
and crank pin circle are marked with the same figures. Another centre locus is
found and marked in the same way, between the rotation of a crank, set 180°
angular distance from the other and rotated with it in the same direction, and the
same divisions in the traverse line as taken in connection with the rotation of the
first crank. This centre locus consists of two half cycloids reversed exactly similar
to the first. In the figure the traverse line produced cuts the major axes of the
two closed curves, forming the centre loci, at their middle point, and the two major
axes make the same angle with this line but in contrary directions. When the
traverse line produced does not pass through the centre O, the line which cuts the
major axes of the curves at their middle point is a line parallel to the traverse line
and midway between it and the centre O. Fixed guides G and H are provided
with their bearing edges parallel to the centre loci as previously described. They.
are fixed in parallel planes. Between them in a parallel plane is a fixed straight
slide F D with a block n sliding in it. The scope of movement of the centre of
the block is a length equal to the diameter of the crank pin circle. A cranked
rod cranked in the middle and ends has the middle cranked part passed
through the block n; the cranked ends are provided with rollers r and which are
fixed in position in the guides G and H. A claviger couple with equal limbs B CA,
is centred on the crank pin at one end and is pivotted to the end A, of the rod A M
at the other. Its centre pivot is the end of the cranked rod, carrying a roller,
which is then over the point in the centre locus corresponding to the points
occupied by the crank pin in its circle and the point A in the traverse line.
Another claviger couple with equal limbs OE A has one end centred on the crank
shaft O and the other end on the pivot A. Its centre pivot is the middle cranked piece
of the cranked rod which passes through the block n. Reciprocal strokes
given at A rotate the crank in either direction as desired. The two fixed guides give
a reciprocal constraint. The fixed rectilinear slide restrains and directs the move-
ment. One cyclodial guide is sufficient when the crank is required to be rotated in
one direction only. Instead of the claviger couple OE A being fixed as shewn in the
figure, it may have one end fixed to a crank opposite to O B at L with its centre
pivot on the cranked end of the cranked rod. The three claviger couples may be
employed together. With two claviger couples as represented in the figure a double
impulse is transmitted to the crank; as the claviger couple OE A holds and moves
the centre of the diameter rk of the generating circle along the line F D with
exactly the velocity required while the claviger couple B C A rotates the rod k r²
upon its centre k with an uniform motion. The rod kr¹ is always parallel to or
in the same straight line with the crank O B. The centre of its cranked ends
and are throughout the movement over the corresponding figures in each cycloid.
They cannot be varied from this position and though the rollers 7 and 7' are free
to run along the guides in either direction they cannot be forced away from
contact with them. The guides are correctly shaped and fixed when the rollers
press upon them the whole distance with sufficient force to turn and run along
with an even motion.
The position and profile of the guides may be readily obtained practically by.
the same method described in article 30. The centre of the pivot at A cannot be.

page_text: moved away from the straight line. When the movement is effected with one
claviger couple only, viz B C A, the end A is constrained to move along the line of
traverse A D by being fixed to a block moving along a fixed straight slide or by
any other effective method of constraint. The line of traverse A D may be of any
length relatively to half the circumference of the crank pin circle. If they differ.
much in length, claviger couples of unequal limbs should be used, and the centre
pivot should be at the centre of force. In this case whatever may be the ratio
between the length of the line of traverse and half the circumference of the crank
pin circle the centre loci are halves of common cycloids reversed. Any points may,
be taken as zero in the circumference of the crank pin circle, but if any points be
taken other than those previously described the two closed curves representing the
two centre loci are dissimilar. They neither of them contain exact halves of
cycloids but are each composed of portions of two adjacent half cycloids. repre-
senting half a rotation of the generating circle, and one guide will generally be
considerably larger than the other. The movement however is not affected. There
is no dead point as in the ordinary way of operating the crank. The points at
which the change of motion takes place may be called neutral points. When the
claviger is on a neutral point it is in equilibrium between movement in either
direction, but the instant it passes the neutral point in either direction there is full
tangential impulse. This movement is a perfect movement.
The
32. Plate 2, Fig. 8 represents the geometrical lines for this movement for one
revolution for each single stroke. The traverse line in the figure is the same
length as the circumference of the circle: Different points are taken as zero.
curves of the centre loci are common cycloids or portions of common cycloids. A
centre locus may be taken wherever among them a complete line of figures can be
found answering to the line of figures along the circumference. In this way the
curves shewn give 8 different centre loci for obtaining one revolution for each
stroke and 6 for obtaining half a revolution at a stroke. The chain of cycloids
may be extended in either direction and if it were possible to construct and handle
claviger couples of sufficient size and strength a line of rectilinear motion
indefinitely long could be converted into an indefinitely large number of rotations.
of the crank.
33. Irregular rectilinear motion of any kind can be converted by this movement
into uniform circular. The line of traverse is divided into lengths inversely
proportionate to the intensity of the force, while the circumference of the crank
pin circle is divided into equal parts. The centre loci are then taken as previously.
described and the parts placed in position as represented in article 13 and
Plate 6. Fig. 3.
Steam may in this way be used expansively after an early cut off and though
the pressure lessens as the volume increases the force is delivered to the crank with
the same virtual moment throughout.
34. The claviger couples for effecting the movements described in articles 31,
32 and 33 may have the fixed guides at one end, while tlie force is exerted on the
centre pivot. The claviger couples may therefore be arranged in three different
positions, depending on the position of the points of application of the power and
the work with respect to the guide. If it be taken that the power be applied in a
straight line to be converted into circular motion then when the guides are between
the traverse line and the crank, as illustrated in Plate 6. Fig. 3. it is a claviger
couple of the first kind. When the crank is between the traverse line and the
fixed guide it is a claviger couple of the second kind. When the traverse line is
between the crank and the fixed guide the claviger couple is of the third kind.
The movement is equally efficient in either of these kinds. When more than one
revolution per stroke is made the third kind is to be preferred.
35. Curvilinear Motion Converted into Continuous Circular. Class A.-
Plate 7, Fig. 1 represents a cranked claviger attached to the crank OB. The
cranked rod is Rc x. The cranked piece C is at the centre between the cranked
ends R and x. CD is a restraining arm with one end centred on the cranked*

page_text: piece C and the other turning on the fixed axis S. The crank OB is in position
for the commencement of one net revolution when it is on a line joining the axis
of the crank shaft O with the fixed axis S. The fixed axis S may be any distance
from O. When the parts are in the position shewn it may be so arranged as to
make any angle with the line O D, and the clavis rod A B may be set at any
angle to the line A D M. The conditions that are essential are the following.
When the parts are in position for the commencement of one net stroke and
revolution as shewn in the figure a point N is taken in the straight line OSN SO
that S N is equal to OS. Draw the straight line A M perpendicular to the line O N.
From the centre N, at the distance N A, describe the arc A E M. The relative
lengths of the clavis rod and the crank are then adjusted so that the line A B is
equal to the line E F. The ratio between them will depend upon the angle made
by the line A B with the lines A D or D B. The arc described by the point C is
of the same angular measurement as that described by the point A but the radius
of the former is half that of the latter. The dead points are marked by the letters y
and z. Each forward movement of the end A along the arc yez turns the crank one
revolution plus the distance from y to; the return stroke is along the same arczey
and moves the crank from z to y. The crank may be rotated in either direction.
The divisions marked on the arc and round the circumference indicate the positions
respectively of the points A and B at equal intervals of time during one revolution.
The cranked rod RC x varies in shape according to the position of the restraining
arm CS. If the clavis rod A B be placed in the middle between the rods RO
and C S the cranked rod will be Ū shaped with the bend downwards at the
commencement of the stroke, as shewn in Plate 4, Fig. 1 and Plate 7, Figs. 3 and 4;
while if the rod RO be placed in the middle between the clavis rod and the rod CS
the cranked rod is U shaped with the bend upwards at the commencement. In all
the forms of cranked clavigers the shape of the cranked piece will depend upon the
position and number of the rods. The necessary work it has to do is to hold the
three points R C and x in their relative positions and allow the points R and
freedom to rotate round their centre C. In the figure the fixed axis S is represented
on the same side of the crank shaft as the clavis rod.
36. Plate 7, Figs. 2 and 3 represent the same movement with the fixed axis S of
the restraining arm on the opposite side of the crank shaft to the clavis rod. The
conditions are the same as those described in the preceding article. When the
restraining arm is a straight rod in the position shewn in Fig. 2 it can only be
used in connection with a single crank at the end of a crank shaft. When the
restraining arm is required to be in the position shewn in Figs. 2 and 3 and to be
used in connection with a double crank on a crank shaft it must be shaped to
avoid the shaft. In Fig. 3 it is represented of circular shape.
The proportions given to, the parts in the movement represented in Fig. 3
cause the motion of the point A of the clavis rod A B, during the forward move-
ment along the are A E M, to have a constant velocity ratio of 2 to 1 to the
motion of the point B of the crank O B during its motion round the crank pin
circle B to B, and the arc A E M is twice the length of the circumference of the
crank pin circle. These proportions are as follows. The angle CSO has the same
ratio to 180° as the length of the crank O B has to the length of the restraining
arm C S. Only a portion of the arcs are shewn in Figs. 2 and 3. The movement
represented in Fig. 2 gives forward impulse during 14 revolutions nearly, and the
return is during revolution nearly. That represented in Fig. 3 gives forward
impulse during 13 revolution and the return is during g's of a revolution. The
traverse ends A of the clavis rods move along the dotted arcs shewn and they
cannot be moved away from them.
37. Either of the movements described in articles 35 and 36 may be employed
for converting rectilinear motion into continuous circular. A hanger claviger of
the requisite dimensions to suit the radius of the arc is pivotted at its crank end
to the end A of the clavis rod. The traverse end of the hanger claviger moves
along a straight line during both forward and backward strokes.
"

page_text: 38. Plate 7, Fig. 4 represents an adaptation of the movement described in
article 35. A second restraining arm is pivotted at A. and centred on a fixed axis
at N. The clavis rod is lengthened to T. During the movement the clavis rod T
A x B passes between the two restraining arms CS and A N. The traverse of T is
a very elongated double loop, only half of it is shewn in the figure. With the
proportions represented in the figure the forward and return traverses are nearly
equal. The proportions are O B, crank 1; TB, clavis rod 10; A D, second restrain-
ing arm 10; the length TA 34.
+
39. Reciprocal Rectilinear Motion converted into Oscillating and thence into
Continuous Circular, and vice versa. Class A. Plate 8, Fig. 1.-The claviger
couple yeg d is connected at one end to the crank o d. Its other end y is centred
on, the fixed stud y. Its centre pivot g is centred on a stud g projecting perpen-
dicularly from the radius rod o'g which is centred at its other end on the fixed
stud o¹. The proportions of the parts and the angle the clavis rods ye and ed
make with each other may vary to any extent. The essential conditions of the
movement with a claviger couple of equal limbs, whatever the proportionate length
of all the parts may be, are that the line do must be equal to the versed sine of
the angle ey g
The point o' must bisect the line oy and the point g must bisect
the line dy. If a claviger couple of unequal limbs be used, the line o o¹ will have
the same ratio to the line o¹ y that the line dg has to the line gy. The sum of the
lengths of the two clavis rods ye and ed must be equal to the line y i, the point i
being on the circumference of the crank pin circle on the same diameter as the
point d. Now if the clavis rod ey be turned upon the centre y so that the point e
moves through the arc e. the crank o d is rotated one revolution. A slight
further movement of the point e along the arc brings the crank to the dead point,
a return movement along the arc continues the rotation of the crank and carries it
round to the dead point on the other side when it is in position for another full
forward stroke. The figure represents the clavis rod e y extended in length beyond
the fixed study to the point b. The part y b forms a radius rod for a right hanger
claviger α x b s. The proportions of the parts represented in the figure are as
follows The angles y e d, yg e, ey z are right angles. The line by is four times
the line do. The lines b x, xa and as are each ten times the line d o. The line a b
is five times the line by. The traverse line a d' and the line ys are each twice the
line ay and eight times the line do. The lines ad¹ and ys are in a parallel
direction, the perpendicular distance between them is eight times the line do. The
traverse line a d' has the same ratio to the circumference of the crank pin circle
as 4 to . Rectilinear motion is given to the end a of the clavis rod axb by a
piston, connecting rod or any other means. It then moves exactly along the
straight line ad and cannot be moved away from it. During the return stroke it
moves back along the same straight line da. The forward stroke gives in full
1 revolution from dead point to point, and the return 4ths of a revolution. The
motions of the point a of the clavis rod along the traverse line and of the point d
of the crank do round the crank pin circle during the forward movement have
almost a constant velocity ratio. The quality of motion of the point A during
the forward movement when the crank is rotated with uniform velocity is the
same as marked along the traverse line in Plate 2, Fig. 7; but the return stroke
approximates more nearly in velocity to the forward stroke than in the movement
illustrated in that figure.
The right claviger a x bs may conveniently be coupled with another pivotted
at band's, the two making a right claviger couple and each of the free ends operated
by a piston or connecting rod. The traverse line a d may be made shorter or
longer with the same crank without affecting the quality of the velocity of a along
it, by shortening or lengthening the radius y b and correspondingly varying the
size of the right claviger a x b 8.
$
40. Fig. 2, represents another form of the same movement. The clavis rod e y
of the claviger couple is lengthened from y to x and this additional length forms
the directing arm of a right claviger a aby. The end 6 of the clavis rod ba is

page_text: I
centred on a stud projecting from the block m which slides along a straight
slotted guide N N whose centre is on the line o o¹ y produced. The proportion of
the right claviger a x by to the other parts determines the length of the traverse
line a d. In the figure the proportions are arranged so that the line a d has a
ratio to the circumference of the crank, pin circle of 4 to . The line ab makes
with the line a y an angle of 45°. The other particulars relating to the movement
of the point a along the traverse line are the same as for Fig. 1 described in the
preceding article.
41. Fig. 3, represents a similar movement to Fig. 1. but the radius y b of the
right claviger abs is taken along the clavis rod e y.
8
42. Plate 9 Fig. 14, represents the same movement as Plate 8, Fig. 1, but slightly
differently proportioned, for converting alternate rectilinear into continuous circular
motion, by manual labour. The two bandles at the ends of the claviger couple are
alternately pulled down by two persons. They move up and down alternately in
a straight line..
43. Rectilinear Motion transmitted in a parallel direction. Class A. Plate 9,
Fig. 20. A right claviger couple A BCS connected to a cranked radius rod O B,
turning on a fixed stud at O. The figure is shewn at the middle of the stroke.
The proportions are A B or B C clavis rod 5 times length of radius rod B O. The
line S B is perpendicular to the line A C. OS is twice O B. A S and S C are
each four times 0 B. Both ends of the claviger couple A and C are free and move
forward and backward along the dotted parallel lines shewn in contrary directions.
They cannot be moved from the lines. The range of the traverses, must not be so
long as to rotate the radius rod.
:
44. Fig. 21 represents a movement for transferring rectilinear motion in a
direction at right angles. Two right clavigers ABS and CBS' are connected at
the ends B of the clavis rods to a radius rod B O. The proportions are the same
as for figure 20 but instead of both restraining arms being centred on the fixed
axis S, the restraining arm x S of the clavis rod A. B is centred on a second fixed
axis S¹. The line S¹ O is equal to the line S O and is perpendicular to it. See
also article 93.
45. Similar movements with free ends to the above can be arranged to transfer
the motion at any angle. Instead of the radius rod B O, a short rod or a shaft
turning in a fixed bearing with a single crank at each end is used. To these
cranks are attached two hanger clavigers. The cranks can be set at any angle
apart and thus the motion is transferred in any direction in the same or parallel
planes. In these movements the velocity is exactly uniform between the two ends.
46. Rectilinear motion transmitted in any direction uniformly multiplied or
reduced in length. The movements are similar to those described in articles 43, 44
and 45, but one claviger in each movement is larger than the other. When they
are both attached to the same radius rod it carries two projecting studs, the stud
to which the larger claviger is attached is longer than the other so that the larger
clavis rod can pass over the other during the movement. When the smaller
claviger is used for the application of the power the movement transfers the
motion at an uniformly increased velocity, and when the power is applied to the
larger claviger the movement uniformly increases the efficiency of the force.
47. Movements for Transferring Rectilinear motion reversed in direction, along
the same straight and along a parallel line, with the centre pivot fixed, have
already been described in articles 4 and 5 and illustrated in Plate 1. Figs. 3 and 4.,
48. Rectilinear Motion transferred as described in the preceding article, with the
resulting line of movement increased or decreased in length. A constant ratio of
two to one may be obtained by centreing one end of the claviger couple on the
fixed stud and applying the force to either the centre pivot or to the other end of
the claviger. In the former case it is a claviger couple of the third kind. In the
latter case it is a claviger couple of the second kind. Any ratio between the power
and the weight can be obtained by employing claviger couples, with one pivot
fixed, of unequal limbs of the first second or third kinds,

page_text: 49. Rectilinear motion transferred in direction at any angle in the same plane.
Plate 1, Fig. 6 represents a movement for transferring rectilinear motion in a
direction at right angles. The movement has been already described in article 7,
when the principle of the claviger was explained. If the guide M N be placed at
right angles to the position shewn in the figure, the centre point being kept over
the same spot the motion will be transferred in the opposite direction to that
indicated by the arrow.
Thus both ends A and C will simultaneously move
towards or away from the angle D. Instead of the constraint represented in the
figure the ends of the clavis rods A and C may be pivotted to rods or shafts moving
in fixed bearings or they may be provided with rollers running along fixed guides
giving a reciprocal restraint as shewn in Figures 3 and 4, Plate 1, or any other
open effective method of constraint may be employed.
In Plate 1. Fig. 1, the lines E D and F D along which the ends A and C of the
clavis rods are constrained to move are the two sides of a right angled triangle and
both lines of traverse terminate at the same distance from the angle.. The line M N
along which the centre pivot S moves is parallel to the hypotenuse and has the
same ratio to half the hypotenuse as either of the lines of traverse of A. or C has to
the sides E D or F D. The direction of the lines E D and F D may be varied so
as to make any angle at D. In fact their direction may coincide with the two
sides of any isosceles triangle, and the line along which the centre pivot moves
follows the same conditions with regard to position and length as just described
for a right angled triangle. When both ends A and C of the two clavis rods are
required to move simultaneously towards or away from the angle the centre locus
along which the centre pivot moves coincides in direction with the perpendicular
line which bisects both the angle D and the base, and has the same ratio to it. that
each of the traverse lines of A and B has to the side of the triangle.
50. Rectilinear motion transferred in either direction, at any angle in the same
plane, and increased or reduced in length so that the operative end of the claviger
couple shall have a constant velocity ratio with the power end. The movements
are similar to those described in article 49, but the triangles are scalene triangles.
The conditions are the same. The lines of traverse, coincide in direction with two
sides of the triangle and the length from the end of each traverse line to the angle
is proportional to the length of the sides. The motion is transferred with the
constant velocity ratio that one side has to the other.
.
51. Reciprocal or Alternate Rectilinear motion transmitted into Reciprocal
Rectilinear in a direction at right angles and multiplied in number or varied in
velocity. Claviger couples are used with both ends constrained and with the
centre pivot attached to a block sliding along a fixed guide similar to those
described in articles 49 and 50. When a line of motion in either direction is
multiplied into two or more lines of motion the sum of whose lengths are equal to
the original line, the centre locus is a zigzag line composed of lines of equal length
at right angles to each other. The slide is made with its inner edges parallel to
these lines. A square block is used, and it is moved along the guide by the action
of the claviger couple. The stroke of the power end of the claviger couple is
multiplied into as many strokes at the other end as there are changes of direction
in the guide, and the velocity of the two ends is uniform.
52. When the sum of the lengths of the transmitted strokes is longer than the
originál line of motion the zigzag lines of the centre locus meet each other at an
acute angle. When the sum of these lengths are less, the lines of the centre locus
meet each other at an obtuse angle. In these cases the block is shaped to suit the
angles of the guide, two of its opposite corners being made to fit into the angle of
the guide. In both instances there is a constant velocity ratio between the power
and operating ends of the claviger couple.
53. In the same manner each return stroke of the multiplied transmitted motion
can be varied in velocity so as to move along the line more quickly than the
forward stroke, the ratio of velocity between the two strokes being according to

page_text: the difference in the angles made by the two series of alternate lines, in the centre
locus, with a line which bisects them all.
54. Rectilinear motion transmitted at any angle in the same plane. Two right
clavigers are pivotted together at one end with a pivot bent to the angle required.
The two restraining arms are centred on a fixed stud bent to the same angle.
Force is applied to one of the free ends towards or away from the fixed stud, the
other end moves in the direction required towards or away from the fixed stud at
the same velocity as the power end. No constraint is needed as the free ends
cannot be moved from the same plane nor diverted from the lines of movement,
which if produced till they meet make the same angle with each other as the
angles in the bent pivot and stud.
of
55. Rectilinear motion transmitted at any angle in a parallel plane with uniform
velocity or with the velocity at a constant ratio. Plate 9. Fig. 8. A right
claviger a x b 8 has the ends of the clavis rod furnished with rollers which roll
along a fixed guide in shape the same as two adjacent sides of a square. The
ends a and b of the clavis rod are thus restrained to move along the lines a s
and a b. The fixed axis S is at the angle a 8 b. At any distance from this
claviger another claviger a¹¹ b' s¹ is fixed exactly similar in every respect to the
other and so that the centres of the fixed axes and pivots 8 b s¹ b' are in a straight
line. The two pivots b b¹ are joined by the connecting rod bb. If the end
the clavis rod ab be now moved along the line as in either direction, the end a¹
of the clavis rod a' b¹ makes the same movement along the line a¹ 8'. Now if the
connecting rod be removed and the claviger a¹¹ b¹s with its fixed guide be
turned upon the line 8 b s b' as an axis to any required angle and the connecting
rod adjusted and replaced the motion given to a will be transmitted to a¹ and it
will move along a straight line at the angular distance required in a paralle!
plane. The direction of the motion of the end a¹ of the second claviger may be
reversed by reversing the position of the second claviger (so that the end b¹ is
nearer the end 6 of the other claviger than is the fixed stud S), and inserting at
some point in the connecting rod a reversing claviger couple as illustrated in
Plate 1, Fig. 3. The length of movement of the end at of the second claviger may
be lengthened or shortened as compared with the length of movement of the
end a of the first claviger and a constant velocity ratio maintained between their
movements in the following manner. The second claviger is proportioned in size
to the first as the traverse of a¹ is to the traverse of a. The two clavigers are
reversed in position and at some point in the connecting rod a reversing claviger
couple is inserted whose limbs are in the same proportion to each other as the two
clavigers.
56. Rectilinear motion transmitted at any angle in any plane with uniform
velocity or with the velocity at a constant ratio. The movements are the same as
those described in the preceding article but the clavigers employed are irregular
clavigers. When the two clavigers are set as explained and joined by the con-
necting rod the corresponding ends of the two clavigers move in planes which are
not parallel.
The angle made by the intersection of the two planes is according to the
proportions of the irregular clavigers. This will be explained by reference to
Plate 9 Fig. 9; bxas is an irregular claviger, and s is the fixed axis. If the
end a of the clavis rod a b be constrained to move along the straight line ry, the
other end will move along the straight line y t. In fig. 8 the right claviger is
shewn when it is in such a position that a sb is an isosceles triangle and the
restraining arm 8x bisects the angle a 8 b and the base a b. The angle a s b is a
right angle. The irregular claviger in Fig. 9 is represented in the same position.
The angle ay b is however an obtuse angle. The size of this angle depends upon
the ratio of the restraining arm x 8 to the clavis rod b a. The position of the lines
of traverse ay and by with respect to the fixed axis 8 is determined in the
following manner. A quadrant man is described from the centre s at the
distance's, the length of the restraining arm. The restraining arm is placed on

page_text: the line dividing the quadrant into octants. The central line of the clavis rod ba
is tangent to the arc at and is the base of an isosceles triangle bay. The
perpendicular line x y bisects the angle y and the base ba. The position of the
pointy along the lines is determined by the fact that the part ye of the line y a
reaching from the point y to the arc m x n, or the part yf of the line y b are each
equal to the lines bx or xa.
57. Plate 9, Fig. 10 illustrates the manner in which the claviger couple can be
used to effect more than one motion in the same movement as well as increasing
the efficiency of the force. The figure represents a right claviger couple of the first
kind with unequal limbs. One clavis rod is shaped to form a handle. By means
of this the hook h can be lifted off its supporting stud m and placed higher up
upon the stud n. Fig. 11 represents a similar movement with a right claviger
couple of the second kind. The bent end of the link I can be taken out of the slot
moved down and replaced in another slot. Any combinations of movement in the
same plane can be effected by it. The handle is moved in the contrary direction
to the desired movement when the claviger couple is of the first kind and in the
same direction when the claviger couple is of the second or third kinds.
58. Plate 9 Fig. 7 represents a claviger couple for riveting, driven by hydraulic
pressure. R represents the bydraulic ram projecting from one end of a hydraulic
cylinder.
59. Plate 9, Fig. 12 represents a double claviger couple of the third kind with
unequal limbs, stayed by additional parallel rods pivotted to the others, for lifting
by hydraulic pressure. S is the fixed axis, and a is the lifting end. Two points x
and y are taken on the straight line joining S and a. The pivots at x and y are
lengthened and carry two rollers which run along the fixed guides m and n which
are on opposite sides of the rollers and give a reciprocal restraint. A vertically
moving ram R is connected to the pivot x. When the ram is moved upwards the
end a moves exactly along a parallel line. The ratio of the line of motion of x to
that of a is as 1 to 8.
60. Plate 9, Fig. 13 illustrates a similar movement. Two double claviger couples,
of the first kind with unequal limbs, a dze and a bz c are pivotted together at z.
The two fixed axes S and S¹ are on a horizontal line. The two pivots x and z are
sufficiently long to carry a roller at each end. The roller at z runs along a double
or slotted guide n, the rods passing between through the slot. The other roller x
runs along the fixed guide m. Both guides are on the same side of the rollers, and
thus reciprocal restraint is obtained. The pressure is applied at x by a vertically
moving ram R which is connected with the pivot at x. The lifting end is marked a.
The ratio of the line of motion of x to that of a is as 1 to 25.
,
61. Weighing and Lifting for moderately heavy goods.-Two double claviger
couples fixed parallel to each other in vertical planes at a sufficient distance apart
to allow of the package to be lifted to pass between. Two of the opposite ends of
each double claviger couple are rigidly fixed together by transverse rods which act
as pivots common to both. The fixed axes of both are in a horizontal line and are
supported at a convenient height. The package to be weighed and lifted may be
vertically under the two transverse rods and under a line joining the two fixed
axes or at any distance laterally within reach of one of the transverse rods, when
the claviger couples are extended, or of chains or ropes depending from it. The
package is attached to the lowermost transverse rod, and weights hung upon the
uppermost one until the package to be weighed is just lifted clear of the floor.
The machine, package and weights are then in equilibrium in whatever position the
machine may be placed. It can then be rotated on the fixed axes, by means of a
slight effort sufficient to overcome the resistances of inertia and friction only, until
the package is lifted to the requisite height and then the machine is elongated
laterally until the package is placed in the position desired.
62. The movement described above is a very suitable one for a ladle crane.
It may also be slightly varied and the lifting effected by hydraulic pressure,
The two parallel double claviger couples are then placed in horizontal planes. Thẻ

page_text: common axis of both is a vertically moving ram projecting from one end of a
hydraulic cylinder. The rods through which the ram passes have deep bearings on
the ram.
The two parallel claviger couples are stayed by four vertical rods passing
through the rods forming the four angles of the outer parallelogram of each set, and
act as pivots common to both. The ladle is fixed at one of the corners and its .
weight counterbalanced at the other corner. The ram lifts the whole arrangement
vertically to the requisite height. The ladle is turned round in any direction on
the ram as central axis and moved inwards or outwards radially by means of the
vertical rods. The force required for this purpose need only be sufficient to over-
come the resistances of inertia and friction. The two sets of double claviger couples
may rest upon friction rollers.
63. Weighing. The arrangement of rods for this purpose is shewn in Plate 9
Fig. 15. It is a right claviger pair described in article 10. The weights P and Q
are in scales hung at the ends of the clavis rods. The arms are joined by means of
blades. The clavis rods form the hypotenuses of two right angle triangles P & B
and QS B. Let a and B respectively be the angles which they make with the
lines Ps and Q S'. The virtual moment of each weight is P tan a, acting upon
the point B and tending to move it along the straight line B S towards S; and Q
tan acting upon the point B and tending to move it along the straight line B St
towards S. When the weights are equal the claviger pair is in equilibrium as
shewn in the figure, and the angles a and B are each 30°. If the weights are
unequal the rods take the exact angle at which the moments of the weights are
equal with respect to the point B. When the weights differ by the slightest
quantity it is indicated by the change of position of the point B. When the
balance is disturbed the weight which moves downwards has only a very slight
movement, the one moving upward and the point B have a greater range, but after
oscillating according to the force used they return to exactly the same position as
before they where disturbed. The weights move up and down in the same straight
lines parallel to each other. It is an extremely sensitive balance of great delicacy
and precision.
64. Plate 9, Fig. 16 represents a claviger pair for lifting weights a short
distance such as is usually performed by a jack. The object to be lifted such as
the, axle of a wheel is placed in the hollow C, by moving the claviger pair into
position under it. The foot is then placed upon the pedal a and pressed down to
the bottom at S. The restraining arms Sx and Sy are double so that the clavis
rods may pass between. The position when the lifting is completed is shewn in
Fig. 17. No pressure at C can then move it back, but a slight kick or lift with
the toe at the pedal A moves it back into the position represented in Fig. 16. and
releases the weight. Very considerable weights can be lifted in this manner.
the pressure on A is sufficient to commence the lifting it is easily continued as the
moment of the force increases the further the pedal is pressed down.
If
The virtual moment of the force acting at A is with respect to its application at
C as follows, Let a be the angle made by the clavis rod A B with the line A. S
and let be the angle made by the clavis rod BC with the line B S¹. The virtual
moment in every position is P tan a tan B. The length of the clavis rod CB
would probably be determined by the height of the article to be lifted. The
claviger ba s may however be varied in size to any extent. The virtual velocity
in all cases varies with the angles and is, P's Vel: W's Vel.:: sin a. sin ẞ: cos a
cos BW P. The ratio of velocity to power during any definite movement is
as follows Let a and B. be the angles at commencement of the movement and a¹
and ẞ be the angles at the finish. P's average Vel: W's av. Vel: (sin a¹—sin a)
(sin sin B): (cos a¹-cos a) (cos B¹-cos B): : Av W: Av. P. For completing a
stroke from any point, P's av. Vel.: W's av. Vel.:: cos a cos B: covers a covers B: 1
Av. W: Av. P.
::
65. Plate 9, Fig. 4 represents the same movement adapted for stamping and
compressing. One clavis rod is lengthened out to form a handle. Fig. 3 is the
same movement for punching plates &c

page_text: 66. Plate 9, Fig. 18 represents a similar movement. It is a claviger chain.
Clavigers of equal size are represented as pivotted together by the ends of their
clavis rods. The fixed axes are 8 8 and 81 situated at the three angles of a square.
A right claviger chain consisting of three clavigers is explained in article 10 and
represented in Plate 1, Fig. 10. These two chains represent the two extremes of
the movement. The moment and virtual velocity of the force are the same as
described for the pair in the preceding article. It may be shortly stated that the
pressure at d in any position of the chain is the intensity of the force multiplied
into the product of the tangents of the three angles which the power ends of the
clavis rods make with their lines of motion in the direction of their movement.
In any chain of three clavigers the force is varied by.
Their angles absolutely,
The difference of their angles relatively, and
The relative positions of their fixed axes.
This movement is adapted for pressing oil from seeds and for compressing cotton,
pulp, artificial leather &c. also for pulling apart, testing the strength of materials &c.
Fig. 18 represents it at the commencement of the movement, The angle xb s
is an angle of 45° The bearing at a is to accommodate n. cross bar which is
pushed along in a horizontal direction. For compressing, the claviger clmin acts
upon the platen at d. The last indefinitely small movement gives a pressure
inconceivably great. No unyielding material strong enough to withstand it.
In Fig. 18 the restraining arms are represented double. The joints should be
well fitted and the rods built up to withstand the necessary pressure without
yielding.
The difference between the two chains represented may be more clearly shewn
by figures. In Fig. 18 let the clavis rods be each 10 feet long and the cross har
pushed along by three or four men with a total pressure of say 400 lbs. The
length to be moved from a to s is a little over 7 feet (7·071068 ft.),
8
The length of the line of motion of the end d is 009543 ft. or about 10th of
an inch

page_text: These two examples represent the two extremes of relative dimensions for the
chain. Anything between can be arranged to suit different requirements. For
seed pressing &c when the length of movement of. d is not sufficient, several
pressings can be made with the same feed by inserting each time metal plates
under the platen. Fig. 19 represents the completion of the movement. No
pressure at d can move it back.
67. Curvilinear Motion converted into Rectilinear. Plate 9, Fig. 1 represents a
lever of the second kind connected to a right claviger. The radius for the claviger
is the part O b of the lever.
The rectilinear motion may be varied in direction with the lever in the same
position by varying the position of the fixed axis S. The lever may also be of the
first or third kind. When of the first kind the part forming the radius for the
claviger may be bent at any angle. Fig. 2 represents the same movement with a
claviger couple giving a reciprocal parallel rectilinear motion such as is used for air
pumps. In both the ends are free and cannot be moved from the straight lines.
68. Plate 9, Fig. 5. A lever of the second kind as is pivotted on the fixed
fulcrum S. Three rods bc, cd, ds are pivotted to it at b, to each other, and to
the fulcrum S, and they form, with the length b's of the lever, a parallelogram.
A rod efw is pivotted at c and f parallel to c b and d s, and on the end wis
pivotted the roller w. The fixed guide g along which the roller moves directs the
motion. The guide supports the fixed axis S, and the lower part of the guide is
curved to fit the roller. When the handle a is depressed the roller w is moved
down the guide drawing with it the connecting rod. This movement may also be
applied to levers of the first and third kinds. The parallelogram can be varied in
position and shape to any extent. The motion can be transmitted in any direction
with the lever in the saine position and it can be built up with additional parallel
rods pivotted together to any desired strength.
69. Plate 9, Fig. 6. A. double claviger couple a b c d having its fixed axis at S
has one of the rods which is centred on the fixed axis lengthened to e forming a
lever of the first kind. The pivots at the angles a and b are furnished with
rollers which run along fixed guides and gl set perpendicularly to each other.
When the handle is depressed the rod cf is raised vertically. Rods may be
attached to a, b and d transmitting motion horizontally and vertically in contrary
directions.
70. The Transmission of Circular Motion. Class A Plate 10.-The first method
to be explained for effecting this is by means of the hanger claviger described in
article 14. Two hanger clavigers are attached to each shaft and set one net
traverse apart. The corresponding clavigers on the opposite shafts are connected
at their traverse ends by transmitting rods or shafts equal in length to the distance
between the axes of the rotating shafts. The component force of the circular
motion of the power shaft is resolved by each claviger alternately and composed
into motion along a straight line. This rectilinear motion is transmitted by the
transmitting shaft to the corresponding claviger at its other end by which it is
again resolved and composed, the resultants then being circular motion given to
the receiving rotating shaft. The action of the second of the two clavigers,
attached to and operated by the rotating power shaft, begins before that of the
first has ceased, so that there is continuous impulse. The quality of the motion of
the rotating power shaft is exactly reproduced upon the receiving rotating shaft
and they move in unison. The motion is therefore perfectly transmitted. The
two clavigers on the same rotating shaft may be connected to it in different
positions, viz both on the same side of the rotating shaft attached to two cranks
set 180° apart as shewn in Fig. 1; both on the same side of the rotating shaft
attached to the same crank as shewn for a different imovement in Fig. 2; on
opposite sides of the rotating shaft attached to the same crank as shewn in Fig. 4;
and on opposite sides of the rotating shaft attached to cranks set 180° apart as
shewn in Fig. 3. If the rotating shafts marked P in Figs. 1 and 2 are the power

page_text: shafts and they are rotated in the sense of the arrows the strain upon the trans-
mitting shafts is tensile only. The same is the case if the opposite rotating shafts
are the power shafts and they are rotated in the opposite direction. When the
clavigers are on opposite sides of the rotating shaft the strain on one connecting
shaft is tensile and on the other compressive. The motion is transferred with
equal perfection when the motion of the power shaft is reversed. The motion
may be reversed at any point without affecting the clavigers. The forward move-
ment in either direction is along the same straight line and the backward movement
in either direction describes the same curve. When the distance between the two
shafts is too great to allow the two clavigers to support the transmitting shaft
without sagging, each transmitting shaft is supported between by a hanger or
hangers at convenient distances. These bangers are clavigers of the same dimen-
sions and fixed in the same manner as the clavigers at the ends of the transmitting
shafts. They are attached to radius rods of the same length as the cranks and
these radius rods turn upon fixed studs. They support the transmitting shafts
and move with them in the same manner as the crank clavigers, see Fig. 1.
71. Circular Motion transmitted any distanco. Plate 10, Fig. 2. The two
clavigers at each end are connected to the transmitting shafts & and d by short
connecting rods c, c, and c¹ c¹. The clavigers and the connecting rods at both ends
are set in the same direction. The transmitting shafts are equal in length to the
distance between the axes of the rotating shafts. They move backward and
forward in a straight line. They may be supported as often as required by fixed
bearings or by friction rollers above and below. In the figure they are each
represented as supported by claviger couples A and B. The transmitting shaft d¹
is attached to the claviger A by a fixed stud b¹ projecting horizontally from the
shaft and forming the pivot for the two clavis rods a¹ b¹ and b¹ c¹. The centre
pivot S¹ is the fixed axis and is attached to the framework. The ends a¹ and c¹ of
the clavis rods are provided with rollers which roll up and down the fixed straight
guide g. The other transmitting shaft d is attached in the same way to a
similar claviger B. These support the transmitting shafts but allow them free
movement forward and backward along the straight line.
72. Circular Motion transmitted any distance between shafts at different angles
or in different planes. The movement is the same as that described in the
preceding article, but the motion is taken from the transmitting shafts in any
direction radially. If the power shaft is a horizontal one and it is required to
transmit its circular motion to a vertical one, the short connecting rods on the
clavigers of the vertical shaft are attached to the transmitting shafts d' and d by
vertically projecting studs placed at the top and bottom of the ends of the trans-
mitting shafts instead of by horizontally projecting studs as represented in the
figure. As the line of forward traverse for the clavigers of the vertical shaft is in
the same direction as the line of motion of the transmitting shafts the motion is as
perfectly transferred as when transmitted to a shaft situated in a parallel plane.
During the return movement the outward curve of the claviger in a horizontal
plane has exactly the same effect, through its connecting rod, upon the return
movement, of the transmitting shaft as the outward curve of the clavigor in a
vertical plane, has through its connecting rod, with it. In the same manner the
motion can be transmitted from the rotating power shaft through the transmitting
shafts to a rotating shaft the axis of which is situated in any direction radially
from the axis of the trausmitting shafts & and d¹, provided the plane of the
movement of the receiving clavigers is at right angles to the axes of the transmitting
shafts. Also the motion may be transmitted to shafts in other planes wherever a.
straight line common to both can be found, which straight line is in direction
perpendicular to both their axes. Where this line cannot be found, the shafts can
be connected by using in addition one of the forms of claviger, couples for changing
the direction of rectilinear motion. The motion may be also equally well trans-
mitted direct from the horizontal shaft P, through the connecting shafts & and d¹,

page_text: to another horizontal shaft in a direction at right angles to the shaft P and
parallel to the transmitting shafts & and d. The direction of rotation may
be reversed in transmission to any shaft without altering its position or the
position of the transmitting shafts, by interposing between the short connecting
rods and the transmitting shafts at one end a reversing claviger couple, and as
one end is constrained to move with the transmitting shaft there is no need of
rollers.
The clavigers
There are some
It is designed
73. Circular Motion transmitted to great distances, the line of transmission
passing through positions difficult of access. The movement is similar to that
illustrated in Plate 10 Fig. 2 and described in the preceding article.
employed have a greater ratio of clavis rod to crank, say 8 to 1.
special features about this method which will shortly be described.
to transmit circular motion to great distances in the open air in order to utilize
water forces in hilly districts, the neighbourhood of which is unsuitable for the
sites of mills, or to carry force obtained from running water, tidal motion, wave
impact &c to places of security or to convenient positions for its utilization.
also intended for distributing power from a centre where it is produced or collected
to houses workshops and mills where it is required.
It is
In effecting these objects the lines of transmitting shafts (and rectilinear trans-
nitters where used), will probably be at some part of their course high in the air
and at others perhaps underground and in other positions not easily accessible for
oiling and cleaning. Also at certain distances along the line of transmission it may
be necessary to reconvert the rectilinear motion of the transmitting shafts into
circular motion and back again into rectilinear motion to other shafts. To meet these
requirements; firstly, the bearings of the revolving and oscillating parts of the
clavigers employed in these positions are made, by means of a new invention, so as
to be absolutely free from sliding friction and hence not requiring lubrication. In
addition, though equally as strong and certain in action as plain bearings, they are
made proof against the intrusion of rain and dust. The wear in these bearings is
extremely small resulting from rolling resistances alone without any interfriction
of the parts, so that attention is required but seldom. As this bearing is a separate
invention, and is applicable to other purposes, a separate application for letters
patent will be made for it. The second requisite is to support the transmitting
shafts securely so as to allow of their freedom of movement without needing
lubrication of the bearings. As the strain of transmission is by tension only, the
transmitting shafts may be light, even for transmitting great power. Shafts of
joined lengths of weldless steel tubing are preferably used. A shaft of 2 inches
diameter, containing in cross section 1 circular inch in area of solid metal should
be sufficient for transmitting the greatest amount of motive power ordinarily
required. A shaft of this dimensions is capable of sustaining a steady pull of
about 15 tons, without sensible alteration, so that if it be pulled with this force
endways at the rate of 1 foot per' second, it will be transmitting work at the rate
of 15 foot-tons per second. Now if the crank on the power shaft revolves at the
rate of say 120 revolutions per minute and the force be transmitted from a
balanced crank, or disc with crank wrist, 4 feet from centre to centre, by means
of clavigers having clavis rods 8 times the length of crank, the transmitting shafts
will be capable of transmitting 90 horse power per second with the same safety as
the 15 foot-tons were transmitted. If the traverse be made twice the length by
doubling the size of the crank and claviger, the same transmitting shafts will
transmit 180 horse power per second, with the same strain, and so on according to
the length of traverse and the rate of revolution of the power shaft. The supports
required for the transmitting shafts have no strain put upon them by the force
transmitted. Their sole office is to support the weight of the line of transmitting
shafts so as to prevent sagging, and side swaying from the effects of wind. For
this purpose at proper intervals along the line of transmission, the transmitting
shafts pass through metal boxes which are supported and held rigidly in position.
The inside length of these boxes is half the extent of the rectilinear movement of

page_text: the shaft. The bottom of each box inside is shaped so as to consist of two planes
intersecting each other at an obtušė angle, the intersection running longitudinally
along the centre. The top of the box is moveable and forms a lid. "When the
box is supported from below or from the sides, the lid fits flat upon the top and
is secured in position by bolts and nuts with adjusting set screws. When the box
is supported from above the top, the bolts of the lid pass through lugs fitting
between the upright attaching arms. The under part of this lid consists of two
planes exactly corresponding with those at the bottom but opposite in direction.
The portion of the transmitting shaft which passes along any part of the interior
'of the box has brazed or otherwise suitably fixed round it a solid piece of metal
having its upper and lower sides shaped to correspond with the inside top and
bottom of the box but the planes are opposite in direction. The sides of the metal
piece and the inside sides of the box are vertical and parallel. If the shaft be now
moved backward and forward horizontally it passes along the box without touching
any part of it. Between the metal shaping of the shaft and the box two spheres
of hard wood or metal are placed one above the shaft and one below. The shaft
rolls upon these balls, which travel backward and forward along the length of the
box and keep the shaft steady against movement in any other direction. If there
is a likelihood of the shaft having to sustain at times great lateral pressure from
wind, the sides of the box and of the metal shaping on the shafts are made to
correspond with the top and bottom, aud two additional spheres are used, one at
each side. This supporting box is described as a neceessary auxiliary for the
effective working of the transmitting shafts under the conditions described, but no
claim will be made in respect of it in the Complete Specification.
In some cases a telescoping adjustment is arranged for very long lengths of
shafting to allow for expansion and contraction due to changes of temperature.
When very long lengths of shafting are used there is a temporary extension of
length due to elasticity. This is reduced and compensated for when the second
claviger of each set comes into action before the action of the first is ended. The
effect being a slight variation in the uniformity of the motion. The length and
weight of the connecting shafts can be increased within very wide limits without
their momentum injuriously affecting the motion. When the limit of the traverse
is being approached the efficiency of the momentum is greatly decreased by the
leverage of the clavis rod and is absorbed by its means to assist the movement of
the crank. The result is the claviger and transmitting shaft slow down before
reaching the limit and then return with an outward curve, thus avoiding the shock
which would be the effect of suddenly reversing the direction of the motion. The
effect of excessive momentum in the transmitting shafts is not to waste force but
to affect the uniformity of the motion. When this occurs it is remedied by more
frequently re-converting the motion to circular, thus shortening the length and
increasing the number of the transmitting shafts,
:
74. Another variety of this method of transmitting circular motion is by
employing the arrangement represented in Plate 4 Fig. 5 which gives one
rectilinear traverse for every revolution. The arrangement is exactly duplicated
on each shaft and placed exactly in the same relative position. The ends of the
two corresponding clavis rods of each set, attached to the power and receiving
shafts, are connected by transmitting rods or shafts, equal in length to the distance
from the axis of one shaft to the axis of the other. If sufficiently long to require
it, they are supported in fixed bearings or by any of the other methods previously
described. The action of the clavigers causes each transmitting shaft to slow down
before reaching the limit of its movement so preventing sudden jars. The forward
movement of each transmitting shaft begins before the forward movement of the
The strain on the transmitting shafts is tensile only, and the motion
is perfectly transmitted with even full aud continuous impulse. The cranked
clavigers for effecting one rectilinear stroke for each revolution are not so perfectly
adapted for transmitting circular motion by combining two as here described.
The reason of this is because when the crank is the power end and circular motion
other ceases.

page_text: is being transmitted into rectilinear there is a neutral point at each half revolution
when the clavigers are for an instant in equilibrium between the forward and
backward movements, see Plate 2, Fig. 7. When the crank is on the line O F
rotating in the direction of the arrow the clavis rod is on the line F D and if, it be
supposed to be entirely without momentum it is as likely to return from D to A
after the half revolution of the crank and half a traverse as to go on to T
corresponding to a full revolution. Therefore if they are used for transmitting
circular motion and it should be the case that the joints are worn or badly fitted
while the movement is slow and the load heavy it might happen that a claviger
on the power shaft would return at the neutral point while the corresponding
claviger on the other shaft might just pass its neutral point in which case a violent
jam with probable breakage of the parts would occur.
75. The slider claviger previously described and illustrated in Plate 3. Fig. 7 is
equally as effective as the hanger claviger in transmitting circular motion by the
Imethods described in articles 70, 71, 72; and the roller claviger previously described
and illustrated in Plate 3 Fig. 7 by the method described in article 74.
76. Another method of transmitting circular motion is effected by attaching to
each shaft a claviger couple in the manner represented in Plate 6, Fig. 1. The
arrangement there shewu is exactly duplicated at each end and the parts placed
in the same relative position with respect to both shafts. The end A of the
clavis rod A B is then connected by means of a transmitting shaft with the
corresponding end of the claviger couple on the opposite shaft. The end A¹ of the
clavis rod AC is also connected by a transmitting shaft with the corresponding
end of the clavis rod of the similar claviger at the other end of the transmission.
The transmitting shafts are equal in length to the distance from the axis of one
shaft to the axis of the other. The transmitting shaft which joins the two ends A
of the clavis rods is for a part of its length, in the vicinity of the receiving
rotating shaft, bent or doubled so as to avoid coming in contact with it. By
the arrangement just described the circular motion of the power shaft is per-
fectly transmitted to the receiving shaft the rotation of both being in the same
direction.
The strain upon the transınitting shafts is tensile only, and their axes move
forward and backward in the same straight lines parallel to each other. The
motion may also be equally well transmitted in the reverse direction. In that case
the arrangement shewn in the figure is duplicated but the relative position of the
parts is reversed, that is, the left side of the arrangement at one end of the trans-
mission is put to the right at the other end, and the right side to the left. The
two corresponding points A at each end are then connected by a transmitting
shaft. The two corresponding points A¹ of the duplicate clavigers A¹ C S¹ are
connected by a line of two transmitting shafts with a reversing rectilinear trans-
mitter (as represented in Plate 1, Fig. 3) between them. When the arrangement
represented in Plate 6. Fig. 1 is employed as just described for transmitting
circular motion the duplicated clavigers, one of which A¹ C S¹ is shewn in the
figure, are preferably made of larger dimensions relatively to the other parts than
there represented.
77. The Transmission of Circular Motion direct from one Shaft to another.
Class B.-The method of effecting this without first converting the circular motion
into rectilinear has been described in article 3, and illustrated in Plate 1, Fig. 2.
It represents a right claviger couple attached by its ends to two cranks on parallel
shafts. The centre pivot is a fixed axis, situated half way between the two shafts,
parallel to them, and in the same plane. Plate 11, Figs. 1, 2 and 3 represent soine
variations in this form. More rods are added to give additional strength for trans
mitting great power. The transinission of the force is subdivided among the rods
however many may be used. In this way any desired strength can be obtained.
The movement of each pivot is only a small fraction of a revolution and of course
the total friction is not increased by multiplying the rods and pivots as the total
friction is subdivided as well as the force and in the same proportion. All claviger

page_text: couples, however the rods may be built together, if the fixed axis is in the centre
and one half of the couple is a duplicate of the other half reversed, are in equi-
librium in every position, and throughout every movement so that no force is
wasted in moving them. Their movement when transmitting circular motion
The scope
is oscillating combined with a lengthening and shortening of the span.
of the movement represented in Fig. 2 is indicated by the dotted lines. Fig. 3,
represents a claviger couple with unequal limbs attached to cranks of different
Bizes. The cranks are proportional to the limbs of the claviger couple. See
article 100.
78. The Transmission of Circular Motion to the various parts of complicated
machinery &c round corners when framework and other parts of the machinery
intervene. The means of effecting this is represented in Plate 11, Fig. 4. The
arrangement there shewn consists of a chain of claviger couples. A crank at each
end of the chain only needed. One crank is attached to the power shaft and the
other to the receiving shaft. There are no guides or supports in the chain but the
fixed studs supporting the centre axes. The chains may be of any length and placed
in any direction. The claviger couples are preferably pivotted together by coned
pins with screws washers and nuts at both ends. When the motion is transmitted
horizontally, the pivot connecting the two clavis rods of each couple is provided
with a roller which runs along a support of the proper shape. This is to obviate
side strain upon the fixed studs. In constructing the chain it is necessary to place
the couples correctly in position. The centres of the circles to be described by
each end of every claviger couple must be in a line with the fixed axis, and each
claviger couple must have more than sufficient span to reach at the same time the
furthest parts of both circles. Circular motion is in this manner perfectly trans-
mitted to any other crank in the same plane round any intervening obstacles. It
may similarly be transmitted to a crank or cranks in any position in a parallel
plane by interposing at some point in the chain a transverse shaft of the requisite
length supported in bearings in a position perpendicular to the two planes. The
shaft has a single crank at each end, one of which receives the motion and the
other transmits it; or the motion may be received by a double crank on the shaft
and transmitted at both ends or from any part of its length. Other claviger
couples or chains of claviger couples may be attached to any of the pivots con-
necting the claviger couples together in the original chain, to carry the motion in
other directions. These subsidiary chains can be made to vary the number of
of revolutions while transmitting the motion so as to suit the requirements of the
different parts of the machinery. The means of effecting this will be explained in
its proper section.
79. Plate 12. Fig. 3, represents a claviger couple for transmitting circular motion
from one shaft to another not opposite to it, the crank pin circles being in parallel
planes. Each shaft has a single crank at the end nearest to the other shaft. The
crank pins are free to revolve in the ends of the cranks which are shaped into a
The crank
bearing for them and are each held in position by a shoulder and nut.
pin is cranked at its end to a right angle, and these form studs upon which the
ends of the claviger couple are centred. The centre pivot x of the couple is a stud
projecting from a short shaft p r which revolves in the fixed bearings m n and is
held in position therein by the two shoulders shewn.
80. Plate 12, Fig. 2 represents another form of claviger couple for transmitting
circular motion in the same direction. The ends of the clavis rods are forked and
are each centred on two studs projecting from opposite sides of a moveable crank
pin, or as shewn in the figure to two studs on a collar free to turn on a fixed crank
pin. The centre pivot x is a stud projecting from a ring or collar piece c which is
free to turn upon the fixed cylindrical rod pr and is held in place upon it by a
shoulder S and a nut n. The common pivot of the clavis rod is formed by two
studs projecting on opposite sides from a ring or collar piece & free to turn round
upon and slide up and down upon the rod pr. The ends of both clavis rods at y
are forked and are attached to the studs on both sides and are free to turn upon

page_text: them. Or the rod pr may be free to move up and down in fixed bearings with
the two clavis rods centred on two studs projecting from it, and the collar carrying
the centre pivot loose upon it. This form of claviger couple is suitable for com-
posing chains of claviger couples for transmitting circular motion in a horizontal
direction round obstacles &c as explained in article 78.
81. The Trausmission of Circular Motion direct from one shaft to another, at a
considerable distance apart, without first uniting the resolved forces into rectilinear
motion. The means of effecting this is represented in Plate 12, Fig. 1. It is an
adaptation of the slider claviger described in article 23. Two parallel shafts shewn
in end view at o and o¹ rotating in the fixed bearings wand w¹ have single or
double cranks ob and o' b¹ of equal lengths. Midway between the axes of the two
shafts and in the same plane is a fixed stud s". A slotted clavis shaft ba and d b'
is attached to each crank by the ends b and b¹ which are free to turn upon the
crank pins. The length of each clavis shaft plus the length of the crank is less
than half the line o o. Two fixed studs s' and glare placed along the line o o¹.
Their distance along the line from each crank shaft is the base of a right angled
triangle of which the crank is the perpendicular and half the clavis shaft the
bypotenuse. The clavis shafts are slotted at their centre and are supported upon
rectangular blocks e and e¹ which are held by the fixed studs 81 and 8111 and are
free to turn. or oscillate upon them. The lengths of the slots are sufficient to allow
the clavis rods a lateral movement, by sliding along the blocks, equal in length to
the diameter of the crank pin circle. The inner ends a and d of the clavis shafts
are connected together by a claviger couple a c d, the centre pivot of which is the
fixed stud s¹. When the power shaft is rotated the circular motion of the crank is
resolved into two sets of rectilinear motions at right angles to each other. One set
is parallel to the line o o¹ and the other is perpendicular thereto. For every
definite angular movement of the crank pin round its circle, taking as zero the four
points. in the circumference made by two diameters, one coinciding in direction
with the line o o² and one perpendicular to it, the corresponding movements
in each set of the resolved rectilinear motions are respectively equal to the sine
and to the versed sine of the angle moved. One of these sets of rectilinear
motion, that acting in a direction parallel to the line o o¹ is transmitted to
the other end of the clavis shaft by direct thrust or pull causing the clavis shaft
to slide along the block, the other set of rectilinear motions is transmitted by
leverage alone. They are composed again at the other end of the clavis shaft,
but it does not move exactly in a circle owing to the clavis shafts being rigid and
consequently of invariable length. The motion of the inner end of the clavis shaft
is transmitted by the claviger couple, reversed in form, to the inner end of the
other clavis shaft which exactly reverses the process of the first clavis shaft.
The motion of the crank on the power shaft is thus resolved, transmitted and
composed simultaneously by the movement, and the crank on the receiving shaft
moves in unison with the crank on the power shaft. The studs s' and '11 may
each be fixed on the line o o¹ half way between the centre stud 81 and the axis of
the shafts. The clavis shafts are made proportionately longer. The claviger couple
a cd then revolves at the same rate as the cranks. The clavis shafts in both cases
may be supported in various ways. They may have fixed studs projecting from
their centres turning in rectangular blocks which slide along fixed straight slides
or the fixed studs may be provided with rollers at each end one running upon a
straight guide above it and the other upon a straight guide below it, or the clavis
shafts may turn upon a short transverse rod rigidly fixed at its ends to blocks
moving along fixed slides, or the necessary constraint may be obtained by any
open effective method. The clavis shafts may be supported at their centres by
links or oscillating rods and thus be compelled to move in the arc of a circle
instead of in a straight line. In that case one shaft must be supported by
a link or rod fixed in a direction exactly opposite to that supporting the other.
In all the cases described the arrangement is in equilibrium in all positions. The
clavis rods may however be supported at any part of their length in place of at the

page_text: 11
centre, and one crank may be longer than the other. The claviger couple at the
centre may be dispensed with and a sliort intermediary shaft in fixed bearings may
be substituted. It has a single crank at each end set 180° apart, and they are
slotted for a short distance along the web. The crank pins are studs projecting
from rectangular blocks fitted into the slots. One clavis shaft is connected to each.
The fixed studs s¹ and s are then half way between the central fixed stud s¹ and
the axis of the two shafts. The length of each of the clavis shafts is twice the
length of the hypotenuse of the right angled triangle made by the vertical crank ob
with half the line o s". During the movement the rotation of the intermediary
shaft is not uniform with the power shaft, and the ends of the clavis rods centred
on the studs attached to the blocks have a slight radial motion along the crank.
The longer the distance between the centres o and o' the less is the movement
along the slots and for moderately long lengths with short cranks no sensible
movement takes place. In such cases one clavis shaft alone can be used for trans-
nitting the motion from one shaft to another, the rotation being then reversed in
direction. Where exactly uniform motion is required the movement must be
duplicated. The slightly irregular motion of the end of one clavis shaft in the
crank of the intermediary shaft is then compensated for exactly by a corresponding
motion being given to the end of the other clavis shaft by the opposite crank, so
that the motion is perfectly transmitted. The intermediary shaft can be placed in
any position relatively to the other two provided that it is situated at an equal
distance between them, and the axes of all three shafts are parallel to each other.
The cranks on the intermediary shaft are then set at the saine angle apart as the
angle made by the intersection of the two planes of the axes of the three shafts,
at the axis of the intermediary shaft. One shaft can thus be near the floor in one
room while the other is in a storey higher, one clavis shaft being carried along
horizontally and the other carried up in the corner, the intermediary shaft being
in the corner near the floor with its cranks set 90° angular distance apart.
82. Plate 12, Fig. 6 represents two cylinders rotated in the same direction. Two
studs a and c project from the ends of the cylinders. They are connected by a
claviger couple a be having its fixed axis s supported by the framework in a line
with the line of contact of the surfaces of the two cylinders. The motion is
transmitted from the power shaft by a claviger couple connected to a crank on it
and to one of the studs à or c lengthened for the purpose. The cylinders may be
of different sizes.
83. Plate 12, Fig. 7 represents a similar movement but the motion of the two
cylinders is in opposite directions. The two studs a and c at the ends of the
cylinders are placed so that a line joining their centres shall coincide with or be
parallel to a line joining the centre of the ends of the fixed axes of the cylinders.
The centre pivot S and the common pivot b of the two clavis rods are studs
projecting from two rectangular blocks which move up and down' in the fixed
straight slide m n. The centre of the slot in the slide is in the same plane as the
line of contact of the surfaces of the two cylinders and is perpendicular in direction
thereto.
84. Plate 12, Fig. 8 represents an arrangement for rotating a long line of
spindles by one movement. The claviger couple a b c is connected to two
double cranks va and v'c on two vertical shafts and v' each turning in deep
bearings ww. One of these vertical shafts receives circular motion from the
power shaft through a crank; not shewn, below the bearing. The upper bend of
the double cranks are cranked again so as to bring the ends in a vertical direction.
The centre of these vertical ends m and n are a short distance laterally from the
axes of the vertical shafts and are in the same direction so that the upper part of
one of the double cranks is shortened and the upper part of the other is lengthened.
The two cranked ends m and n thus form two short cranks m v and n v' rotating
in the same direction and parallel to each other. They are connected together
by the straight flat rod ŕ t. At equal distances along this rod it is pierced by
holes through which are passed the crank pins of the double cranked spindles s¹ s²

page_text: 83 84 &c all placed in the same direction. The spindles turn in fixed bearings
above and below the rod. When either shaft or is rotated both turn
together in unison and rotate all the spindles on the rod simultaneously. The rod
may be conveniently fixed if made in two pieces, the division being longitudinally
along the centre. When placed in position the two pieces can be securely attached
by screws, or by clamps at each end r and t. The cranks on the spindles are the
same length as the short end cranks m v and n v¹.
.
"
85. Plate 12, Fig. 9 represents a claviger couple adapted to rotate a number of
cranked shafts situated in the same plane and parallel to each other. The claviger
couple is built up with parallel rods sufficient in number to furnish two for the
fixed axis S, and one for each of the cranks.' The cross rods are extended so as to
reach the cranks which are of different sizes. The two outer cranks and the two
outer rods in the claviger couple regulate the position and lengths of the others.
The distance between the cranks may be variable in which case the lengths
and arrangement of the rods and the lengths of the cranks must correspond.
Thus 8m:80::se: 8 g :: sa: 8c::ap: ct::mpot and so on for each crank.
If any one of these shafts is rotated it transmits the motion to all the others and
they all rotate in the same direction simultaneously.
SIT
86. Circular Motion transmitted. from one shaft to another not parallel to it,
both shafts being in the same or in different planes. Plate 12 Figs. 10 and 11.
illustrate the manner of employing claviger couples to transmit circular motion
from one shaft to another shaft situated in any direction. The centre locus of the
circumference of the two crank pin circles described by equal sized cranks upon
any two shafts however situated is either a point or a straight line. "The zero
points are taken on the two circumferences at the points which are "hearest
together and the points which are furthest apart. Fig. 10 represents the claviger
couple connected to two cranks on two shafts in the same plane, perpendicular to
each other. The ends a and c of the claviger couple a b c 8 are forked and
centred on two projecting studs on the pins g h and m n which pass through
bearing holes in the forks of the forked pieces e and f. The shanks of these
forked pieces pass through bearing holes in the cranks r t'and 'r¹ t' in the position
of crank pins. This arrangement of joints allows free movement in three directions
at right angles to each other. A rod m' n whose axis coincides with the line of
the centre locus is free to turn and move up and down in the fixed bearings w
and w. The centre pivot S of the claviger couple is a fixed stud projecting.
perpendicularly from the rod mn. When the arrangement is placed in position
and fixed as shewn in the. figure and one of the shafts is rotated the circular
motion is perfectly transmitted to the other shaft, though it may be at any angle
in any plane and the two shafts move in unison. During the movement the
rod m n has a motion of partial rotation on its axis and moves endways up and
down in its bearings. Fig. 11 represents an alternative method of attaching
the claviger couple to the cranks, which is effected by means of ball and socket
joints.
If f
can
87. Circular Motion transmitted from one shaft to another in the same line. The
arrangement shewn in Plate 12 Fig. 4 is to avoid the great torsional strain upon
the shafting when circular motion is transmitted by a long shaft rotating on its
axis. The motion can be transmitted entirely by the
arrangement shewn
or it
be alternated with lengths of rotating shafting. a b is a lever which for part of
its length at the centre may be double as shewn in plan view fig. 5. Its fulcrum.
is formed by two short projecting arms o o¹ of the short shaft 88 and projecting
perpendicularly from it. The short shaft è & is free to rotate in the fixed bearings
and z and it is held in place by the shoulders r and r and by the nut n. The
lever a b is pivotted at its centre upon the arins o o'. The lever at each end
passes through bearing holes in the ends of one or two cranks as shewn in the
figure. These bearing holes are inclined at an angle of the line'c d.
A line passing
through the centres of these bearing holes of both sets of cranks at both ends
of the lever passes through the point of intersection of the axis of the arms o o¹

page_text: with the axis of the shaft S S. When either crank shaft is rotated the lever a b
has two movements in a direction at right angles to each other, it moves up or
down upon its pivots at o and o¹ and it partly rotates upon the axis of the short
shaft 8 8.
The crank ends turn once at every revolution of the shaft round the
lever ends which pass through the bearing holes in them, but there is no sliding
movement of the lever in them. The motion is thus perfectly transmitted to the
other shaft. During the movement the centre line of the lever generates a cone
of two equal nappes of which the point of intersection of the axis of o o¹ and S S
is the common vertex.
88. Circular Motion transmitted from one shaft and reversed in direction to
another shaft in the same line, and closely contiguous to it. Plate 8. Fig. 4. Two
shafts S and S are in the same line with their ends sufficiently far apart to allow
of the passage between of the parts to be described. Two single cranks S x
and S¹y are on the ends of the two shafts. Between them there is fixed a straight
slide mՆ ԴՆ
Two clavis rods A B and C B are pivotted at their centres x and y
on the two cranks, which thus form the two restraining arms for the claviger
couple A B C. Both clavis rods are between the cranks and they are pivotted
together at B B by a short rod which allows a spaco between them slightly longer
than the width of the slide. The centre longitudinal line of the slide cuts a line
joining the axes of the two shafts and these two lines are perpendicular to each
other. The slide is cut through at its centre to allow passage of the rod or
pivot B B¹. The outer ends A and C of the clavis rods are each pivotted on a
stud projecting from a block. The studs are on opposite sides of the slide and the
blocks are arranged to pass each other in the slide during the movement. When
the power shaft, say S, is rotated, say in the sense of the arrow, the crank on it
during its revolution carries the centre of the clavis rod round with it, the end A
moves along the line S m while the end B moves in a straight line along B S.
When the end A has reached its limit towards m the end B is at the centre line S.
While A is returning to S the end B is moving beyond S in the opposite direction.
When the end A reaches the centre S, the end B is at its highest point. While the
end A is moving to its limit towards n the end B is returning towards the centre S.
Similar relative motions complete the revolution. During the movement the end B
carries with it the end B¹ of the other clavis rod giving throughout exactly the
same motion reversed to the crank S¹ y on the other shaft and causing it to revolve
in the opposite direction. The blocks are sufficiently long to allow their safe
passage past the cut out part of the slide. The quality of the motion of either of
the cranks and of either the ends A or C and of the end B is exactly the same as
shewn in Plate 6. Fig. 1, which illustrates a different movement.
89. Circular Motion is also equally well transmitted by the claviger couple from
a crank in a shaft turning in fixed bearings to another shaft or shafts which have
a traversing movement or any other movement of translation in addition to the
movement of rotation to be given by the claviger couple. To effect this the centre
pivot is constrained by any of the methods previously described to move along the
centre locus between the line of motion of the shaft and the centre of the crank
pin circle. The motion of the centre pivot along this locus does not affect the
transmission of the circular motion in any way.
90. Universal Transmitter.-Plate 12. Fig. 12 represents a claviger couple a b c s
with double restraining arms, the centre pivots are two studs or wrists projecting
at right angles from a short shaft free to rotate in the fixed bearings m and m' and
held in position therein by the shoulder and the nuts n and n or by any other
equivalent means. Any movement in any direction given to one end of the claviger
couple is exactly reproduced at the other end reversed in direction.
91. When the claviger couple has a fixed axis for its centre pivot it will transmit
motion reversed in the same plane. Thus if a pencil be fixed in each of the ends
of a claviger couple the points of which rest upon two slates and a message be
written upon the slate at one end, the writing is exactly reproduced at the other
end but upside down. If the message be written on the slate in vertical lines

page_text: commencing each line at the bottom, it will appear at the other end in vertical
lines with the commencements at the top and can thus be easily read.
With a
claviger couple moving horizontally the message is transmitted correctly for
reading when the transmitter and receiver face in opposite directions. By means
of the chains of claviger couples previously explained the writing can be trans-
mitted to moderate distances, and increased or reduced in size by employing
claviger couples with unequal limbs.
92. The universal transmitter described in article 90 can be similarly employed
to reproduce casts models &c. When made with unequal limbs the transmitter
will exactly reproduce models for statuary &c in any size required.
.
93. It was omitted to be stated in article 44 in the description of Plate 9, Fig. 21
that the arrangement of two clavigers there illustrated for transmitting rectilinear
motion along a straight line in a direction at right angles will transmit the motion
along a straight line at any angle according to the position of the fixed axis S
along the semicircular line 8¹8 x¹. The angle the line of traverse of the end C
makes with the line of traverse of the end A when both are produced till they meet
is the same angle made by a line joining SO with a line joining S¹ O. The length
of the lines traversed by the ends A and C varies according to the position of S
along the arc 88 x¹. When the fixed axis S is in a line with S¹ and O both lines
of traverse are nil as the length is reduced to a point only; when both the fixed
axes are at S¹ the length of each line of traverse is four times OB; this position
is shewn in Fig. 20. The length of the line of force transmitted can be varied by
lengthening the rod O B and attaching to it another stud on which the second
claviger which is of proportionate size to the lengthened radius rod is centred.
94. Continuous Circular Motion converted into Oscillating or vice versa.
Class A This is effected by adding to the arrangements shewn in Plate 7 Figs. 1
and 2 an additional oscillating rod centred on a fixed axis at N and pivotted at A.
This gives an oscillation forward and backward for every two revolutions of the
crank. The motion of the oscillating rod has very nearly a constant velocity ratio
with that of the crank. The length of the arc traversed by the oscillating rod may
be increased to any extent by lengthening the rod past the pivot at A or by
carrying it past the fixed axis at N.
95. Continuous Circular Motion converted into Oscillating or vice versa.
Class B.-Plate 19. Fig. 1. A shaft O rotating in the fixed bearing W has a
single crank O C at one end. Closely contiguous to it and in the same line is
another shaft 01 with a single crank O'R at its near end, or the cranked rod O¹R
may be centred on a fixed axis in a line with the axis of the shaft O. Circular
motion is given to the crank OC and it is required to oscillate the rod O R. Any
number of oscillations for one revolution of the crank may be obtained. When the
number is determined upon, the circumference of the crank pin circle is divided
into the same number of equal parts. An arc e f is then described by the end R of
the oscillating rod O' R equal in length to one of the divisions in the circumference.
In the figure one revolution of the crank is represented as changed into four
forward and four backward oscillations of the rod. The rod O' R has two studs or
crank wrists projecting from it one at its centre z and the other at the end R.
The wrist at has centred upon it a wheel or a system of rigid cross rods or any
efficient equivalent arrangement for carrying four studs upon which are centred
four rollers 1 2 3 . The radius from the centre of each stud to the centre of
the wrist z is half the length of the crank O C. The studs correspond in position
to the four divisions in the crank pin circle. The number of studs carrying rollers
are the same as the number of complete oscillations of the rod O¹R per revolution
of the crank. A right claviger couple R BCS of sufficient span is attached to the
crank at the end C and to the wrist R on the rod O R. Its centre pivot is one of
the studs, extended in length, which carry the rollers. A centre locus is taken
between the two complete movements of the points C and R. An outer guide mn
whose inner bearing edge is parallel to the centre locus and distant therefrom the
radius of the rollers is fixed in position round the centre locus and the four rollers,

page_text: When the crank is rotated in either direction its circular motion is perfectly
converted into the oscillating motion of the end R of the rod OR along the arc ef
and the vertical of both is uniform. The rollers revolve round the centrez at the
same rate as the crank, and the line Sz is always parallel to or coincident in
direction with the crank CO. The wheel and rollers run easily round the guide
and the rollers are always in contact with it.
'
196. Continuous Circular Motion converted into Reciprocal Rectilinear any number
of reciprocal strokes of any length per revolution. Class B.-The traverse of the
end R of the claviger couple in the movement described in the preceding article
may be backward and forward in' a straight line instead of along the arc ef. In
that case the rod O' R is dispensed with. The wheel and claviger couple remain
but the centre locus is slightly changed and therefore the fixed guide is made to
correspond. The claviger couple R B C has for its centre pivot the same stud but
it is placed behind the guide instead of in front of it as represented in Fig. 1. A
second claviger couple has one end centred on the shaft O close up to the crank and
is carried down in front of the guide and the lower ends of both claviger couples
áre pivotted together at R. Its centre pivot is a stud at z at the centre of the
wheel. This stud passes through a rectangular block which moves along a fixed
straight slide set parallel to the line of traverse of the end R. The length of the
linė of traverse of R may be increased to any extent (without altering the crank
wheel or fixed guide) by employing claviger couples with unequal limbs. The
motion is perfectly converted!
97. Continuous Circular Motion converted into Oscillating or vice versa, the
crank and oscillating rod being placed in any position relatively to each other.
Class B. Plate 19. Fig. 2. OC is the crank and MA the oscillating rod. The
latter is represented as a crank on a shaft turning in a fixed bearing. A fixed
stud N is placed in position at the centre of a line joining the points M. and O; and
the rod N P, 'half the length of the rod M A, has one end centred on the fixed stud.
The other end is centred on the middle of the cranked rod S Pz. The cranked
rod has rollers turning on the cranked ends S and z and running along the inner
edges of two parallel fixed cycloidal guides, the arrangement of the cranked rod,
rollers, centre locus and guides being the same as described in detail for another
movement in article 31. The arc A. G is equal in length to half the circumference
of the crank pin circle. The two rods N P and M A are connected by the rod E F
pivotted at its ends on studs projecting from the other rods. The rods NE, E F
and F M 'with the 'line joining the two centres M and N form a parallelogram. The
crank C and the end A of 'the rod MA are connected by the claviger couple A BCS.
Its centre pivot S is the cranked end S of the cranked rod. The rod M A is
moved once forward and once backward along the arc for every revolution of the
crank, whether' the crank be turned backward or forward. If the power be
applied to the rod the crank is turned in either direction according as it is started.
In both cases the motion of crank and rod are uniform and the motion is perfectly
converted.
98. The Pendulum and Works of a clock connected by direct motion. Plate 19,
Fig. 3. An axis O rotating in fixed bearings is connected with the mechanism
supplying the power. It is bent at the end into the single crank O C. Another
axis O in a line with it is connected with the train of the clock. It is bent at
the end into a single crank O¹ C¹ of the same length as O C. The two cranks face
each other' and are in position when set 180° angular distance apart. Between
the two axes and cranks the pendulum yz is hung, the centre of its support y
being in 'the line of the axes. A convenient length of the pendulum y R is taken
and at that point two studs are fixed in the pendulum on opposite sides parallel to
the line of the axes O and O. Midway between y and R a bearing hole wis
made through the pendulum; through this hole the cranked piece m wn is passed.
The length of wm or wn is half the length of the crank OC or O C. It has a f
crank wrist at each end set in opposite directions. RBC is 'a claviger couple
centred at one end on the crank OC and at the other on the stud R. Its centre
+
414

page_text: pivot is the crank wrist n. Another claviger couple R¹ B' C₁ has one end centred
on the crank C and the other on the stud R' on the opposite side of the pendulum
to R. Its centre pivot is the crank wrist m. The wrists m and n are provided
with rollers. The circumference of the crank pin circle is divided into any
number of equal parts, the zero points being the two points on the vertical
diameter. The arc described by the point R during the vibration of the
pendulum is marked. A parte rather less than the whole, is taken equal
in length to half the circumference of the crank pin circle. It is divided both
ways into the same number of parts as the circumference. The divisions mark
the position of the point R at equal intervals of time during the time of oscillation.
A double centre locus is taken as described in article 31 and two fixed parallel
guides g g and h h¹ placed in position as described in that article. The ends of
the fixed guides are however left open sufficiently wide for the rollers to pass out
for a certain distance. The arc ei is now extended to p and q and the lengths pe
and iq are divided in the same manner as the length e i. A double centre locus
is taken between them and the zero points in the circumference C₁ C. The fixed
guides are carried along one side of this additional double centre locus. When the
cranks are rotated in the sense of the arrows the guides are extended on the sides
shewn in the figure. If rotated in the opposite direction they would be ou the
other side of the line. The crank O C on the axis O is connected with the weight
while the crank O'C' on the axis O¹ is connected with the train, and the pendulum
is between them connected to both. The weight, resistances and pendulum are
nicely adjusted together so that the cranks make one revolution in rather less than
a second. During the time of oscillation the cranks make half a revolution and
are held motionless for a small fraction of a second before the next half revolution,
during the next oscillation, is made. The arc traversed by the point R is by con-
struction longer than the arc ei and it is only during the time the pendulum is
oscillating between e and i that the cranks can move. During the time the small
parts of the arc between e and ig are traversed the crank O C is held against
the pull of the weight by the rollers on the cranked piece running along the
profiles of the fixed guides parallel to the parts of the centre locus marked o.
This is effected without any stress upon the pendulum and it is as entirely free in
its swing as if unconnected with any other movement. The crank O C by means
of the claviger couple R B C exerts upon the pendulum while it is traversing the
arc e i the full pressure which it obtains from the weight, while the claviger couple
R B C transmits the power to the crank C¹ O¹ to be conveyed by the axis O¹ to
the train of the clock. The pendulum is thus placed between two equal pressures
viz. that of the weight and that of the resistances. The two claviger couples in
every position are in equilibrium and are equally balanced upon the pendulum.
Now if through any cause the weight slightly exceeds the resistance the pendulum
is moved more quickly along the arc and the crank O' C¹ makes half a revolution
in a correspondingly shorter period but this is compensated for by an increased
amplitude and consequently a longer interval of time during which the cranks are
at rest. On the contrary if the power is somewhat short of the exact amount the
amplitude is less and the interval the cranks are at rest corresponds. In this way
by delicate adjustment a perfect compensation may be obtained. The pendulum is
in equilibrium between the power and the work and regulates and controls them
by compensating for a slight variation in the equilibrium by a corresponding
variation in the are described. The action of the pendulum is noiseless.
99. The Claviger Clutch. Plate 13. Figs. 1, 2 and 3. A disc having a
projecting rim is rigidly attached to a shaft S which in the position represented
in the figure is extended on the opposite side of the disc and revolves in fixed
bearings. A centre part of the shaft S or of the disc is extended inwards beyond
the face of the disc and forms the axis S¹ for two restraining arins S¹ and S¹ y
which are connected with two clavis rods A B and B C thus forming a right
claviger couple with equal limbs having its centre pivot at St. The ends A and C
of the clavis rods are branched out into bearing pieces Am and n which are each

page_text: •
in one rigid piece with the clavis rod. The profile of the outer edges of both
bearing pieces is an arc of the circle described by the inner surface of the rim l¹;
The total length of each clavis rod from a point in the bearing edge f along a
straight line through to B must be slightly greater than the radius S₁f of the
inner circle. The clavis rod A B is lengthened so as to extend beyond B to F. At
the end F there is a fixed stud e projecting from the clavis rod in a direction
parallel to the stud S¹. This stud has a rectangular block turning upon it.. The
axis S¹ is extended sufficiently far to form the axis for another disc L which is free
to turn upon it and moves inside the rim of the other disc. A short slot P is cut
in the disc L forming a slide to accomodate the pivotted block at F. The power
may be applied to the disc L by a rotating shaft or by a crank. In the former
case the axis S¹ is lengthened so as to extend through and beyond the disc L. A
shaft or axle moving in fixed bearings is rigidly attached to the disc L round the
axis S. The shaft or axle is hollow as far as the nearest crank in it and the
lengthened axis S' passes along the centre and is secured by a nut and washer at
the other end leaving it free to rotate inside the shaft or axle when the movement
requires it. When the motion is delivered to the disc L by a claviger couple a
crank wrist R is fixed at any convenient point on the disc. When the disc L is
rotated in the sense of the arrow the slide on the end of F is carried round and
moves along the slot Pa short distance towards the axis S₁ causing the bearing
pieces A m and Cn to press against the interior of the rim of the disc and carry
it and its shaft round with it. The position of the claviger clutch is then as
represented in Fig. 2 and the pivotted block is at the end of the slot nearest the
centre. When the forward movement of the disc L is relaxed stopped or reversed
so that the disc is moving with greater velocity than the disc L, the bearing
pieces. m and n immediately move away froin the rim and the parts assume the
position represented in Fig. 1, the pivotted block being then at the outer end of its
slide as-represented in Fig. 3. The difference between the relative position of the
parts represented in Figs. 1 and 2 and the length of the slide in Fig. 3 are
exaggerated so as to more clearly illustrate the movement.
If the interior surface
of the rim and the bearing surfaces of the pieces A m and C n are true and well
finished the movement of the recoil is very slight. An alternative form of the
clutch is represented in Fig. 4. The clavis rod A.B is not continued past the
common pivot B. There is an additional link or rod B G pivotted on B. At
the end G it carries a fixed stud or wrist which passes through a hole in the disc L.
This is arranged so that the stud G cannot pass the line extended from S¹ passing
through B. The form represented in Fig. 4. is preferable to the other where the
velocity is great as there is no radial motion of the stud G in the disc. When the
forward pressure is applied at F or G the bearing arcs m and n move outward and
grip the rim with the whole length of their bearing surfaces at the same instant.
The outward pressure on the rim exactly in a radial direction from the centre S¹ is,
in the position shewn in the figures, about 10 times greater than the rotatory force
acting at F, so that slip is impossible. When the shaft S is being rotated by
impulse through the clutch all the parts move together as one piece. When the
impulse ceases the bearing arcs m and n are instantly thrown off the rim and move
inward along radial lines to the limit allowed and the axis S¹ rotates inside the
bearing parts of the restraining arms and of the disc L. The clutch has thus
instantaneous grip and release, and is free from wedging, sticking slip and
backlash.
100. The following remarks in this article should have been inserted in
article 77. When circular motion is transmitted between two shafts, situated
a considerable distance apart, by a right claviger couple of equal or unequal limbs
it is desirable that the length of the clavis rods should be in a certain fixed ratio to
the distance the shafts are apart. If the clavis rods are made only slightly longer
than is necessary to span the distance between the crank pins when they are
furthest apart the common pivot of the two clavis rods has an unnecessarily long
range of motion and has a velocity at some parts of its course considerably greater

page_text: than the velocity of the crank pin. The claviger couple is in this case proportioned
in the best manner when the movement of the common pivot of the clavis rods is
nearly circular and of about the same length as the circumference of the crank pin
circle. To effect this the clavis rods should be in the following proportion.
Let d = distance between the axes of the two shafts. The length of each clavis
rod is ✓. The best form of claviger couple for transmitting circular motion
between two shafts at a great distance apart is the irregular claviger couple repre-
sented in Plate 11. Fig. 2. It is varied by having the clavis rods longer in
proportion with more transverse rods and the length of the latter more nearly
approaching in length the diameter of the crank pin circle. A claviger couple of
this kind is represented in Plate 15, Fig. 3. It has in the figure, unequal limbs.
For transmitting circular motion it should have the fixed axis in the centre of the
middle transverse rod and the cranks should be shorter than half the length of a
transverse rod.
101. Continuous Circular Motion Transmitted, the revolutions being multiplied
or reduced in number in the transmission. Plate 14. Two cranks one on each
shaft are connected together by a claviger couple. When the claviger couple is of
the first kind with equal limbs the relation between the lengths of the cranks
should always be the same as the velocities, that is the radii of the crank pin
When the
circles should be in inverse proportion with the number of revolutions.
lengths of the cranks are out of proportion to the velocity a claviger couple with
unequal limbs is employed, the centre pivot being at the centre of force. That is
the product of the length of each crank into the number of its revolutions during a
complete movement, multiplied by the length of the further limb of the claviger
couple is the same amount for each crank. When the claviger couples are of the
second or third kind the crank which is situated in the centre is half the length
only it would be in a claviger couple of the first kind. The centre pivot is not
fixed but is constrained to move along the centre locus taken between the two
complete movements of each crank. The zero point in each crank pin circle is
preferably taken at the two points in each circumference which are nearest
together. The two complete movements of the cranks are accomplished when
they both reach their zero points again at the same time. The centre loci
When the
are in all cases symmetrical figures composed of trochoidal curves.
cranks are rotated in the same direction the curves are common epicycloids
when they are rotated in opposite directions the curves are common hypo⚫
cycloids. A fixed guide can be made with its bearing surface parallel to every
part of any combination of these curves. In the case of epicycloids the guide
is placed inside the centre locus and in the case of the hypocycloids it is placed
outside. When the cranks and claviger couples are not proportioned in the
> way described the curves of the centre locus are either contracted or elongated
epicycloids and hypocycloids. In the former case the guide and rods are larger
than necessary and in the latter a guide cannot be constructed parallel to the
curves, as they form loops. Plate 14 Fig. 1 illustrates this movement. The two
cranks A B and CD are connected by the right claviger couple A EC c. It is
3 required to transmit circular motion in the same direction from one to the other,
the cranks A B and C D to revolve with a constant, velocity ratio of 2 to 1. The
length of CD is twice that of A B. The centre locus is a common epicycloid
generated by a point in the circumference of a generating circle, the diameter of
which is equal in length to the crank A B, which rolls along the circumference of
a directing circle the diameter of which is equal in length to the crank C D minus
the crank A B. When the cranks are rotated in opposite directions the centre
locus is a common bypocycloid generated by a point in the circumference of a
generating circle, the diameter of which is equal in length to the crank A B, which
rolls along the concave side of the circumference of a directing circle whose
5 diameter is equal to the length of the crank CD plus the length of the crank A B.
When a right claviger couple is used this relation between the diameters of the

page_text: 0
generating and directing circles and the lengths of the cranks exists whatever may
be the ratio of the velocities. When the centre locus is composed of epicycloidal
curves their number is one less than the number of revolutions of the smaller
crank during one revolution of the larger, and when the centre locus is composed
of hypocycloidal curves their number is one more. The centre pivot of the claviger
couple, see Fig. 1, also passes through a bearing hole in the end of a rod c d equal
in length to the crank CD. The centre pivot also carries a roller and another
roller is carried by a fixed stud projecting from the end d. Half way between the
centres of the shafts B and D there is fixed a stud b upon which is centred at one
end the rod ab half the length of the crank A. B. This rod has at its other end'a
crank wrist a which is passed through a bearing hole to correspond in the centre
of the rod cd. A fixed inner guide gg is shaped and placed in position with its
outer edge parallel to the centre locus and' distant therefrom the radius of the
rollers on c and d. The rollers c and d are always in contact with the guide.
The rod a bis throughout the movement in a line with or parallel to the crank A. B
and the rod o d is in a line with or parallel to the crank CD. The fixed guide g g
is represented as supported by the brackets m n from the bearings of the crank
shafts. This is not a perfect movement with one claviger couple because when the
points Ac and C are moving in a direction parallel to each other the impulse is nil
and the assistance of inertia is necessary. To make it a perfect movement two
claviger couples must be employed either giving a duplication of the movement as
represented in Fig. 2 or a duality of impulse as represented in Figs. 3 and 4.
Fig. 2. represents the movement when the cranks are rotated in opposite directions.
The shaft D has a second crank D G of the same length as D. C set 180° angular
distance apart from it. A second claviger couple A F G d connects the crank D G
with the crank A B or with another crank on the shaft B parallel to A. B. Its
centre pivot is the pivot at d carrying the roller. The claviger couples are on
opposite sides of the fixed guides. The radius rod at the centre of the rod c d is
dispensed with as there is no means of supporting it. The rollers at c and d roll
evenly round the interior face of the guide and cannot be moved away from it.
The impulse is carried alternately by each claviger couple so that there is full
impulse during the movement. The movement is stronger the greater the ratio
between the velocity of the two cranks. If the ratio is 3 to 1 there are threo
rollers, if 4 to 1 there are four rollers and so on according to the ratio; the rollers
are an equal angular distance apart and are connected together and held in placo
by a cicular rim or by straight rods forming a rigid rectilineal figure carrying the
studs upon which the rollers revolve. The movement represented in Fig. 2 is
suitable for either speeding up or down, as either crank shaft may be the power
shaft and the rotation may be in either direction. If the rotation be reversed
there is no backlash and this remark applies to all claviger movements. The
crank shafts are shewn in the figures very near together owing to the exigences
of space. They may be placed any distance apart without affecting the size of
the guide.
102. Plate 14, Fig. 3 represents the movement for speeding down only. B is the
power shaft and the ratio of the revolutions of the two cranks as shewn is as 3 to 1.
In place of the single cranked rod represented in Fig. 1. a short shaft rotating in a
fixed bearing through the centre of the fixed guide is substituted.
It has a single
crank at each end set in the same direction. The rigid piece carrying the rollers is
pivotted at its centre on the crank pin a. The two cranks A B and C D are
connected by a claviger couple A E C with its centre pivot at c. A second claviger
couple A F D is placed on the other side of the fixed guide. One end of it is
centred on the shaft D and the other end on the crank A. B. Its centre pivot is
the crank pin of the crank parallel to a b at the other end of the short shaft b.
A double impulse is given by this means. The crank AB by means of the claviger
couple A¹ F D rotates the crank a b synchronously with itself. The latter carries
round with it the centre of the wheel or system of rods carrying the rollers. Its
force acts upon the latter as a lever of the third kind, each roller alternately acting

page_text: as fulcrum, while the fixed guide restrains the movement of the rollers to the
centre locus. By this means the stud at c which is the centre pivot of the claviger
couple A E C c is carried round the centre locus and is at every instant in the exact
position required by the claviger couple A E Cc and resists as firmly the strains
of the latter as if it were held by a fixed axis. The whole of the force transmitted
through the claviger couple A ECC is expended upon turning the crank CD.
An alternative arrangement is to dispense with the claviger couple A' FD. The
short shaft b has then the single crank at the other end of the same length as the
crank A B and set in the opposite direction to the crank a b that is it is set
180° angular distance from it. It is then connected with the crank A B by a
claviger couple with a fixed stud or axis for its centre pivot.
103. Plate 14, Fig. 4 represents the movement for speeding up only. The figure
represents the movement with claviger couples of unequal limbs. The shaft D is
the power shaft. The claviger couple A EC c is connected with the parts in the
same manner as previously described in articles 101 and 102. The second claviger
couple B F C has one end centred on the crank D C and the other end centred on
the shaft B. Its centre pivot is a stud projecting at 6 from the rod cb which is
pivotted at its other end on the stud c which is the centre pivot of the claviger
couple A E C. The rod cb is parallel to the crank A B. With a claviger couple
of equal limbs the length of the rod c b would be half the length of the crank A B.
With a claviger couple of unequal limbs as in the figure its length is as follows.
Let x =
length of the rod be with any claviger couple of equal or unequal limbs,
= length of crank A B, m = a straight line joining the two points A and c, and
n = a straight line joining the two points c and C. Then x =
1. n.
1771
104. Plate 14, Fig. 5 represents the movement with claviger couples of the third
kind. It is arranged for gearing down and the centre shaft B is the power shaft.
The fixed guide gg is at one end and it and the parts moving upon it are arranged
in the same manner as in Fig. 3. The cranks a band a bat each end of the rod b
are twice the length of the crank A B. The claviger couple CE c has one end
centred on the stud at c and the other on the crank CD. The second claviger
couple D Fa has the end D centred on the shaft D and the other end centred on
the crank a b of the rod b on the other side of the fixed guide. The centre pivot
of both claviger couples is the crank pin of the crank A. B. Fig. 6 shows a vertical
section through the centre of the guide g g and through the shaft b when the
cranks a band a¹ b are in the vertical line. In this movement both cranks rotate
in the same direction.
105. Figs. 7 and 8 represent tho elevation and section of this movement with
irregular claviger couples of the second kind, with unequal limbs, for gearing down
only, the rotation of the two cranks being in opposite directions. The end shaft B
is the power shaft. Figs. 9 and 10 represent the elevation and section of this
movement with irregular clavigers of the third kind with unequal limbs for gearing
up only, the rotation of the cranks being in opposite directions. The centre shaft B
is the power shaft. The arrangement of the fixed guide and the parts connected
with it may be the same as represented in Fig. 4. The arrangement of rods illus-
trated in Figs. 9 and 10 in connection with the fixed guide gives additional strength
to the restraint and direction by supplying the crank a b, corresponding to the
crank a b in Fig. 3, and by supplying the axis b upon which the crank a b rotates.
The axis b rotates in the opposite direction to the crank a b. The fixed parts only
are shaded in the sections represented by Figs. 6. 8 and 10. In all of the movements
represented in Plate 11 the cranks may be rotated in the sense indicated by the
arrows or in the opposite direction. The number of revolutions of the more rapidly
revolving crank must be a multiple of the number of revolutions of the other during
a given time.
106. Figs. 11, 12, 13 and 14 represent geometrical figures of the movements
explained in articles 101, 102 and 103. Instead of fixed cycloidal guides, discs

page_text: representing the generating and directing circles explained in article 101 are
employed, the cycloidal movement of the centre pivots of the claviger couple
being obtained by the discs rolling along the circumference of fixed circular guides.
In order to maintain the rolling discs in contact with the fixed circular guides an
additional disc is employed. When the fixed circular guide is at the centre
between the rolling discs a loose annular rim is fitted over the rolling discs so as
to surround them all, and it is carried round by them in the same direction as they
revolve round the fixed guide. When the fixed circular guide is outside the rolling
discs they are held in place by a loose disc or wheel rotating on a fixed axle at the
centre of the circle of which the interior of the fixed guide is the circumference.
Slip of the rolling discs is prevented by a method of slightly increasing the thick-
ness of the fixed guidés or discs to be explained in article 123, by which the
rolling discs are compressed between the fixed circular guides and the loose disc or
rim with sufficient force. The discs are not limited in number as is the case with
the rollers previously described but they must not be sufficiently numerous to
touch each other. By this method when right claviger couples with equal limbs
are employed the motion is perfectly transmitted, varied in velocity according to
the longths of the cranks though one crank may not be an even multiple of the
other. In the geometrical figures the fixed guides and fixed bearings are indicated
by small crosses, the axes of rotation are perpendicular to the plane of the figures,
upon which plane all the parts are represented as projected.
It is con-
107. To Multiply the number of revolutions. Plate 13, Figs. 5 and 6. Fig. 5
shews an elevation of the arrangement and Fig. 6 the geometrical lines of the
movement. Two cranks A P and C W on the shafts P and W are connected by
the claviger couple A B C 6. A third shaft F is placed half way between the
shafts P and W and parallel to them, with the axes of the three shafts in the
same plane. The three shafts are free to rotate in fixed bearings. The shaft F
carries at its end the straight slide m n rigidly fixed to it in a line with the
two cranks. The centre pivot S of the claviger couple ABCs is a stud pro-
jecting from a block fitted to move along the slide. The scope of the movement
of the stud S along the slide is the length of the diameter of either of the
crank pin circles when the cranks are equal in length. If the cranks are
of unequal lengths it is half the sum of their lengths. The parts are placed
in position as shewn in Fig. 6. Let the shaft P be the power shaft.
nected with the shaft F by any of the arrangements herein described so that when
the shaft P is rotated in either direction the shaft F will be rotated with the same
velocity in the contrary direction. Now when the shaft P is rotated say in the
sense of the arrow, the crank A P carries the end A of the claviger couple round
with it in one direction while the slide m n carries round the centre pivot S in
the contrary direction with the same angular velocity. The effect upon the
crauk CW through the other end C of the claviger couple is that it has an
angular velocity given to it of three times that of the crank A P. During the
inovement the centre pivot S moves up and down along the slide describing the
centre locus shewn at F, Fig. 6. It is a symmetrical figure composed of four
elongated hypocycloids with the multiple point in a line with the axis of the
shaft F. This figure may be described by a point on the circumference of a
generating circle, whose diameter is equal to the length of the crank A P,
invariably connected with another circle concentric with it, whose diameter is one-
third the length of the crank C W, the latter circle rolling along the concavo side
of the circumference of a directing circle whose diameter is equal to the sum of
the diameters of the other two. Any uniform angular velocity may be given to
the shaft F, greater or less than the velocity of the shaft P. The shaft W and the
shaft P have in all cases a constant velocity ratio, and the locus described by the
point S corresponds. In a given time the number of revolutions of the crank CW
is equal to the number of revolutions of the crank A P plus twice the number of
revolutions of the slide m n. When the cranks are not equal in length a claviger

page_text: couple of unequal limbs must be employed. The movement represented in the
figure is that of a claviger couple of the first kind. The movement is equally
effective with claviger couples of the second and third kinds.
108. To Double the number of revolutions. Plate 13. Figs. 7. 8 and 9. Fig. 8
shews the geometrical lines of the movement and it will be convenient to explain
it first. From the centre b at the distance bz describe the circle cx d. From the
same centre with the distance by, which is twice the length of b x, describe the
circle f y e.
From the centre b draw the radius line 6 c. Bisect the line b c at a.
From the centre a at the distance a b describe the circle c w b. Divide the
circumference c wb iuto any convenient number of equal parts, and the circum-
ference fye into twice the same number of equal parts, number the corresponding
points, as shewn in the figure. From each point in the circle c w b draw lines of
the same length as the radius by in a direction towards the corresponding points
in the circle f y e. When the lines are not long enough to touch the corresponding
points they must be drawn to the radius line upon which the corresponding point
is situated, each of these lines is bisected by the circumference cx d. Join the
points in the lines, made by the intersection with them of the circumference, with
the centre b. Join each point of division along the circumference c wb with the
'centre a. The figure will then represent the position of the different parts of the
At e and the lines
arrangement at equal intervals of time during the movement.
touch the circumference, while at y' and b¹ they are at their furthest point from it,
The locus of the ends of these lines is a double reversed contracted epicycloid
scarcely differing from an ellipse with e f for its major and b¹ y¹ for its minor axis.
Reference is now made to Fig. 7. The same letters of reference represent the same
positions as in Fig. 8. The centre a is the centre of a shaft and the radius a bis
the length of a single crank a a¹ upon it. The lines c b and cy' in Fig. 8 are
represented in Fig. 7 by the clavis rods a¹ b¹ and a¹ y¹ attached to the crank a a¹;:
the radius lines b u and b v in Fig. 8 are the restraining arms buand bv in
Fig. 7. The four rods thus for the right claviger couple, with equal limbs, b¹ a¹
yb and the crank pin at a¹ is the cominon pivot of the two clavis rods. The
centie b in Fig. 8 is the centre pivot or axis for the restraining arus. The centre 6
is also the centre of another crank shaft B carrying at its end rigidly attached to
it the bar ef whose length is equal to the line o o¹ Fig. 8. The two shafts a and B
have their axes perpendicular to the plane of the figure and in opposite directions
from it. The single crank and the bar are at the ends of the shafts face to face.'
The ends e and fof the bar are connected to the ends b' and y¹ of the claviger
couple by the connecting rods e b² and fy¹. The bearings of the two shafts are
marked and s. The centre pivot b is a continuation of the shaft B, narrowed in
diameter. Now when the shaft B is rotated in either direction the motion is
transmitted to the crank a¹ a causing it to make two revolutions for every
revolution of the bar e f. The force is delivered to the crank as a full tangential
impulse all round, and the motion of the crank has very nearly a constant angular
velocity ratio of two to one to the motion of the bar. The variation is so minute
There is no fixed
as to be inappreciable. This movement is a very desirable one.
5 part except the fixed bearings and s of the two shafts. The movement and
consequently the friction of the joints is much less than would appear at first sight.
Half the force is transmitted by each claviger which for estimating the friction is
the same as if all the force passed through one claviger. The total movement
of the crank end of the clavis rod upon the crank is one third of a revolution
while the crank is making one revolution; during the same time the movement
on the pivots b, v and y¹ are each one sixth of a revolution. But only the
half of the force due to leverage affects the friction of the pivots b and v, so
that the total friction for the movement is only equal to the friction of about
two thirds of a revolution of one pivot under the full stress of the force traus-
mitted. The crank shaft a may be provided at its other end with a bar similar
to that on the shaft B and the motion delivered again doubled in velocity to a
third cranked shaft and so on within a short distance the velocity can be doubled.
7

page_text: each time and a very, high, velocity reached. For reducing the number of
revolutions the crank shaft is employed as the power shaft. Fig. 9 illustrates
the perfect form of this movement. In place of the connecting rods the claviger
ends are pivoted on two studs carried by two blocks sliding in short slots towards
the ends of the bar, which is lengthened for the purpose. Fig. 9 represents the
movement a quarter turn of the crank further forward than in Fig. 7. The
angular velocity of the crank to that of the bar in the movement represented in
Fig. 9 has a constant ratio of two to one. That this is so may be shewn as follows,
As explained in the opening article the ends of a right claviger couple with equal
limbs are always in a line with the centre pivot, the two ends of the claviger
couple represented in Fig. 8 are therefore always both, on the same diameter. The
angle made by a line drawn from the common pivot of the two clavis rods (in this
case the crank pin a') to the centre pivot o makes a right angle with the diameter
upon which the ends of the claviger couple are at the instant touching; and this is
the case in every position. Let the line bo in Figs. 10 and 11 represent the
radius of the circle fye (Fig. 8) and the line o s the radius ba of the
circle cwb. The axes of rotation o and s are perpendicular to the plane of the
figure. Let the lines bo and o 8 be the initial positions of the radii and let b' o be
the position of the longer radius at the end of a certain interval of time. As the
angle bom must by the construction be a right angle the position of the smaller
radius at the end of the interval will be m s. The angle m so is twice the size of
the angle bob and this is the case for any movement during the whole revolution.
The motion of the radius ms has therefore a constant angular velocity ratio of two
to one to the motion of the radius bo. That the angle m 8 o is twice the angle b₁ ob
may be proved in the following manner, leaving out steps in the reasoning which
are apparent. Bisect the line mo at n, draw the perpendicular n 8 bisecting the
angle m 8o. The angles bob and mos are together equal to a right angle; and
the angles n 8 o-and-m-o 8-are together_equal to a right angle, therefore the
angle blob is equal to the angle n so. But the angle so is half the angle mso;
therefore the angle blob is half the angle m. so, and the line ns is parallel to the
line b¹ o.
It is also evident from this proof, that the two radii may be any length
relatively to each other. The practical effect of this is that the bar and claviger
couple may be any convenient length relatively to the length of crank. The
essential point is that the crank and shaft shall be so proportioned and placed in
position that the projection of the axis of the shaft carrying the bar shall touch the
circumference of the crank pin circle and be in direction perpendicular to its
plane.
109. Plate 13, Fig. 9a illustrates the movement described in the preceding article
adapted to the hanger claviger for converting alternate rectilinear into continuous
circular motion. The hanger claviger is proportioned in such manner that when
the end A is moved along the straight line CD the end B moves along the
epicycloidal curve from f to e giving one revolution of the crank a¹ a for each
forward stroke. The relative dimensions are crank a a¹, 1; clavis rod a' B, 4;
clavis rod A B, of the right claviger A B 8, 13. The traverse line CA D is
perpendicular to the line eba D. The fixed axis S is on a line s b B parallel to
the line CA. D. The line s b is equal to the line A D and half the line CD. The
pivot at the centre of the clavis rod a¹ B is a fixed stud on the block m which
moves round the circular guide g g attached to the bearing of the crank shaft.
The centre of this guide corresponds to the circle c d x in Fig. 8. This means of
carrying the pivot v round the circle instead of by the restraining arm bv shewn 5
in Fig. 7 is necessary because the latter would be intercepted in its movement by
the shaft a. The crank a at must be a single crank. The movement is duplicated
at the other end of the shaft. The shaft a is only of sufficient length to carry a
double crank at its centre, between the two fixed guides, from which the circular
motion is transmitted. The whole forward stroke from dead point to dead point 5
gives about 1 revolutions of the crank and the return is effected during the time
the crank is making 3rds of a revolution.

page_text: 110. Plate 13, Fig. 10. shews the same movement doubled and adapted to revolve
in opposite directions two single cranks a o and a¹ o' at the ends of two parallel
shaft o and of giving four revolutions each for every two reciprocal strokes delivered
at the pivot B. The relative proportions are the same as described in the preceding
article. The two clavis rods A B and C B are pivoted together at B, and the two
restraining arms bx and by are pivoted together by the stud b projecting from the
block m.
The four rods A B C 6 thus form a right claviger couple of equal limbs
and b is the centre pivot. The centre locus between the motions of A and C is a
straight line perpendicular to the plane of the axes of the shafts. The block m
carrying the centre pivot b is constrained to move in the centre locus by the
straight slide G G. When pressure is exerted on B it moves along the straight
line B D to a point E, BE being twice B D. This is the net forward traverse
and gives two revolutions to each crank. During the movement part of the force
acts automatically upon the centre pivot b moving it up and down the slide in the
centre of a line joining the points A and C. The pivot at B may also be a stud
in a block sliding along a fixed straight guide, in a plane parallel to the plane of
the other fixed straight guide. The end B moves in the straight line B D E
during both forward and return strokes. When the loads carried by the shafts o
and o are exactly equal there is no need for the straight guide G G, and the
piston rod is connected direct to B. The entire forward stroke gives 23 revolutions
to each crank and the return stroke gives 1 revolutions. The cranks may be
extremely small even on very thick shafts without affecting the movement beyond
shortening the length of the traverse. This is a movement suitable for operating
twin screw propellers for boats and ships. The motion of the piston rod is carried
to the point B by a built up: irregular claviger couple with unequal limbs of the
kind represented in Plate 15, Fig. 3. A represents the piston rod, S is the fixed
axis and the end B¹ is attached to the pivot at B Plate 13 Fig. 10. The pivot at B
is then the shank end of a T shaped rod. The end B₁ of the claviger couple which
transmits the force from the piston rod is forked and pivoted on the cross piece.
The planes of the movements of the two claviger couples are perpendicular to each
other.
111. To Multiply or Reduce the Number of Revolutions of a Shaft. In all the
movements of this section the axes of the two shafts are in a straight line and the
two contiguous ends: terminate in single cranks facing each other, with just
sufficient space between for the free passage of the rods connecting the two cranks
together. The crank pin circles are concentric with each other, or stated more
exactly the centre lines of the two crank pins describe two cylinders which have
their axes in the common projection of the axes of the two revolving shafts. The
first method to be explained for effecting this purpose is an adaptation of the roller
claviger and is represented in Plate 23, Fig. 1. The shaft connected with the smaller
crank is supposed to be cut through near the bearing and the figure represents a side
elevation of the arrangement. The shaft O is cranked at its end into the single
crank O B. The other shaft O' in the same line with the shaft O carries at its end
the single crank O'D. At the centre between the points O and D a crank wrist C
is fixed parallel to the wrist or pin D, which is parallel to the shaft O. A B is
a clavis rod of the same length as the crank O D. At its centre it carries a
fixed stud and c¹ upon each side of the rod. At the end A the clavis rod is
finished into a T shaped end forming two studs A and A' projecting in opposito
directions. The four studs are parallel to the shaft O. The end B of the clavis
rod is pivoted on the crank pin B. A connecting rod C x¹ is pivoted at one end
on the stud C and at the other end on the stud ! thus connecting the centre of
the crauk O D with the centre of. the clavis rod A B. On the stud A a single
cranked rod A¹ y equal in length to the crank O B is pivoted with its wrist or
crank pin y. parallel to and in the same direction as the crank pin B. A connecting
rod Dy is pivoted at one end on the stud D and at the other on the crank pin y.
The studs x and y are provided with the rollers and r¹. The length OC of the
crank O D is a multiple of the length of the crank O B. The angular velocities of

page_text: the cranks OC and OB are inversely proportionate to their radii. The two cranks
are rotated with a constant velocity ratio and the loci of the points x and A are
marked. A fixed guide g g is placed in position within the locus of the point x.
Its outer edge is parallel to the locus and distant therefrom the radius of the
roller r.
Another fixed guide gi gl is placed in position outside the locus of the
point A. Its inner edge is parallel to the locus and distant therefrom the radius
of the roller r¹. When either crank is rotated the motion. is perfectly transmitted
to the other and both cranks rotate with a constant augular velocity ratio. The
arrangement gives a reciprocal restraint and the double impulse conveyed by the
two connecting rods C x¹ and Dy obviates the possibility of wedging. The leverage
part of the transmitted force operates the roller claviger B x A alternately as a
lever of the first and third kinds. The crank A y is parallel to or in the same
direction as the crank O B at all points in the movement. An alternative arrange-
ment is as follows. The connecting rod Dy is pivoted on the stud A', the
crank Ay being removed. A single cranked rod similar to A¹ y and half the
length of OB is pivoted on the stud and the end of the connecting rod C x¹ is
removed from the stud r¹ and pivoted on the crank pin.
1
112. As previously explained in connection with the description of movements
for converting rectilinear motion to continuous circular the length of the clavis
rod BA and therefore of the crank O D relatively to the length of crank O B may
be varied as desired and the position of the pivot or fulcrum and consequently
of C may be changed to any position along the rod, the lengths of the short
cranked rods corresponding. These variations also apply to all the methods for
multiplying or reducing the number of revolutions in continuous circular motion.
In describing the various movements in connection with this invention the method
of attaching the rods together as represented in the figures is explained for clearness
-but-not-with the intention of limiting the movements to these exact details of
construction. The method of pivoting together-may be varied and at the point
of connection either rod may revolve upon the other or any other open effective
method of connecting the rods together may be employed to carry out the principle
practically. In describing the following movements the relative lengths and
positions of the parts are those which are most advantageous for the movement
and it is to be understood they may be varied as previously explained when
describing the principle of the claviger power in connection with other move-
ments.
113. Plate 15, Fig. 1 illustrates an arrangement for multiplying or reducing the
revolutions of a shaft by means of claviger couples of the first kind. The shafts
are situated as described in article 111. The shaft O terminates in the single
crank OB. The shaft O carries the bar D F rigidly attached to it at the end
facing the crank. The proportions designed in the figure are to multiply or reduce
in number the revolutions of one crank when transmitted to the other in the ratio
of six to one. The length of O D or OF, being each half the bar, is six times the
length of the crank O B. At the ends of the bar are two crank wrists D and F.
Halfway between the centre and the ends are two other studs or crank wrists C
and E. On C and E are pivoted two single cranks C and E y each half the
length of the crank O B. Two right claviger couples Dc B and Fe B' have their
ends B and B centred upon the crank pin of the crank O B, their other ends F
and D are each pivoted on the studs F and D at the ends of the bar. The centre
pivots of each claviger couple are respectively the crank wrists x and y. These
two crank wrists are supplied with rollers. The centre locus is a symmetrical
figure composed of five common epicycloids; a fixed guide gg is placed in position
within it, with its outer profile parallel to the locus. Either shaft may be the
power shaft and may be rotated in either direction and the motion is transmitted
to the other rotating it in the same direction with a constant angular velocity
ratio of six to one or one to six as the case may be. It is a perfect movement..
When the ratio is 3 to 1, 5 to 1 or any other odd number to one, the bar is bent
to an angle so as to reach two corresponding points as nearly opposite as possible.

page_text: 114. Plate 15, Fig. 2 represents a similar movement to the last, but it is more
particularly adapted for speeding np than down. The rotation is represented in
the figure as transmitted reversed in direction, the revolutions being increased
in number in the ratio of six to one. The movement is effected by claviger couples
of the third kind. The crank and bar are of the same relative lengths as described
in article 113 and the bar has four studs or crank wrists in the same positions.
Both ends B and B₁ are also centred on the crank pin of the crank O B. On the
studs D and E at the ends of the bar two cranks Dd and Ff, each equal in length
to the crank O B, are pivoted so that their pins d and f project in the opposite
direction to the crank pin B. The two outer ends of the claviger couples are centred
on the crank pins & and f. The centre pivots of the two claviger couples are the
studs or crank wrists C and E. The two crank pins d and fare provided with
rollers. The circle described by the points C and E is the centre locus between
the crank pin circle of the crank O B and a symmetrical figure composed of seven
common hypocycloids. A fixed guide G G is placed in position outside the locus
with its inner profile parallel to the locus. A rod d f equal in length to the bar
DF has its ends pivoted on the crank pins d and f. The rod is bent or looped at
its centre in order to avoid coming in contact with the shaft O. The four rods
DF, df, D d, and Ff form a parallelogram and give reciprocal restraint to the
rollers at d and f. The motion of the shaft O¹ in either direction is perfectly
transmitted to the shaft O rotating it in the contrary direction with a constant
angular velocity ratio of five to one. Any other velocity ratio can be obtained
by varying the lengths of the two cranks, the longer one being a multiple of
the other.
115. Plate 16, Figs. 1 and 2 represent another variety of this movement, more
particularly adapted for speeding up. Fig. 1 a is side elevation with one of the crank
shafts cut through, and Fig. 2 is a front elevation of the movement when both
cranks are for an instant in the same plane, the fixed guides being cut through in the
plane of the cranks and represented in section. The same letters of reference apply
to the same parts in each figure. Two shafts 0 and 0¹ are in a line and each
terminates in a single crank O Band O'S. A claviger couple a c b 8 has one end b
centred upon the crank pin B, the other end a is bored out to accommodate the
rod or short shaft A¹ A which is partly passed through it and rigidly fixed into it
about the centre. This rod or short shaft forms the axle for two rollers r¹ and r
which are free to revolve upon it. The centre pivot of the claviger couple is the
crank pin S of the crank O' S. The fixed bearings of the shafts O and O' are
respectively marked m and n. The restraining arms of the claviger couple are 8 y¹
and sx and are pivoted respectively on the fixed studs y and x projecting from
the centres of the clavis rods b c and a c. The common pivot of the clavis rods is c.
In Fig. 2 it is hidden by the centre pivot. The claviger couple is of the third
kind. The shaft O¹ is the power shaft and its crank O' S is represented three
times the length of the crank O B, giving three revolutions of the crank O B for
every revolution of the crank O¹ S. The crank O B is represented in thefi gure a
as being rotated in the opposite direction to the crank O' S. The locus of the end
of the claviger couple is found. As the crank pin circle of the crank O¹ S is the
centre locus the relative lengths of the cranks would give an angular velocity ratio
of six to one with an outer locus composed of common hypocycloids. As the ratio
is taken as three to one according to the lengths of the cranks the locus of the
point a or A is four contracted hypocycloids. The contraction is sufficient to allow
of the outer profile of an inner guide g¹ g' and the inner profile of an outer guide
gg being made and fixed in position both parallel to the locus. The guides are in
parallel planes and are arranged so that each is opposite a roller as shewn in Fig 2.
This gives reciprocal restraint. When the crank O' S is rotated in either direction
the motion is perfectly transmitted to the crank O B which is rotated in a
contrary direction with a constant angular velocity ratio of three to one. The
crank O B may equally well be rotated in the same direction as the crank O' S

page_text: and in either direction with any other constant angular velocity ratio by varying
the length of the cranks and the shape of the guides to correspond as previously
explained.
.
116. Plate 16, Figs. 3 and 4 represent another form of this movement more
particularly suited for speeding down. One claviger couple is used as in the
movement described in the preceding article. It is also a claviger couple of the
third kind, but the centre pivot is now the crank pin of the smaller crank O B.
The claviger couple A b n c'has one end n centred on the crank pin N of the larger
crank O¹ N. The other end A is bent at a right angle for the stud A A¹ upon which
is placed the roller r. The lengths of the cranks are represented as eight to one.
This allows of an angular velocity ratio of four to one with an outer locus con-
sisting of five common hypocycloids. The guide gg is placed in position outside
the locus in the manner previously explained. A single crank u ulv, twice the
length (along u¹ v) of the crank Ob is pivoted upon the crank pin N outside the
claviger couple. Its pin u u' carries the roller 7 which is free to revolve upon it.
Other rollers are provided so as to make up a number equal to the number of
revolutions made by the smaller crank while the larger is revolving once. The
centre points of the axes of these rollers are an equal distance apart round the
circumference of a circle whose centre is in the centre line of the crank pin B or
in that line extended. In the movement illustrated the number of rollers are four.
Their axes or spindles are held in position by a rigid piece, represented in the
figure by the square 8 8 8 8. This gives a very strong reciprocal restraint to the
roller r.. None of the rollers can be moved from the guide while the rollers are
inside it, yet they roll round the guide with a smooth and even motion, the move-
ment of each roller being composed of two motions one motion round the crank
pin B and the other an oscillating motion round each of the rollers in turn as a
centre. The motion is perfectly transmitted with a constant angular velocity ratio.
It may be varied in direction and velocity as previously explained.
117. Plate 16, Figs. 5 and 6 illustrates another variety of this movement equally
applicable for speeding up or down. Fig. 5 represents an end elevation and Fig. 6
a longitudinal section through the centre of the shafts with the crank and bar
placed in the same plane. The fixed parts only are shaded. The two fixed bearings
of the crank shafts are marked m and n. The axes of the shafts O' and O are in
a straight line with each other. The shaft O terminates in a single crank O B.
The shaft O' carries at its end rigidly attached to it the bar CC. The two arms C
and C are equal in length. Another bar or rod AA equal in length to CC is
pivoted, with a deep bearing at its centre, on the crank pin B. The ends of the
bar CC and of the rod AA are thicker than the main part and are bored out
forming deep bearings for two crauked rods x y and u v. The lengths of the
cranksy and u¹¹ on the two rods are each equal to the length of the crank O B.
The straight part of each rod y¹y and vv is sufficiently long to form an axis for
a roller and 72. In all measurements the length is taken from centre to centre.
The length of each arm'C of the bar CC is shewn in the figure as four times the
length of the crank O B. The crank O B is to be rotated in the opposite direction
to the bar so as to make four revolutions during the time the bar is revolving once.
A centre locus is taken between the circumference of a circle whose diameter is
twice the diameter of the crank pin circle and the circumference of a circle whose
diameter is twice the length of the bar. This centre locus is a symmetrical figure
composed of five common hypocycloids. A fixed guide gg is placed in position
outside the locus with its interior edge parallel to the locus and distant therefrom
the radius of the roller. This arrangement of rods when represented geometrically
forms an irregular claviger couple with equal limbs, and is composed of two equal
parallelograms, the centre line being common to both. When the shaft O' is the
power shaft it is a claviger couple of the second kind with the fulcrum alternately
at either end. When the shaft O is the power shaft it is a claviger couple of the
third kind with the fulcrum alternately at either end. When the bar is rotated

page_text: the crank is rotated in the opposite direction with an angular velocity ratio of four
to one or any other angular velocity ratio inversely proportionate to the lengths of
half the bar and the crank. This is not a perfect movement because there is not
full and continuous.impulse. At two points during every revolution of the smaller
crauk for an instant the impulse is nil. Though this is the fact theoretically, it is
practically of little importance as the momentum of the moving parts carries them
past the neutral points. The perfect form of this variety of the movement will
now be described.
118. Plate 17. Figs. 1, 2, 3 and 4. Fig. 1 shews a front view of a fixed guide
inside a centre locus composed of four common epicycloids. This is adapted to
increase the number of revolutions in the ratio of 1 to 5. The locus is found in
the manner described in the preceding article. Fig. 4 is a longitudinal section
through the centre of the shafts. The fixed parts only are shaded. . The bar.
represented in Plate 16 Figs. 5 and 6 is here replaced by the disc CC, see Figs. 3
and 4, rigidly attached to the shaft O¹.. Fig. 2 represents a wheel W. W., Through
the rim and projecting from both sides perpendicularly are five studs at equal
distances apart s¹ to 8. Five rollers 1 to 5 are placed upon the studs on one
side. The centre of the wheel, forms a hub through which is, a bearing. hole
sufficiently large to accommodate the crank pin B and allow it to turn round inside.
On the face of the disc CC Fig. 3 there are also fixed five studs at equal distances
apart projecting perpendicularly from it. The distance of the centre of the fixed
studs in each case from the centre of the wheel and from the centre of the disc is
five times the length of the crank O B. On the studs projecting from the face of
the disc C C there are pivoted five links to with a bearing hole in the end of
each sufficiently large to allow the studs on the wheel W W to pass through and
turn round in them. The length of each of these links, from centre to centre, is the
same as the length of the crank O B. The studs, on the wheel on the opposite side.
to the rollers are then passed through the bearing holes in the links on the disc.
The disc and the wheel together are then approached to the crank and fixed guide..
The wheel W W is hung upon the crank by passing the crank pin B through the
bearing in the hub.; Whatever position the crank may be in the rollers all fall in
place and are in, contact with the guide. The relative, positions of the rollers in
contact with the guide are shewn in Fig. 1 by the circles r¹ to ³. The parts are
then fixed in position as shewn in Fig. 4. If the shaft O' be rotated the motion is
perfectly transmitted to the crank, O B, and it is rotated in the same direction with
a constant angular velocity ratio of five to one. The method of pivoting represented
in Plate 16, Fig.6 may be adopted and the crank rods can have a deep bearing in
the disc.. Double guides, one on each bearing n and m, may conveniently be used
where great strength is required. The ratio of revolutions should not be less than
1 to 3 with this movement otherwise it is not a perfect movement. The ratio may
be as large as desired. The larger the ratio the stronger the movement as all the
rollers are in contact however numerous they may be, but the rollers must, not
exceed in number the number of revolutions the crank makes to one revolution of
the disc. The friction is pivotal only and it is the same in, amount for the same
load per revolution of the crank however large may be the ratio between the
angular velocity of the two shafts.
I r
119. The guides have been fixed in all the movements described in articles 111
to 118. They may be made to revolve and some other part, of the movement may
be fixed without affecting the efficiency of the movement. The ratio of the angular
velocities and the direction of the rotation are however changed. Either of the
cranks, where two are employed, or the crank or the bar or disc may be dispensed.
with and the guide rigidly fixed to the shaft and carried round by it. The end of
the claviger couple which had previously been attached to the displaced crank or.
bar is now pivoted on a fixed, stud placed in any position along the line of its
former travel. The claviger couples in this position have an oscillating motion,
instead of a rotary one.., There are thus three methods of arranging the movements,
according to the position of the fixed parts. The manner in which the angular

page_text: velocity ratio and the direction of the transmitted rotation are affected is shewn in
.the.following table:-
Let n represent the number of convolutions in the guide,
120. One of the methods of varying the fixed parts in connection with the
variety of the movement represented in Plate 16 Figs. 5 and 6 and in Plate 17
Figs. 1, 2, 3 and 4 is shewn in Fig. 7. An interior epicycloidal guide gis
represented. It is rigidly attached to the shaft O¹. The cranked rods x yuv &c
which carry the rollers are cranked at both ends, and the end of each crank is
pivoted on fixed studs s² to 8³ &c. The cranked rods and rollers revolve round the
fixed studs. Another method of varying the position of the fixed parts in con-
nection with the movement shewn in Plate 17, Figs. 1, 2, 3, and 4 is as follows;
The rollers may each be placed on a separate fixed stud projecting from the frame-
work and the guide taken from the shaft O and hung upon the crank pin B, the
latter being made to fit the bearing hole through the guide. Studs are fixed into
the face of the guide equal in number to the rollers. The studs may be placed at
any convenient part of the guide at an equal distance from each other and from
the centre of the guide. The fixed studs on the disc C are placed in corresponding
positions on the disc and the bearing holes in the ends of the links are passed over
the studs on the face of the guide. Or the studs carrying the links as shewn in
Fig. 3 may be fixed to a framework in the vicinity of the bearing n n and the
loose guide hung upon the crank B. Fixed studs project from the back of the
guide corresponding to the fixed studs carrying the links. The studs on the back
of the guide are then passed through the bearing holes in the links. The disc C C
is dispensed with and in its place the wheel W carrying the rollers is rigidly
attached to the shaft O¹. The wheel and shaft are then brought up to the guide
and the rollers take up their positions in contact with it. The guide in this form
has an oscillating movement only and does not revolve, but it rotates the crank
upon which it is centred. The quality of the oscillating motion is such that during
the passage of a roller over four-fifths of each cycloid represented in Fig. 1 every
point in the guide describes a circle of the same diameter as the circle of the crank
pin B and each point at every instant is in the same relative angular position with
respect to the centre of the circle it describes as the crank and the links, which are
always parallel to each other, are in with respect to the centres of the circles
described by them.
In all the movements previously explained in which a cycloidal guide is
employed the diameter of the rollers is arbitrary, and the radius of the rollers
determines the distance of the profile of the fixed guide from the locus. The

page_text: movements have all the ease and smoothness of rolling contact with absolute
precision.
121. To Multiply or Reduce the Revolutions of a shaft in any ratio.―The
principle of the movements is the same as previously described. The shafts are
in the same line. The necessary directing restraint required by the movements is
obtained by rolling wheels or rollers along circular guides upon which they are
compressed with sufficient force to prevent slipping. Plate 17, Figs. 5 and 6 shew
the geometrical lines of the movements described in article 118. The small circles
represent rollers of the same diameter as the generating circles. The radius of
each is equal to the length of the crank represented by the line o b. The directing
circles are e f g. They represent fixed circular guides. The centres of the rollers
or the axles passing through their centres are connected together and held firmly
at an equal radial distance from the centre o by a wheel or any rigid system of
rods, which is firmly attached at its centre to the shaft O. A stud is fixed with
its centre on the edge of the periphery of each roller. The studs are passed
through corresponding holes in the rim of a wheel or in any rigid system of rods
so as to hold the studs at an equal distance from the crank pin b. The wheel or
system of rods has a bearing hole at its centre through which passed the crank
pin b. The rollers are moved round the directing guide by rotating the shaft O.
The crank o bis rotated once for every rotation of the rollers round their axes.
The angular velocity ratio is inversely as the lengths of m o to o b.
The directing
guide may be made to rotate or oscillate and some other part of the movement
may be fixed as previously described. Plate 18 represents in detail some varieties
of the movement described in this article.
122. Plate 18, Figs. 1 and 2 represent one variety of the movement described in
the preceding article. The fixed part is the rigid piece carrying the studs which
support the rollers. The rollers may be as numerous as desired provided they do
not touch each other. The more numerous they are the less pressure is required
to prevent them from slipping. Fig. 1 is an elevation of the movement looking
along the crank shaft. Fig. 2 is a section along the line a¹ O B c. The fixed parts
only are shaded. Two shafts O' and O are placed with their axes in a straight line.
The shaft terminates in the single crank OB. The shaft O₁ carries at its end
rigidly fixed to it the wheel or cylindrical disc C C, the periphery of which is
covered with leather. The six rods a a &c which connect together the studs on
the rollers form a double claviger couple with the two inner cross rods extended.
If they are pivoted together and the rods are free to turn upon the pivots the
two parallelograms will nevertheless remain squares and the pivots are rigid and
immoveable when in position on the rollers as the distance from joint to joint is
invariable during the movement; the joints may therefore preferably be riveted.
Or the studs on the rollers may be connected together by a ring forming the rim
of a wheel connected by radial supports to. a central hub which is hung upon and
supported by the crank pin B. The bearings of the shafts are respectively m m
and n n.
AA is a portion of the fixed supporting framework of wood or metal.
The part of each stud 8' to 8 which projects beyond the roller is rectangular in
section. A groove is cut in the fixed framework A. A in the proper position for
each stud. These grooves are open towards the outside and ends allowing the stud
carrying the roller to be readily placed in them. They are shaped to the studs so
as to allow no lateral movement but they allow an adjustment of the stud in a
radial direction. At the bottom the groove is widened out somewhat at each side
to accommodate a rubber pad vv &c. The rubber pads are smaller than the
recesses provided for them so that when the thickness of the pads is required to be
reduced by pressure there may be room to accommodate their increased length
and breadth. Outside each groove rigidly attached to the framework is a metal
bracket tt &c. Each bracket is tapped and threaded with two internal or concave
screws through which two solid screws ww pass and act upon a metal plate u u
which is the same shape as the outer rectangular surface of the stud and rests upon
it. The screws may be conveniently finished with square or polygonal flat bọļt

page_text: heads. By the aid of this arrangement the studs are held firmly in position and
the rollers are one by one easily compressed upon the leather covered wheel C C
with sufficient force to prevent slipping under any load, as one roller cannot slip
without all the others slipping too. When the rollers are compressed with sufficient
force the wheel or other arrangement of rods a a &c is then fitted on the crank
pin B and on the studs y y₁ &c so that the latter may easily revolve in the
bearings; either shaft may be the power shaft. If the shaft O¹ be taken as the
power shaft and rotated in either direction, the motion is perfectly transmitted to
the shaft O and it is rotated in the opposite direction. The angular velocity ratio
of the shafts is inversely as the radius of the disc C C is to the radius of the roller.
The studs y¹ toy which project from the ends of the rollers may be in any position
between the perimeter of the roller and the stud upon which it revolves without
affecting the ratio of the velocities. The crank O B must however in all cases be
equal in length to the distance between the centres of the stud s and the stud y.
123. Plate 18 Figs. 3 and represent the movement described in article 121 with
the circular directing guides fixed., Both figures represent longitudinal sectious
through the centres of the shafts when all the parts of the movement are in one
plane. The fixed parts only are shaded. Fig. 3 represents the movement with an
interior fixed guide and Fig. 4 with an exterior one. Both movements have
a device for compressing the rollers on the fixed guide to prevent slip and cach
moveinent has an additional loose wheel which bears. the strain due to the com-
pression of the rollers and prevents it falling upon the bearings. The two shafts O'
and O, see Fig. 3, have their axes in a straight line. The sliaft O' carries at the
end rigidly attached to it the wheel ua i u. It has deep bearings uu in the rim
at equal distances apart, one for each roller. It is connected by radial arms to a
central hub ii which is keyed upon the shaft 01. Another wheel, exactly similar
is centred at the hub upon the crank pin B of the crank O B. The rollers have
each a cylindrical recess in one end. The projection of the interior circular
surface of the recess is concentric with the projection of the periphery of the roller.
A stud s. of sufficient length is firmly fixed into the recess of each roller. The
stud is of smaller diameter than the recess and it is fixed with its centre line
coinciding with the axis of the roller. There is thus left in the end of each roller
a symmetrical annular recess. The bearings of the shafts are m m and n n.. The
periphery of the cylindrical part of the fixed guide A. A is covered with a leather
ring. It is made by stamping out of the hides, rings or portions of rings of the
width of the intended thickness of the covering. The interior or concave diameter
of the rings is rather less than the diameter of the circular guide. Sufficient rings,
are stamped out so that when they are placed side by side with their edges
outwards and inwards they will build up a ring of leather rather wider, than the
length of the rollers. The ring of leather so built up is made pliable and placed
upon a slightly coned drum. The smaller diameter of the druin is arranged to
ällow the ring to be readily placed upon it. The larger diameter is at the opposite
-end of the drum and it is equal in diameter to the diameter of the cylindrical
guide A A. The drum is then brought up to the guide and the built up leather
ring is forced along it on to the guide. When it is in position on the guide as
shewn in section at e e its exterior surface is rolled down with considerable pressure.
The effect of these two processes is to make the built up leather. ring thinner and
wider. The rollers rr, às numerous as desired, are then placed on the leather ring
and temporarily held firmly in place at equal distances apart. A loose annular
wheel w w is then fitted to pass over the rollers. An annular disc cc is held to the
face of the fixed guide by the bolts and nuts zz which pass through the disc and
the fixed guide. The outer edge of the disc is bent to accommodate and hold the
leather ring. When the bolts are tightened up by turning the nuts the leather
ring is compressed in the width and increased in thickness so as to assume very
nearly its original dimensions. By this means the rollers, can, be compressed
between the fixed guide and the loose annular wheel with sufficient force to
prevent slip under any load. At equal distances round the projecting edge c¹ of the
J

page_text: The
annular disc cc holes have been previously punched opposite the centre of the
thickness of the ring, and corresponding holes-are now bored through the leather
ring and into the fixed backing. Nails made of round wire, clinched up at one end
for a head are passed through the holes. By this means the leather ring is held
firmly in place. The hub of the wheel a a is then placed upon the shaft O' and
the bearing holes uu in its rim are passed over the studs & on the rollers.
wheel is then keyed or otherwise rigidly fixed to the shaft O¹. A crank hy equal
in length to the crank O,B is keyed shrunk or otherwise rigidly fixed to the end of
each of the studs s which project from the rollers. The roller stud and crank then
revolve together as one solid piece. The crank pins y are placed through the
corresponding bearing holes in the rim of the wheel x b b x. The crank shaft O is
then brought forward and the pin B of its crank O B is passed through the bearing
in the hub ff. Either shaft may be the power shaft. If the shaft O¹ be the power
shaft and it is rotated in either direction the shaft O B is rotated in the same.
direction with a constant angular velocity ratio. The number of revolutions made
by the shaft O while the shaft O' is revolving once is equal to
Diameter of fixed guide
Diameter of roller
+1.
Fig. 4 represents the same movement with an exterior annular fixed guide.
The same letters of reference refer to the corresponding parts in each figure. In
Fig. 4 the wheel aa has a stud al projecting at right angles from the rim for
'every roller.
These form the supports upon which the rollers revolve. The
wheel w w is a loose wheel riding upon an extension of the shaft O¹. The loose
wheel is surrounded by the leather ring and it also carries two annular discs onė
on each side with the bolts and nuts for compressing the leather ring as previously
described. The single cranked rods hy are rigidly attached to the ends of the
rollers. The two shafts rotate in opposite directions. The number of revolutions
made by the shaft O while the shaft O' is revolving once is equal to
The interior diameter of the fixed guide 1. .
.."
Diameter of roller
In both movements the loose wheel is carried round in the same direction as the
shaft O¹.
124. Fractional Variation of the number of Revolutions by means of hypo-
cycloidal and epicycloidal curves. The method to be explained in this article has
for its object the transferrence of rotary motion from one shaft to another, the
velocity being varied in transmission so that the angular. velocity ratio of: the
two shafts shall be as 1 to 1 and any, fraction, or as 1 to any fraction greater than
a half, without employing the method of frictional rolling explained in articles 121,
122 and 123. Reference is made to Plate 17, Fig. 7. Let the circumference CC
represent the interior of a rim on a disc of which the point x is the fixed centre.
B is a circular disc represented in the figure of a radius th the radius C C. Let
the point o on the disc B bet aken as a generating point. If the disc B be rolled
along the interior surface of the rim, say in the direction indicated by the large
arrow, until it has made one revolution round the centre x and returned again to
its original position, the point o will have generated six common hypocycloids.
Let it be supposed that the point o carried a pencil during the movement and
described these curves on the inner face of the disc. Let D represent a rod pivoted
at one end on the fixed centre at x and with the other end bent to a right angle
and passed through the centre of the disc B. A circle uy is described on the
disc from the centre x with the radius z b. Any point y is taken in a plane
parallel to the disc on the projection of the circumference uy, this point represents
a fixed stud, supported from the direction opposite to the disc. A fixed stud is
พ
placed in the same position on the disc B. A rod E of the same length as the
rod D is pivoted at its two ends, on the studs wand y. It is assumed that the
disc B presses upon the rim with sufficient force to prevent slipping. The rod D

page_text: is revolved round its centre x say in the sense of the arrow with an uniforių
velocity, carrying round with it the disc B. The two rods D and E with the two
lines zw and x y form a parallelogram of which the side x y is immoveable. The
radius zw of the disc B must therefore remain parallel to the line x y during the
movement. The point w describes a circle round the point y and every point in
the circle wb describes a circle round the corresponding point in the circle u y.
The disc B presses upon the rim and carries round with it the disc C C. At the
end of one revolution of the rod D the disc B is again in its original position as
shewn in the figure and the disc C has been moved round in the same direction as
the rod D'one revolution minus a length of its circumference equal to the circum-
ference of the disc B. And as the radius zx plus the radius z b is equal to the
radius C x, any given point on the circumference CC has been moved round a
distance equal to the circumference described by the point 2, (the centre of the
disc B) that is, the angular velocities of the rod D and of the disc C are inversely
as the radii. During the movement the pencil at o has exactly traced over 5 out
of the 6 curves which were described by it when the disc B was rolled round the
rim of the then fixed disc C C. The disc B has not actually rotated, but with respect
to its pivot z and the centre x it has apparently rotated once backward in the sense
of the small arrow. Its effect upon the rotation of the disc C is precisely the same as
if it had actually rotated backward once on its axis. The same results follow if the
rod E be rotated instead of the rod D. Fig. 8 represents the disc B on the exterior
surface of the disc C. If the disc B be released from the rods and rolled round the
disc CC (which is four times the radius of the disc B) the generating point o will
generate four common epicycloids. Let the disc B be connected with the rods D
and E as described in connection with Fig. 7. It is carried round by revolving
either of the rods D or E on the axis x or y as just explained. When it has made
one revolution and again regained its original position it has rotated the disc C C
one rotation plus a length of circumference equal to the circumference of B that is
the angular velocities of the rod D and of the disc C C are inversely as the radii.
During the movement the point o will have passed over the four curves and in
addition will have passed over the first curve a second time. The application of
this principle is as follows. Plate 17. Fig. 9 represents a longitudinal section of
the movement. An internal wheel w with curved teeth outside and parallel to the
hypocycloids described by the point o in Fig. 7 is rigidly fixed to the end of a
shaft O. The position of the axis of the shaft O corresponds to the point x in
Fig. 7. A front view of the wheel is similar to the fixed guide G G plate 15
Fig. 2; the periphery however should preferably be cylindrical. Another shaft 01
is fixed in the same plane as the shaft O but not in a line with it. The position of
its axis corresponds to the point y in Fig. 7. The shaft O¹ has the disc d d
rigidly fixed to the end facing the wheel. Five pins or studs p p are firmly fixed
into the disc at equal distances apart. The number of pins is always wy see Fig. 7.
The distance of the centre line of each pin from the centre of O¹ is equal to the
line wy. Each pin is supplied with a roller rr free to turn upon it. The radius
of the rollers is equal to the distance of the profile of the curved teeth from the
hypocycloidal curves. When the shaft O¹ with the disc is brought up to the
wheel w the rollers fall into the curves and are all in contact with them. If either
shaft be rotated the other shaft will be rotated in the same direction. The motion
of the shaft O has a constant angular velocity ratio to that of the shaft O¹ as 5
to 6. While the shaft O¹ is making one revolution the shaft O makes a fraction
of a revolution which may be expressed as follows for any dimensions
x y

page_text: the rollers on the disc attached to the other shaft O¹ are represented in the same
figure by the circles to 75. The angular velocity ratio of the shaft O to the
shaft O is as 5 to 4 and may for any dimensions be expressed as follows,
No of teeth + 1
No of teeth
The motion is smooth and even. There is no slip, wedging or backlash. Half
the number of teeth drive or are driven at every instant throughout the movement.
Both movements are the counterparts of the geometrical diagrams Figs. 7 and 8
just explained. In all cases, whatever the number of teeth, the radius of the
generating circle must be equal to the difference between the radius of the directing
circle and the arm D or E, and the eccentricity of the axes of the two shafts when
projected on the same plane must be equal to the radius of the generating circle.
The movement represented in Fig. 9 is to be preferred to the other. By means of
either of these movements the angular velocity ratio may be varied in the following
manner 2 to 3, 3 to 4, 4 to 5, 5 to 6, 6 to 7 and so on in the same sequence.
Other ratios are best obtained by making two changes. Say 3 to 5 is required.
The changes are 3 to 6 and 6 to 5. Or say 5 to 7 is required. The changes are
5 to 6 and 6 to 7.
Any ratio may be obtained in one movement as follows. Suppose the ratio
required is as 3 to 5, the centre locus is taken as described for Fig. 1, between the
two motions during a complete cycle. The centre locus in this case is the series of
curves which would be obtained by rolling the generating circle twice round the
directing circle. These curves intersect each other. This increases the number of
teeth and part of the profile of the curves is consequently cut away, but this is
compensated for by twice the number of rollers being allowed upon the disc d d.
125. In all the articles referring to the multiplication of revolutions the velocity
has been increased or reduced with a constant ratio. It may however be varied in
any manner either in velocity or direction according as the profile of the bearing
edge of the fixed guide is shaped. Plate 19. Fig. 4 represents a movement of this
class. It is the roller motion in wool combing machines. The claviger couple,
cranks, and shafts are similar to those in the movement illustrated in Plate 16,
Figs. 1 and 2 and described in article 115. There is only one roller however as
the interior and exterior parts of the fixed guide are in the same plane. The
longer crank O' S attached to the power shaft is extended to t, the length O' S
being equal to the length St. The end t carries a pin parallel to the pin S.
A short rod At equal in length to the crank O B is pivoted at one end on, the pin t
and at the other on the pin A A¹ which passes through the roller and the end of
the claviger couple. The smaller crank O B is connected with the roller by the
short shaft O. The back of the guide is removed. When in place it is supported.
on the fixed bearing m and it holds the shaped parts of the guide. Another plate
in front supported on the bearing of the shaft O' closes in the movement from
dust &c. During the movement the roller bears alternately against the outer and
inner bearing pieces of the guide. When the force is being transmitted by direct
thrust and leverage combined the roller runs along the outside pieces of the guide.
When the force is being transmitted by direct pull and leverage combined the
roller runs along the inner pieces. At the positions where the change of stress
occurs the opposite profiles of the guide are only one diameter of the roller apart.
Part of the bearing surface of the guide is represented as broken away to shew the
parts more clearly. While the shaft O₁ is making one revolution the roller
connected to the crank O B makes one third of a revolution backward, then two-
thirds of a revolution forward, then stops during one third of a revolution. This
series is repeated at every revolution of the shaft O. Both cranks make an equal
number of revolutions per minute.
126. Propelling and Restraining "Cycles."-Generally in designing machinery
considerable latitude can be taken with respect to the positions of the power
shaft, the transmitters and the operators, and they are arranged in the most

page_text: convenient positions for the work. In pedomotive road carriages however the correct
relative positions, of receivers, transmitters and operators in the different classes of
machines are strictly defined by the size and, position of the driving wheels, the
requirements of equilibrium and safety of the driver and the need that his position
should be the best for economically applying his power. The claviger movements
represented in Plates 7, 21 and 22 combine the methods of conversion, and trans-
mission of motion already separately described so as to meet these requirements
both by means of clavigers alone and in combination with levers., In every
movement represented the force, is received by a pedal, shewn in end view and
marked, P. They are carried at, the traverse end of the clavis rod or of the lever
by means of a pin which is clamped at one end to the rod. The pedal is attached
to a tube which turns upon the pedal pin and it thus accommodates itself to the foot.
Or the pedal can be placed above the end of the rod supported on rockers. The
line of movement of the feet is either vertically downward in a straight line or it
is along a curve not differing much from such a line. Great force can be applied
by the rider as the motion coincides with the natural movement of the strongest
chain of muscles in the human body. The length of movement of the foot for
stroke and recovery is only about of the movement for operating a pedal
revolving with the crank, with the length of stroke the same in both cases, so that
a considerable amount of fatiguing exertion is avoided. The pedals may be
operated and the machine driven by the weight of the rider, or by muscular
energy using the weight; as resistance, without any necessity for a seat or saddle.
The object of a seat is twofold; (a) to support the rider in equilibrium which
otherwise, could not be maintained by the feet on revolving pedals and (b) to
enable him to vary the propelling force according to varying resistances and the
pace desired.. Otherwise the seat is an impediment. With the claviger move-
ments no seat is required. As one pedal commences to descend before the descent
of the other is completed and as they are arranged to move in a vertical direction,
the operator has always a steady support for one foot and the weight can be
employed with full advantage. There is also relatively a wide margin in time
allowed for change of weight from one foot, to the other so that if changed too
quickly or too late for making an exact half or full revolution with each foot no
ill effects follow. The force applied can be varied with great nicety by pressing
on the ascending pedal with the foot thus allowing it to lift part of the weight.
The balance between the total downward pressures of the feet on the ascending and
descending pedals respectively is the force employed and the fatigue corresponds.
When muscular energy is used directly to propel the machine, the body is
sustained by the muscles at the same distance from the surface travelled over, and
its weight used as resistance. When the weight, is directly employed, the body is
rapidly lifted from the lower pedal to the higher by muscular exertion, the leg
straightened and the weight supported by the bones. The weight of the body
then more slowly descending acts upon the pedals and drives the machine. This
way of utilizing the weight is especially suitable for luggage and parcel carrying
machines. A considerable amount of luggage, besides the weight of rider and
machine can in this way be moved along a good surface at a faster rate than
walking, pace with scarcely more expenditure of muscular energy than in walking.
In walking force is expended in lifting the body against gravity at each step and
most of this is wasted by the concussion of the descending foot with the ground.
In skating the sudden descent and shock of walking is avoided, and a great part of
the force which is wasted in walking is employed in producing speed by utilizing
the gradual descent of the centre of gravity of the body. By the methods of
propulsion described herein the whole of the muscular energy is usefully employed.
As the impulse is applied continuously with uniform intensity to the axle cranks
in a direction tangential to the crank pin circle there is no need for speed and
power appliances. The length of traverse, and of the wheel movement must be
apportioned so that the full weight of the rider shall be at least sufficient to move
the machine when the resistances to be overcome are at the maximum. The only

page_text: effect then of varying resistances, with the same force applied, is varying speed.
The proportion between the length of traverse and the resulting length of move-
ment of the periphery of the driving wheel can be varied at will by affixing two
or more pedals to the clavis rod; or the proportion can be arranged to suit the
average of varying resistances by giving rather greater length to the clavis rods or
levers and slotting them for a short distance so that the correct position for the
pedal is the centre of the slot. The pedal can then be adjusted and clamped
nearer to or further from the crank to suit different requirements.
T
A very important part of a velocipede is the apparatus for restraining it while
descending hills or when a stoppage more or less sudden is required. Most of the
brakes for that purpose employed are liable to overturn the machine, or they
cannot be applied with sufficient force or their application is uncertain difficult or
inconvenient.
When the claviger is used for propelling either alone or in combination with
levers no brake or any other arrangement for restraining is required. All that
is needed is a sufficient downward pressure of the foot on the ascending pedal.
The virtual velocity of the ascending pedal for a considerable part of its movement
gives an efficiency of about three times the weight so applied. Thus in an
emergency, by bearing his full weight on the ascending pedal, the rider can, with
safety and with perfect efficacy, exert a restraining pressure three times greater
than the strongest pressure he can exert for propelling the machine. The move-
ment and consequently the friction in the joints of the claviger is much less than
would appear at first sight. The restraining arm makes about one-seventh of a
revolution on its fixed axis for each half revolution of the crank and the pivot in
the clavis rod makes only one-thirtysixth of a revolution and back in the same
time. The claviger clutch can be used with niost of these arrangements. The
pedals are then moved upwards as well as downwards in a straight line. The two
pedals are connected transversely by a claviger couple, so that the descending
pedal carries up the other into position. The rider can by its use vary the length
of his stroke, the rapidity of its delivery and the amount of force applied as he
pleases. Without a seat he can support himself on the pedals without using more
weight than he desires, sometimes standing still on them while the machine is
running down inclines, or employing small force by giving.an oscillating motion to
them or full force of weight and length of stroke for great speed or to overcome
great resistances. The time of making the strokes need have no connection with
the number of revolutions of the driving wheels, the frequency as well as the
length of stroke being at the will of the operator. When the normal form of
hanger claviger, which ordinarily gives a half revolution per stroke, is used in con-
nection with the clutch the full stroke gives a forward movement with a 44 inch
driving wheel equal to a gearing up of 60 inches. The slider claviger with quick
return is a convenient means for propelling a parcel carrying "Cycle." Only one
claviger is employed, with one pedal at the traverse end. Its other end is pivoted
directly to the end of a claviger couple the centre pivot of which is a fixed axis or
stud held by the framework, the other end of the claviger couple being centred ou
the crank of the axle of the driving wheels. The parcels are carried in a suitable
receptacle supported by the framework, mainly over the two driving wheels.
There is a rear trailing wheel behind the driver attached to the framework by
means of a strong pivoted head. The driver has a fixed stand supported by the
rigid framework between the driving wheels and the head over the trailing wheel.
This stand is to the left of the pedal and the pedal is operated by, the driver with
the right foot by directly using his weight. At the back of the receptacle a long
traverse handle is fixed within convenient reach of the driver. This is to steady
him and enable him to steer by moving the forward part of the machine in the
direction required by main force as is the case with a hand cart. This can readily
be effected though the driver himself is supported by the framework to be moved.
Great leverage is given by the handle and the driver's weight falls mainly upon
the pivoted hind wheel which gives the purchase.

page_text: -
The differential motion of the two driving wheels essential in turning is pro-
vided for in those movements where the clutch is not used, by a simple epicyclic
train. In all the different arrangements described herein for cycles with two
driving wheels requiring a claviger or a lever for each foot, only one crank is
required upon the axle of the driving wheels. A solid axle is cranked at any
convenient, point, preferably the centre. Each of the driving wheels is firmly
attached at the hub to a length of tubular axle. One of these lengths carries at
its inner end rigidly fixed to it an internally toothed wheel, the other length at the
inner end rigidly fixed to it an externally toothed wheel. The crank pin of the
crank on the solid axle is hollow. A spindle passes through the crank pin carrying
at each end a small pinion wheel, each of a different diameter, firmly bolted to the
spindle. The solid axle is passed through the tubes and the hubs of the wheels
and properly secured on the outsides. The two wheels at the interior ends of the
two lengths of tubular axle are in this manner brought into gear with the two
pinions. The teeth on the pinions and wheels are arranged so as to give equal
value to the same divergence either to right or left. The gear can be neatly boxed
in to keep out the dust. When the velocipede is being driven straight forward
the axles and gear move as one solid piece otherwise the power is apportioned by
the balance-gear to each wheel as the change of direction requires and the tubular
axles revolve upon the solid one in opposite directions. The machine can be
driven backward with equal facility. No exclusive right is intended to be claimed
in these movements besides the claviger movements themselves and the movements
combining the claviger and lever. The other movements and arrangements are
described as necessary auxiliaries for the effective application of the movements
claimed. The "cycle" movements included in the same sheet are all drawn to the
same scale. The diameter of the largest dotted circle in Plate 21 Fig. 5 represents
a length equal to 10 inches. The diameter of the driving wheels given in the
descriptions of the movements is approximate only and may be varied an inch or
two either way without altering the proportions of the movements.
Plate 21, Fig. 4 shews a movement for propelling a tricycle with the driving
wheels in front of the rider. A x B s is a hanger claviger of normal dimensions
attached to the wheel axle. A lever of the second kind P s turning upon the fixed
fulcrum S is situated below the axle. The end A of the claviger is connected to
the lever by the link A y which is pivoted at each end on the two fixed pins A
and y. The arrangement is duplicated for the other foot. The parts are pro-
portioned for 50 inch driving wheels giving a half revolution for each stroke.
Length of traverse for a half revolution 11 inches. Lever 12 inches long.
Connecting link 134 inches. For propelling a similar machine with the driving
wheels behind the rider the lever is fixed in the reverse direction.
'
Plate 21, Fig. 1. Apparatus for propelling a tricycle having two 50 inch wheels
behind the rider. The pedal P is attached to the end of the rod P c which is the
clavis rod cy extended in length. The dimensions of the hanger claviger of which
it forms a part are S₁ c radius inch, S¹¹ restraining arm 1 inch, c y clavis
rod 3 inches. Total length of the rod P c 12 inches. Traverse for half a
revolution 10 inches. A hanger claviger Ax B 8 of the same dimensions is con-
nected with a crank O B on the wheel axle. The ends of the two clavis rods are
connected by the link A y which is pivoted at each end on the fixed pins A and y.
The parts are connected together so as to assume the relative positions shewn in
the figure which represents the commencement of the operative part of the stroke
for the left foot. The same parts are repeated for the right foot but the upper 5
claviger is attached to the same crank. The fixed axis of the upper claviger for
the right foot is situated as much above the axle o in a vertical line as the fixed
axis S of the other claviger is below. Also while the left upper claviger commences
its movement from a horizontal position the right hand one terminates its move-
ment in that position; the connecting link for the right foot is therefore 3 inches 5
longer than A y. The fixed axes S¹ and S" are supported by the framework at
both ends and they are common to both pedal rods. The two links are nearly

page_text: close together on the insides of the two pedal rods while the pedals are fixed so as
to project outwards from the rods. The two sets can be attached to two cranks on
the axle set 180° apart but one crank is preferable. The strain on the links is
tensile only and they retain a vertical position throughout the movement.
Plate 21, Fig. 2 represents the same apparatus differently arranged for propelling
a tricycle with two 50 inch driving wheels in front of the rider. The lower
claviger y c 81 is larger than the upper one; the effect of this is to prevent the
radius rod s¹c revolving, it oscillates only and the pin y moves up and down in a
vertical straight line. The point P describes a forward curve (a contracted cycloid)
both up and down.
Plate 21, Fig. 3. Apparatus to enable a rider to propel a bicycle with the driving
wheel of larger diameter than is possible with axle crank pedals. Traverse for
half a revolution 11 inches. Crank O B 1 inch. A hanger claviger A x B 8 of
normal dimensions with its fixed axis S above the axle is attached to the
crank O B. A claviger couple of the second kind P A S¹ C has for its centre
pivot a pin fixed at A on the clavis rod B A. The pedal P is fixed to the free end
of the claviger couple. When pressure is éxerted on the pedal it is moved down
It
along the vertical straight line P m and can move in no other direction.
describes a straight line twice the length of A z. The forward curve described by
the end A in its return movement is exactly reproduced by the point P but twice
the size. The traverse line P m can be placed nearer the ground by 5 inches
with the same crank and clavigers by starting the crank from the opposite side,
the claviger being then horizontal and the two fixed axes S and S¹ 5 inches lower
down. The vertical traverse line P m may be varied in position as desired both
laterally and vertically by varying the position of the fixed axis S¹ and making
the dimensions of the claviger couple to correspond. The stress of the pressure
and of the riders weight falls within the wheel base and a very powerful and
effective restraint can be safely exerted by pressing the feet upon the ascending
pedals.
Plate 21. Figs. 5 and 6 illustrate a method of safely propelling a bicycle without
any risk of a header for those riders who might possibly prefer the rotary motion
of the foot. The pedal is connected with the crank by a claviger couple of unequal
limbs. That represented in Fig. 5 is a claviger couple of the first kind and that in
Fig. 6 of the second kind. There is only one fixed point viz. the fixed axis S.
The pedal P is attached to the free end of the claviger couple, the centre of its
spindle describes a circle and cannot be moved in any other direction. The
arrangement must be duplicated on the other side of the wheel. The position of
the circle described by the pedal may be located in any direction round the axle
by varying the position of the fixed axis S and it may be any distance away from
the axle by increasing the size of the claviger couple. The size of the circle
described by the pedal may be varied as desired by making the position of the
fixed axis S adjustable along the line joining the centres of the two circles. It
may be rigidly attached to a rectangular bush supported in a slot in the fixed
framework and clamped in position. A very slight movement of the fixed axis S
makes a considerable difference in the movement of the pedal. Fig. 7, represents
the complete movement with the circle described by the pedals some distance below
the axle. Fig. 8 represents a similar movement but the inner ends of the claviger
couples are each attached to a hanger claviger instead of being directly attached to
the axle crank, the hanger clavigers being interposed between the cranks and the
claviger couples. The traverse in this case is along the vertical straight line P P¹
and the return along a forward curve.
Plate 22. The movements on this sheet are drawn to a larger scale than those
on Plate 21. The line A C in Fig. 6 represents a length of 10 inches. Fig. 6
represents a movement for propelling a tricycle with 50 inch driving wheels situated
OG is a crank
5 behind the driver. O represents the section of the wheel axle.
upon it. O' is a short subsidiary shaft parallel to the axle with the crank O' E
at its centre. It also has the single cranks O' B and O¹ D at the ends. To these

page_text: single cranks are attached the two clavigers A y B S, and C x D Shaving their.
common fixed axis on the short transverse rod S. The pedals are attached to the
free ends, A and C of the clavigers. The two cranks O G and O¹E are equal in
length and are connected by the claviger couple E F G S¹. The fixed parts are m
and n the bearings of the shafts, and the fixed axes Sand S¹ and they are in a
straight line vertically under the axle. The axle may however be in any position.
relatively to the subsidiary shaft O!. The traverse is.along the straight line A C
and the return describes a forward curve. The balance gear may be at the centre
of the subsidiary shaft O¹. In that case both clavigers are connected to the central
crank which is then equal in length to the line O B and the single cranks at the
ends are equal to the line-O.E. Both of these single cranks are then connected
by claviger couples with single cranks of the same size at the inner ends of two
short lengths of axle rigidly fixed to the hubs of the wheels and supported by
bearings in the fixed framework between the cranks and the hubs. The machine
is thus left open between the wheels. The driving wheels may be speeded up or
down so as to move more or less than a half revolution forward for each stroke of
the foot by inserting in the subsidiary shaft between the end cranks and the
central one two sets of the movement. represented in Plate 17, Fig. 9 and
described in article 124. Or this movement may be supported in bearings midway
between the shaft 01 and the axle O, Fig. 6, Plate 22. The two short shafts O
and. O, Fig. 9 Plate 17, have then a single crank at each end equal in length to
the cranks OE and O G, Fig. 6 Plate-22. Let these cranks be called respectively
x and and it is required to speed the driving wheels up. The crank O' E is
connected to the crank by a claviger couple and the crank y is connected by
another claviger couple with the crank O G. The remaining movements to be
described give one revolution of the driving wheel or wheels for each stroke of the
foot, thus allowing small. driving' wheels of 25 to 35 inches in diameter to be
employed. Great saving in material and weight is thus effected. The excessive
vibration usually experienced in the use of small wheels is avoided by employing
my invention for. "Improvements in India. Rubber Tyres and Metal Felloes
for Velocipedes" secured by Letters Patent N° 608 January 4th 1884. When
the different forms of claviger for obtaining one revolution for each stroke are
operated by alternate rectilinear pressure instead of by reciprocal there is a
possibility under certain circumstances of the ascending pedal returning after it
has reached the centre of the traverse line instead of continuing past the centre for
the whole traverse. See Fig. 4 Plate 23, when the ascending pedal has moved
from m to S it is at S theoretically in equilibrium between movement towards P
or back again towards m, without affecting in any way the motion of the crank O B
If sufficient force be applied by the foot exactly at S it will return. If no pressure
of the foot be applied at this point the forces which determine its course are (a) the
weight of the parts which dispose it to return, (b) the momentum gained during
the first half of the upward movement which dispose it to continue its course.
Except the pace be exceptionally slow the latter is the governing force, as should
the centre of the pedal be carried a hairs-breadth past the centre of the traverse
line it must continue its course. A perfect remedy for this possible defect is
obtained by connecting the two pedals by a claviger couple placed transversely
across the machine. Or if this method be not practicable in all cases and any
difficulty should be experienced on this account it is easily overcome by fixing the
sides of the pedals with a spring clip which should be sufficiently strong to allow
the pedal to be carried up past the centre by the foot at any pace and yet have no
hold on the rider sufficient to embarrass him when dismounting.
Plate 23, Fig. 4 illustrates a movement for propelling a bicycle or tricycle with
the driving wheel or wheels either before or behind the rider, one revolution at a
stroke. The traverse line A m represents a length of 10 inches. The proportions
of the parts as represented are crank O B 1 inch, and clavis rod A. B slightly over
7. inches. The line A S must be equal to the line Sn. The fixed axis S is opposite
the centre of the traverse line. The particulars of the curve described by the

page_text: point A and the manner in which it can be varied are explained in connection with
the description of Figs. 2 and 3 on this sheet. The direction of the traverse line
allows the main part of the force to be applied directly from the bip joint while the
curve at the top and bottom admits of the application of as much additional
muscular action of the feet and ankles known as ankle action, as can be usefully
employed, and the curve can be flattened or rounded to suit different requirements.
Plate 7, Figs. 5 and 6 are adaptations of the movement previously described in
article 35 and illustrated in Fig. 1 on the same sheet. The scale is the same as that
on Plate 22. The pedal is attached to the end of a lever S¹ P turning upon the
fixed fulcrum S¹. The part of the lever S¹ y corresponds in length and direction to
the line NA in Fig. 1. It is placed lower down than the corresponding position in
Fig. 1 and the two points a and y are connected by the link ay which is pivoted
upon two fixed pins at a and y. The link ay retains a vertical position throughout
the movement. This movement is for propelling a bicycle or tricycle with the
driving wheel before the rider one revolution at a stroke. The two figures shew
how the position of the pedal can be varied, without altering the length of the
traverse line, by varying the dimensions of the claviger.
Fig. 7 represents a similar movement for propelling a bicycle, the driving wheel
of which is behind the rider. It is an adaptation of the movement described in
article 35 and represented in Fig. 2 of this sheet.
Plate 22 Figs. 1, 2, 3, 4 and 5 are adaptations of the movement described in
article 39 and illustrated in Plate S, Fig. 1. The same letters of reference
represent the same parts in all.
Fig. 1 is a movement for propelling a tricycle with the driving wheels in front
of the rider, one revolution for each stroke of the foot. It shows the complete
arrangement for both feet. The two claviger couples de yg and de¹ y¹ gare
quite distinct and are attached to the same crank O d. The fixed stud 0¹ is
supported laterally from the centre and it is connected downwards with the
fixed studs y and S. The stud O' carries at both ends pivoted upon it the two
cranks O¹g and O'g', the pins g and g of which form the centre pivots of the
two claviger couples. Or O may be a short shaft with a single crank at each end
supported in a fixed bearing. The two rods ye and y el form the radius rods for
two hanger clavigers of normal dimensions Pe S and P¹ e¹ S with their common
fixed axis at S. The pedals move up and down in a vertical straight line. This
movement is very suitable for operating the machine without a seat by standing on
the pedals. Diameter of driving wheels 30 to 35 inches, traverse 6 inches, clavis
rod 12 inches.
Fig. 2 represents the movement for propelling a bicycle with the driving wheel
before the rider, giving one revolution for each stroke. The pedal is attached to
the end of a lever S P, the fixed fulcrum S of which is vertically under the fixed
axis y of the claviger couple. The length S z of the lever is equal and parallel to
the clavis rod y fe. The common pivot at c is lengthened and there is a fixed pin
at z; the two are connected by the link ez which is pivoted at each end on the
pins. The three rods y e, 8 and ez with the fixed line y S form a parallelogram
and the rod e z remains in a vertical position throughout the movement. Slightly
varied it is a movement for propelling a tricycle with the driving wheels before the
rider. For the same length of traverse the claviger couple and the crank O d are
smaller, the lever is longer and is placed lower down so as to clear the axle.
Figs. 3 and 4 represent the movement for propelling a bicycle with the driving
wheel before the rider, one revolution at each stroke. In Fig. 3 the clavis rod ye
of the claviger couple is lengthened to P forming a lever of the second kind. In
Fig. 4 the clavis rod e y is lengthened to P forming a lever of the first kind.
Fig. 5 represents the movement for propelling a bicycle with the driving wheel
behind the rider. The spindle passing through the pedal furnishes the common
pivot for the claviger couple. An immense variety of combinations of claviger
inovements may be arranged for driving " Cycles," those here given are some of the
simplest and most distinctive.

page_text: Plate 23, Fig. 6 illustrates the adaptation for velocipedes of the clutch movement
previously described in article 99 and shewn in Plate 13 Fig. 4. As there repre-
sented it will only drive in one direction. A clutch for a velocipede should not
only allow the wheel to outrun it, and thus move faster than the corresponding
movements of the pedals, for turning &c, but it should be efficient. for driving the
machine backwards and for restraining it when back pressure is applied to the
pedals. The driving wheels are not connected by a through axle, and the machine
is therefore left open between the wheels. The clutch as previously described
consists of a claviger couple, in this adaptation it is a claviger pair. . A disc d is
rigidly fixed by a short shaft to the hub of the inner side of the driving wheel, this
disc has a wide circumferential rim or flange having a smooth circular interior
surface. A fixed pin or stud S projects from the centre of the disc.
This pin is
the fixed common axis of the two clavigers axbs and cyes, set in opposite
directions. The extreme length of cach clavis rod ab and c ye is slightly greater
than the radius of the interior surface of the rim. The restraining arms x 8 and
y 8 are quite distinct from each other and are both centred at their ends upon the
common fixed axis S. The, clavis rods are widened out at their outer ends into
the feet or clutch pieces b b¹ and o o¹. The outer bearing profile of these pieces is
an arc of a circle shaped to fit the interior of the rim when the clutch is in action.
The fixed axis S is extended outwards into a pin of smaller diameter. The end a
of the clavis rod ab has two fixed pins projecting from opposite sides giving it
a T shaped end. The end c of the clavis rod c e has a fixed pin projecting towards
the disc. The two corresponding pins on the side, adjacent to the disc are con-
nected by a short rod a c slotted for a short distance at its centre and pivoted at
each end on the pins. This rod connects the two clavis rods together, and its
length regulates the extent of the clearance for the recoil. The slot is passed over
the pin upon which it slides. A T shaped rod ca is pivoted at the end upon the
pin a. The short arm of this rod adjacent to the disc carries the roller r. The
length of the stem Ca of the rod plus the radius of the roller must be slightly
longer than the radius of the inner surface of the rim. On the outer short arin of
the T shaped rod the end C of a claviger couple A B C S is pivoted. The other
end A of the claviger couple is pivoted upon the crank pin A of the single
crank A O on the subsidiary axle O. The length of the crank A O must be equal
to the radius of the inner surface of the rim minus the radius of the roller r. The
arrangement is repeated in connection with the other wheel. The power is com-
municated to the subsidiary axle O by means of a crank at its centre, operated by
the pedal rods. The bearings for the driving wheels are fitted on the short shafts
connecting the discs with the hubs. These bearings are connected and carried by
a Ushaped framing passing downwards towards the ground with branches for
supporting the fixed axis S, the bearings of the subsidiary shaft O, the steering
wheel &c. The driving wheels may be before or behind the rider.
When the crank A O is rotated in the sense of the arrow, the roller r rolls a
short distance along the inner surface of the rim and forces the point a towards the
fixed axis S, this brings the clutch piece b b into contact with the rim and it
presses upon it directly in a radial direction all along the surface of contact with
great force.
With the relative positions shewn in the figure the virtual moment of
the outward pressure of the clutch piece on the rim is forty-eight times that of the
force acting through the claviger couple A B C S at C. The vertical moment of
*the pressure can be varied to any extent in accordance with the explanations pre-
viously given in article 64 when dealing with the principles of movements composed
of claviger pairs. The clutch disc and wheel are now practically one piece and the
driving wheel is rotated-synchronously with the subsidiary axle. The other clutch
piece e e¹ has been carried by the same movement quite clear of the disc. Should
either wheel outrun the motion of the subsidiary axle as in turning corners the
disc flange throws off the clutch piece leaving both clutch pieces clear to the extent
allowed by the clearance. Two or three powerful and rapid strokes may be given
to the pedals and then they may be beld stationary by the feet while the machine

page_text: runs freely forward until the force of the impulse is exhausted.
When running
down inclines by the force of gravity the driving wheels run free and the pedals
are held stationary and used as foot rests. Suppose now the velocity of the
machine is too great and it is desirable to restrain it, the pedals are pressed back-
ward by the feet, the roller C rolls backward along the rim and brings the clutch
piece e e¹ into contact with the rim with great pressure. The parts are immediately
locked together as one piece and they so remain while the back pressure upon the
pedals is continued. The subsidiary axle is then driven by the driving wheels and
their velocity is reduced by increasing the load, by the back pressure upon the
ascending pedals.
When the machine is at rest it can be driven backwards by operating the pedals
in the reverse direction. The roller cannot in any case be removed from contact
with the interior of the rim during the movement.
Plate 21, Fig. 9 represents an arrangement of mechanism with the claviger
movement for operating the steering wheel of velocipedes. A steering handle his
attached to a spindle c which for about half its length from the junction with the
handle is threaded with an exterior screw of coarse pitch. The threaded part of
the spindle passes through a fixed tubular stud S which is rigidly attached to the
framework. The stud is threaded with a corresponding interior screw. The lower
part of the spindle carries the tubular collar e within which the spindle is free to
turn: The tubular collar is held in place by the ring r above it which is screwed
or rigidly fixed in any way to the spindle and by the flat annular nut n which is
screwed on the lower end of the spindle. On opposite sides of the loose collar c
are two fixed pins upon which are pivoted the two forked ends of a clavis rod A & B.
The restraining arm x y has its fixed axis y vertically under the fixed tubular
stud S. A connecting rod Az is pivoted to the end A and is connected at the
other end with the steering wheel. When the steering handle is very slightly
screwed down the claviger moves the rod Az a much longer distance horizontally
towards the reverse is the case when the handle is screwed up. The sensitive-
ness of the movement may be varied to any extent by varying the size of the
claviger relatively to the distance Sy.
Plate 23, Fig. 7 represents a claviger adapted as a safety brake for tricycles.
operated as at present by chains and chain wheels, with balance gear inside a
tubular axle. It is more particularly suitable for those tricycles with driving
wheels before the rider. They are generally restrained by a band brake acting
upon the periphery of a drum fixed upon the axle and this is operated by a
lever. The centre of gravity of the rider is nearly vertically above the axle
and when the brake is applied with any force the reaction upon the frame-
work of the machine causes the rear part of the machine with the rider to revolve
upon the axle.
In Fig. 7 the axles are represented in cross-section; O is the solid
axle and a the tubular one. The disc d with the circumferential rim or flange fis
fitted upon the tubular axle. A claviger bado has the axle a for the axis of its
restraining arm z o. The sum of the lengths of o x and x d is rather longer than
the radius of the interior surface of the rim. The clavis rod bad is broadened
out into the foot or brake piece a d¹. The outer profile of this is an arc of a circle
of the same radius as the interior surface of the rim and it is made so as to fit the
interior surface of the rim when the brake is in action. The clavis rod da bis
extended in length to n and is bent upwards into a curve at b so as avoid coming
in contact with the axle. A fixed stud S supports and holds the rod n b d in a
convenient position by means of the slotted piece m which slides down and up
against the stud when the brake is applied and released. The brake piece da d¹
is held away from the rim when not in action by a light coiled spring attached to
the stud S and to the top of the slot in m. This holds the rod n d firmly against
the stud. The bearing edge of the brake piece should preferably be covered with
leather. The brake is applied by pressure of the foot or feet upon the end of the
rod towards n which is shaped to accommodate the feet and act as a foot rest
while descending hills. Very delicate and gradual application of the brake can be

page_text: effected in this manner as well as an extremely powerful pressure when desired
without any danger of the machine being thrown over, as the only reaction upon
the machine is through the restraining arm o upon the axle, which has no effect
whatever upon the stability of the machine. This brake may also be conveniently
fitted upon the short axle carrying the lower chain wheel.
127. Clutch Motion for operating Drill Braces &c. Plate 23, Figs. 8, 9 and 10
represent three variations of the claviger clutch previously described for turning
Drills or for other tools requiring a step by step movement with free return of the
handle. Fig. 8 is similar to the clutch shewn in Plate 13, Fig. 4. The disc
having the circumferential flange is attached to the spindle or stock of the tool.
The handle H B is pivoted at B on the common pivot of the claviger couple
forming the clutch. At p on the inner side of the handle there is a fixed pin
carrying the roller r, which rolls along the inner surface of the rim. The handle,
roller, and guide thus form a roller claviger. The distance of the pin from the
end B is arranged so that when the clutch is in action, with the full pressure, the
line P B makes an angle with the line B s¹. The larger the angle the greater the
pressure. A similar arrangement is illustrated in Fig. 10. It is intended for
transmitting great force and the bearing surfaces are made correspondingly large
to prevent the surface of the rim being crushed or worn uneven. The ends a
and c of the claviger couple are pivoted upon strong pins fixed to the segmental
pieces m and n. The handle is similar to that shewn in Fig. 8 but it is pivoted
at e on a pin fixed in another segmental piece p. The convex edges of these
pieces are finished to fit the inner surface of the rim. The grip can be arranged
to have any ratio to the force applied to the handle. The length of movement at
the release is very slight and it is regulated by the space which intervenes between
the two pieces m and p. The arrangement represented in Fig. 9 is similar to the
preceding. The segmental piece p is omitted and the handle is obtained by
extending the clavis rod b c. In all three examples the clutches are shewn in action.
When the handle is pulled in the direction indicated by the arrow the clutch
instantaneously grips the disc, the force of the grip varying with the force applied
to the handle but very greatly increased and is more than sufficient to overcome
any resistances. The length of clearance at the release for the clutches shewn in
Figs. 8 and 9 may be regulated by connecting the centres of S and B or b by a
small wire double link.
128. Arrangement for Driving Locomotive Engines with four coupled wheels,
giving one revolution of each driving wheel for cach stroke of the piston. Plate 23,
Fig. 3. The ends of the driving axles are represented by the circles O and O¹.
The crank pins A and A' are fixed in the bosses of the driving wheels. The two
crank pins are connected by the right claviger couple, with equal limbs, A B A' S.
The two ends of the claviger couple A and A¹ are centred upon the crank pins
and are free to turn upon them. The fixed axis S is situated in the centre of a
straight line joining the centre of the two axles. The centre line of the fixed axis
is parallel to and in the same plane as the axes of the two axles O and O'. The
length of each clavis rod A B and A¹ B must be equal to the line So plus the
length of the erank OA. The cylinders are outside and are in a vertical direction.
above the fixed axis S. The piston rod is connected with the common pivot B by
a short connecting rod z. The position shewn in the figure is the commencement
of the upward stroke. At the completion of the upward stroke the common pivot
is at D on the vertical straight line DS B. This is the commencement of the
downward stroke, at the termination of which the common pivot is again in the
position shewn in the figure. The locus described by the point B during the move-
ment is the Lemniscata shewn by the dotted lines in the figure. The positions of
the point B at equal intervals of time during the movement are indicated by the
numerals. The lemniscata is exactly symmetrical, and the multiple point is on the
projection of the centre line of the fixed axis S. The upward and downward
stroke for each revolution are therefore exactly equal. The two driving wheels
are in this manner directly driven simultaneously, the force being equally divided

page_text: between them. The relative lengths of the major and minor axes of the lemniscata.
depend upon the relative lengths of the clavis rod and the crank. The cranks on
the driving wheels on the opposite sides of the engine are set 180° angular distance
apart.
Plate 23, Fig. 5 represents a movement for driving four coupled wheels half a
revolution at a stroke. The cylinders are outside and in a horizontal position.
They may be either above or below the axle. Two right hanger clavigers B z As
and B¹ y A¹s are attached to the cranks OA and O¹ A¹ which are set in opposite
directions. The free ends B and B¹ of the clavis rods are connected by the
rod B B¹ which is pivoted at each end on pins fixed to the ends of the clavis rods.
At the centre of this rod is a fixed pin V. Upon this pin is pivoted the end v of
the connecting rod zv the other end of which is pivoted upon the cross-head pin,
The cranks on the driving wheels on opposite sides of the engine are set in the
same direction. With compound cylinders the return stroke is effected by using
the steam expansively. Six, eight or more coupled driving wheels may be directly
driven in the same manner. For more than four the cranks and clavigers are all
set in the same direction and the free ends of the clavis rods connected by a rod.
The connecting rod z v is pivoted upon the end B of the clavis rod nearest to the
cylinder.
Any of the movements previously described for converting rectilinear motion
into continuous circular may be employed with inside or outside cylinders, and the
wheels may be coupled by claviger couples.
The
129. Plate 23, Fig. 2 represents a variation of the movement shewn in Fig. 3:
The two clavigers here form a claviger pair instead of a claviger couple. The
common pivot of the two clavis rods is the crank pin B of the crank B O.
revolving shaft O is situated in the position occupied by the fixed axis S in Fig. 3
and the two fixed axes S and S₁ are in the position of the two shafts in Fig. 3.
The two ends of the clavis rods A and A¹ are joined by short connecting rods to
the piston rods of two cylinders. The steam is admitted to each alternately so
that one is at the centre of the stroke when the stroke of the other is commencing.
130. Automatic Governor for Steam Engine. Plate 20, Fig. 1, gives a general
view of this arrangement of claviger motions. It is designed for using in connection
with the movements previously described for converting alternate or reciprocal
rectilinear motion into continuous circular, for alternate motion with two cylinders
and for reciprocal with compound cylinders when the return stroke is effected by
employing the steam expansively. It may be more clearly understood by first
describing the parts in detail and then explaining the operation of the movement
as a whole.
Three fixed tubular studs m n and p are attached to the supports (not shewn) in
a vertical line. Ot is a vertical cranked shaft passing through the tubular studs m
and n and free to revolve inside them, it is held in place by the knob O which fits
into a recessed bearing in the upper surface of m and by the fixed collar r which is
seated upon the upper surface of the tubular stud n. The lower part of the shaft
is tubular and terminates in the shoulders S and S¹. These are cut out at the
centre and form a double fork. Through these are passed two pins S and S¹ pro-
jecting on both sides. Two rods, which are restraining arms, 8 x and s¹ y are
pivoted upon the centre of the pins in the forks. These rods at x and y are
finished with T shaped ends. Two rods bs and 61 8 forked at one end and
provided with bearing holes are pivoted upon the pins S and S¹. A vertical
rod u w passes through the fixed tubular stud p and into the tubular end of the
shaft Ot and is free to revolve or move up and down in them. Towards the
upper end it carries two small wing pieces f and f¹ through which are passed
the fixed pins g and g₁ projecting from both sides. The pins are equidistant from
the axis of the rod u w and are parallel to and vertically under the pins S and S¹.
Towards the lower end of the rod below the tubular stud p are two fixed rings C
and C and between them is the loose collar i. Two balls a and a¹ are attached to
two rods b d and b¹ which are pivoted at the ends to the rods 68 and 6¹ s¹ at b

page_text: and 6. At e and e¹ upon the two rods carrying the balls are two fixed pins
projecting on both sides; two rods shewn in projection in the figure as one e¹ y g¹
are pivoted upon the projecting pins e¹y and g¹. Similarly on the other side are two
rods shewn in the figure as ex g pivoted on the studs ex and g. The combination
of pivoted rods thus forms a right claviger couple of unequal limbs with the fixed axes
at S and S¹. The essential point is that the centres of the balls and the centres of
the pins S and S¹ should be in a horizontal line. At the bottom of the rod u w sup-
ported by the nut v is the weight W. A claviger pair a 611 c11 811 111 has the end of
the clavis rod a pivoted upon a pin on the loose collar i. The end of the other clavis
rod c has a weight W, less than the weight W, hung upon it. The fixed axis of
the restraining arm s¹¹¹ is a fixed pin on the tubular stud p, the other axis S!! is
a pin upon a rectangular block sliding in the fixed slide 7. A connecting rod z is
pivoted to the other side of the block and is attached at the other end to a handle
working over an indexed disc. A right claviger m¹ n¹ o¹ t'; the restraining arm of
which n¹¹ is equal in length to the rod as, is pivoted at o¹ upon a pin carried by
a lug projecting from the loose collar i.
The restraining arm is bent at the end to
a right angle and passed through a bearing hole in a lug t' projecting from the
fixed tubular bearing p. The points s, g, t, and o¹ are in a vertical straight line.
The end m¹ is pivoted to a horizontally placed rod m¹ D which passes through the
fixed bearing M. The rod HA is connected with a hanger claviger attached
to an eccentric on the crank shaft, it moves up and down in a vertical direction
through the fixed bearing N. It is pivoted at A to a claviger couple A B C S.
The end C of the clavis rod is pivoted upon the rod F G which moves backwards
and forwards through the fixed bearings R. and T. The centre pivot S of the
claviger couple is a pin projecting from a short-sleeve sliding upon the rod jk.
This rod is bent under at both ends, at the upper end it is pivoted to a fixed stud Q
and at the lower end it is pivoted upon a pin in a segmental block sliding in a
fixed slotted guide 1, the inner surfaces of the slots being arcs of a circle described
from the centre of the stud Q. The rod m¹ D. is connected with the segmental
block by a short rod D E. Another claviger couple, not shewn in the figure of the
same size as A B C S is also pivoted to the end A of the rod H A. It is pivoted
at the other end to a horizontal rod parallel to the rod G F and closely contiguous
to it. The centre pivot is a fixed pin on a short sleeve piece sliding on a rod
similar to the other but the rod is fixed at the ends and makes an angle of 45°
with the horizon. The horizontal rod to which it is pivoted is attached to a
flat slide valve, with an invariable travel, which regulates the distribution of the
steam, such as admission, exhaustion and lead. The rod F G is attached to a cut
off slide working in the main slide valve. Motion is communicated to the Governor
by means of the crank on the vertical shaft Ot. The governor maintains the
speed of the engine at a fixed standard, whether the load be increased or diminished,
by regulating the amount of steam admitted into the cylinder by means of a
variable cut off. The balls of the governor are in equilibrium in any position, the
effect of gravity upon them being always the same as they move only in a
horizontal plane. They are carried outwards by centrifugal force and brought
inwards by the operation of the weight. These two forces can be adjusted so as
to maintain the speed at any standard required. The rod HA is shewn at its
highest point. In this position the centre pivot of both claviger couples are
opposite each other in a horizontal line. Let it be supposed that the moveable
rod ej which is pivoted at Q is at an angle of 45° and is parallel to the fixed rod
carrying the centre pivot of the other claviger. For clearness the latter claviger
which is not shewn in the figure will be described as the parallel claviger. The
engine is working at the standard speed with an average load and the governor
is in equilibrium. Each downward stroke of the rod HA is transmitted by the
clavigers to the horizontal rods with which they are connected into a movement
exactly similar but in a horizontal direction. During the movement the centre
pivots on the sleeves slide down the rods in unison. The result is the valve and
cut off slide-are-moved-exactly together as one piece and the cut off takes place at

page_text: the average point. Now suppose the load is reduced, the speed of the engine is
correspondingly increased, the centrifugal force predominates over the weight, and
the balls move further out. The rod u w is raised as a result of this movement,
this lifts the loose collar i which moves the end m' of the claviger m² o¹ t¹
towards M. The motion of m¹ is exactly of the same quality as the outward
motion of the balls but to half the extent. The motion of m³ is carried to the
block E and the latter is moyed along the segment shaped slide towards thus
sloping the rod k j to a greater angle. The rod GF now makes a longer stroke
than the rod HA. It has exactly the same quality of motion as the latter but it
has an increased velocity which has a constant ratio to the velocity of the rod H A.
The result is that the cut off slide travels faster than the main valve and closes
the port earlier in the stroke than before thus reducing the amount of steam
proportionately to the reduction of the load and bringing the speed down to the
standard. The same effect is reached in the contrary direction when the load is
increased. The radius of the circle described by the centre of the balls is an index
of the load and the amount of steam used. The centrifugal force however varies
according to the extent of the circle described and it is necessary to vary the
weight W in a corresponding degree so that it may hold the centrifugal force in
equilibrium whatever may be the radius of the circle described. The shape of the
valves causes also some variation. These differences can all be nicely adjusted by
the arrangement of weights shewn to the right of the figure, and on an enlarged
scale in Fig. 2.
As the weight W ascends it increases in force see Fig. 2. The weight W in all
cases includes the weight of the vertical rod which supports it. The pull of W is
for any position W
-
W¹ x box ac
od x ab
Any rate of variation can be obtained by this means. It is affected by the
relative dimensions of the two paired clavigers which need not necessarily be of
the same size, the distance apart of the fixed axes, and the proportion of the weights.
So far the governor gives a fixed standard of speed with a fixed or variable load.
Any speed within reasonable limits can be obtained at will with any load fixed or
variable, always supposing that if the speed be increased with a heavier load there
is sufficient reserve of steam in the boiler or the production of steam.can be made
to keep pace with the requirements. This variation in the speed is effected by
varying the pull of the weight W by means of the handle attached to the other
end of the rod 8111 z. When the axis S is moved towards the axis. S the pull
of W is increased and it is. decreased when the axis S¹ is moved further away.
131. Arrangement for fully utilizing the Expansive force of steam.
When high ranges of expansion are used with cylinders of the ordinary size
with steam at ordinary boiler pressures, the limit of economy is soon passed. The
average pressure of the steam is low and as the dead load has to be overcome at
each stroke the balance of effective, work.is comparatively.small..
The object of the arrangement shewn in Plate 20, Fig. 3 is to extend the
principle of using steam expansively by increasing the average pressure and
adjusting it to suit the load and by maintaining the moment of the pressure with
respect to its application at the crank pin, the same throughout the stroke."
When the machinery is driven by the force of expanding steam the pressure of
the steam uniformly diminishes in proportion to its cubical expansion. The work
developed in any indefinitely small advance of the piston taken at any part of the
stroke is the product of the area of the piston by the space through which it has
moved and by the pressure of the steam. This value is equalized in this arrangement
by retarding the increase of volume when the pressure is greater and accelerating
it when the pressure is less than the average pressure during the stroke; the
retardation and acceleration of the increase of volume being in the same proportion
as the pressure is greater or less than the average.
The retarding and accelerating is effected by increasing and decreasing the
distance the load is carried relatively to the distance moved by the piston. The

page_text: stroke is delivered with uniform velocity and force to the crank pin in a direction
coinciding at each instant with its motion. The result with a constant load (or
with a variable load and an automatic cut off) is an uniform velocity of the
machinery while the piston moves with different velocities varying inversely
according to the pressure. The cylinder employed is rather more than twice the
length of the usual cylinder for the same length of crank. The dotted line A B
represents the length of the travel of the piston rod. It is divided into lengths in
arithmetical progression, according to the numerals placed opposite the divisions.
Thus the length 2 to 3 has the same ratio to the length 7 to 8 as 3 to 8 and so
with all the other divisions. If the divisions were made indefinitely large in
number the average length would be at 5. From the centre 5 with a radius equal
to A B describe the arc C¹ D' and from the centre B with a radius equal to
half A B describe the arc A¹ B'. Through the point of intersection draw the
line B C equal in length to the line A B. The piston rod Z is equal in length to
line A B. It is pivoted at d, (which is the cross-head and pin, represented in the
figure conventionally) to the clavis rod dcf which is equal in length to the
line AB. The end d is placed at A and the end fat B. The piston rod-is then
moved down to B while the end f is guided along the straight line B C to C the
locus described by the centre C of the clavis rod is noted. It is an are of a circle.
Its centre is found at S". A fixed stud is placed at S¹ and the restraining
arm 8c is pivoted upon it at one end, the other end being pivoted to the centre
of the clavis rod. O is the crank shaft and Oba crank upon it. a x bs is a
hanger claviger of normal dimensions attached to the crank, the fixed axis S is on
the line S O which is parallel to the line B C. The size of the hanger claviger
and crank is regulated by the length of the line B C. This is the extreme length
of the traverse line for the forward stroke of the hanger claviger carrying the
crank from dead point. to dead point. The two clavis rods are connected by the
rod f a.
When the piston rod is moved down the line A B with an uniformly
.accelerated velocity so that it passes over each division in an equal interval of time
.the crank is rotated from x to z and the velocity for the half revolution from S
to y is uniform. Allowance may be made for a steeper reduction of pressure
caused by radiation, steam friction &c by correspondingly reducing the size of the
angle A B C.
The connecting rod fa may be dispensed with and the clavis rod d f connected
directly to the traverse end of the clavis rod of any of the forms of clavigers
previously described for giving one revolution for each stroke of the piston, and
which move backward and forward along a straight line. In both cases two
cylinders are, employed and the crank operated by alternate strokes. The steam is
admitted into the cylinder at a very high initial pressure and the cut off takes
place early in the stroke. The initial pressure and the average point of cut off
should be arranged to allow of the pressure of the steam at the end of ths of the
stroke of the piston to have to the load at the required velocity the ratio
of 3.1416 to 4.
This is a movement suitable for utilizing any explosive of not too rapid ignition
and combustion. The crank and other parts are in that case made of greater
dimensions.
The line of travel of any piston operated by steam with the cut off at any point
can be changed into a line of motion of uniform velocity and pressure. The line
of travel is divided into parts each of a length inversely according to the pressure.
A line is drawn perpendicular to it but the nearest ends of the two lines are a
short distance apart. This is divided into equal parts and the centre locus found.
The two lines are then joined by a claviger couple of sufficient span to more than
reach the furthest parts of each. The centre pivot is provided with a roller which
runs along two guides parallel to the centre locus on opposite sides and in parallel
planes. One end of the claviger couple is guided along one of the straight lines
in any way previously described. It will be found that the centre locus in almost
all cases of moderately early cut off is very nearly the arc of a circle and may

page_text: practically be treated as such. In that case the roller and guides are dispensed
with, and the centre pivot is carried by a restraining arm with the fixed axis at
the centre of the circle of which the arc forms a part.
132. Arrangements for operating Brakes for Restraining and Stopping Railway
Trains.
A claviger couple is supported by a horizontal bar carried by the axle trees at
each end. The fixed axis is at the centre of the bar and the common pivot of the
two clavis rods is a short distance above it. Two brake blocks formed of two
equal segments are bolted to the ends of the clavis rods. The centre of each brake
block, in the vicinity of the bolt, recessed to accommodate a rectangular block
through which the bolt is passed. The two rectangular blocks slide for a short
distance along grooves in the upper surface of the bar. The length of the clavis
rods is arranged so that when the brake is applied, the common pivot of the
claviger couple is at a slightly higher level than the fixed axis. The brake is
operated by the common pivot being forced vertically downward causing the brake
blocks to press against the periphery of the wheels. This is effected by a claviger
pair, one end of which is pivoted on the cominon pivot. The claviger pair passes
through a slit in the bottom of the van. The common pivot of the pair travels in
a horizontal line between the two fixed axes. The free end of the pair is towards
the top of the van and its line of travel is vertical. The same arrangement is
repeated on the other side. The two upper ends of the claviger pairs on opposito
sides are pivoted at the ends of a transverse rod which passes across the van.
When the brake is to be applied the guard seizes the transverse rod and applying
his weight pulls it down in a vertical direction. When the brake is taken off the
transverse rod is pushed back until caught and held in position by a spring catch.
Any amount of pressure may in this manner be applied to the wheels.
All the carriages in the train are fitted with the bar, claviger couple, and brake
blocks and they are all brought under the control of one guard by the following
arrangement. A smaller claviger is pivoted at one end on the common pivot of
the claviger couple carrying the brakes. The fixed axis is just under the carriage
floor and the vertical motion of the common pivot of the claviger couple of the
first brake applied is transferred by it into horizontal motion which is transmitted
from carriage to carriage by a horizontal rod moving backwards and forwards in
bearings, and operating clavigers of the same size set to the same angle and
attached to the common pivots of the other block carrying claviger couples. If the
carriages are supposed to be equally loaded so that the heights of the frames are
the same throughout and the distances between the carriages are supposed to be
invariably the same then all the brakes could be simultaneously applied by a rigid
horizontal rod running from end to end. But these conditions never obtain. The
arrangement shewn in the skeleton diagram in Plate 20 Fig. 4 is for the purpose
of connecting the horizonta! rods between each carriage. With this connection the
carriage frames may be on different levels, the distances between the carriages may
vary within the limits allowed by the couplings and buffers, and the carriages of
the train may at the moment be moving at different velocities without these
conditions in the slightest degree affecting the application of the brakes. They
are applied and taken off under any or all of these conditions simultaneously
throughout the train, and each horizontal rod has the same range and quality of
motion. A double claviger couple a b8 811 composed of six rods of equal length
is pivoted at S on a fixed stud or pin in the frame of one carriage and at $¹ on a
fixed stud or pin in the frame of the next carriage. The two cross rods are pivoted
together at O by a loose pin. The fixed pins S and S¹ are on the same level as
the fixed axes of the clavigers connected with the claviger couple carrying the
brake blocks. The claviger mg ds is connected with the horizontal rod m t at m;
the fixed axis is at S, and the claviger below it. A similar claviger set to the same
angle, with the fixed axis at S¹, but situated above it, is connected at n with the
horizontal rod nr. The two ends c and d of the two clavis rods c n and m d are
connected by the claviger couple c e do which has its centre pivot on the pin at.O.

page_text: Horizontal motion given to either of the rods t m or nr is exactly reproduced in
the other in the opposite direction, notwithstanding. that each set of the fixed
points S and S and the bearings of the horizontal rods may have an independent
differential motion.
The skeleton diagrams Figs. 5 and 6 represent arrangements of clavigers for
utilizing a part of the momentum of the train itself to generate the retarding force
for destroying the remainder. Fig. 5 represents the brake apparatus previously
described. The claviger previously described which is connected to the common
pivot bis represented by the lines abs, it is pivoted at.a to the horizontal rod a f
which passes through the bearing y fixed to the framework of the carriage. The
rod af is tubular at the end for the length df. A strong coiled spring de is
placed in the tubular end of the rod af. The rod eg which carries the buffer
is carried through the fixed bearing z and into the tubular end of the rod af where
it acts upon the spring as a plunger. It is held in place against being drawn out
too far by a fixed collar and nut. There is a fixed collar con the rod af between
the end a and the bearing y. A light spiral spring is coiled round the rod and
fixed at the ends to the fixed collar c and the end of the fixed bearing y. The
claviger a abs is duplicated on the opposite side of the fixed axis S forming the
claviger couple a ba¹ s The horizontal rod springs, buffer &c. are also duplicated
in connection with it. Its operation is as follows. When a retardation has been
caused in front by the application, of the brake or by the reversal of the engine the
buffer strikes against the buffer of the preceding carriage and brings the brake
blocks into use by means of the clavigers. A very small pressure at the buffers
will put on the brakes with great force. The force can be varied according to the
angles at which the clavigers are set and according to the length and strength of
the spring. If after the application of the brake to its full extent, the carriage
through possessing greater momentum should move faster than the preceding
carriage the further pressure on the buffers is expended in compressing the coiled
spring d e. These buffers do not supersede the main buffers.
When the pressure
is relieved the brake blocks are brought away from the wheels by the action of the
light coiled spring at c. To prevent the application of the brake during shunting
a bar is pivoted at the centre on the fixed pin S. It has a short circular shaped
recess towards each end which, when placed in position, fits over the pins forming
the pivots at a and a¹ and is held in position by a spring or a pin inserted through
it. The pressure on the buffer r is then expended entirely upon
the spring.
The skeleton diagram in Fig. 6 represents a somewhat similar arrangement to
the preceding but the force obtained by the pressure on the buffers is used to lift
the carriage bodily from the rails and place the weight upon a sledge. The sledge
slides along the rails until the momentum is expended, and thus the wheels are
saved from being worn. The line indicates the sledge. A strong curved
bar o y s¹s s¹¹ zo is supported by the axle trees O and O¹ and grasps them
above and below. At s¹s and 81 are three strong pins forming at s and 8" the
fixed axes for two clavigers cx d s¹ and a a¹ b s¹ having rods of sufficient strength
for the purpose. The two ends e and a are connected by the claviger couple ceas,
the fixed axis of which is S. Two fixed bearings m and n vertically above the axle
trees are supported from them. The rods carrying the buffers pass through these
bearings. These rods with the springs &c in connection are precisely similar to
those previously described and represented in Fig. 5, though the details are not
indicated in this figure. If either of the buffers be struck with sufficient force both
clavigers will be operated the ends a and c will move to 811 and s¹ and both
clavigers assume the appearance of rigid vertical supports bearing upon the sledge
which rests upon the rails. During the movement the fixed pins s and s" and the
curved bar to which they are attached have been moved upwards a short distance
and as the curved bar is attached, to the axle trees the whole carriage is lifted
with it. If the coiled spring represented at c, Fig. 5 were not used it would
remain in this manner supported by the sledge until one of the buffers, were pulled
outwards. Avery, slight pull on the buffer, or Luffer rods is sufficient. The

page_text: operation of the forces when the carriage is lifted on the sledge by the recoil of the
buffer caused by a retardation in front is as follows, lengths and weights being
given for additional clearness. A low velocity is taken as the momentum and
consequently the force available for lifting is then less. Let the lines c d or a b
represent a length of 30 inches, c s or a s¹¹ a length of 74 inches, the lower. surface
of the sledge being about four-fifths of an inch from the rail. Suppose the
arrangement is attached to a truck and that the truck and load, weigh 20 tons.
The truck is moving on a level with a velocity of 4 feet per second. The preceding
truck has been lifted upon the sledge and its.velocity at the moment of contact of
the two brake buffers has been reduced to say 3 feet per second.. Its rear brake
buffers are withdrawn 7 inches. The truck under consideration moves forward
11 inches before the sledge attached to it touches. the rail. During a further
forward movement of 33 inches the truck is lifted up one-fifth of an inch and. its
weight is supported by the sledges. If the pressure be sufficient to commence the
lifting it must go on to the full height allowed by the clavigers as the moment of
the force very rapidly increases.
W
V
2
5600 units
Part of the momentum
To lift 20 tons one-fifth of an inch requires about 675 units of work." The units
of work conserved in a body weighing W lbs moving with a velocity of V feet a
second is equal to
where g is 32, the measure of the force of gravity.
The effective velocity is the excess of the velocity of the truck over the preceding
one which excess is taken at 1 foot per second. This worked out gives 700 units
of work. This force acts through a length of 34 inches at the commencement
with a virtual velocity of 8 to 1, and with a mean virtual velocity throughout
of 17 to 1. Its efficiency to lift the truck is then at least 700 × 8
being more than 8 times the force required for the purpose.
to be destroyed is thus used to destroy the remainder.
133. Utilization of the force of Waves. Plate 18 Fig. 5. The figure represents a
barrage or revetment wall partly in vertical section, the sloped profile being the
sea face; and a side view of the arrangement of clavigers for receiving and trans-
mitting the force of the impact of the waves. RR R represents the wall. From
R to R¹ is a narrow embrasure or opening sufficiently wide to allow of the free
movement of the parts to be described. A fixed stud S is firmly fixed into the
masonry on each side the embrasure. Another fixed stud S¹ is the centre of a
curved iron rod supported at the ends in the masonry on both sides of the
embrasure. Another fixed stud S is supported in a suitable manner on the land
side. A rod DBQ is pivoted near its centre on the fixed stud S. At B is a fixed
pin upon which the end of the clavis rod A x B is pivoted, the restraining arm
is C which is pivoted upon the fixed axis S₁, the part SB of the rod D B Q
forms the radius rod of the claviger. The part S D of the same rod forms the
radius rod of another claviger Dy E S' set in the contrary direction on the land
side with the fixed axis on the stud S. The rod D BQ carries at the end the
counterweight W. The end A of the clavis rod A x B is extended in length to L.
It is broadened out to form a support at the back of a rectangulár leaf L¹ L
shewn in end view in the figure. The leaf is constructed with a view to
lightness and strength and consists of a steel framework covered with planking.
The counterweight arranged so that when the leaf is free from the pressure
of the waves the parts will be brought to the position shewn in the figure.
The leaf is then preferably at an inclination of 45°. At P and PI on the
face of the wall there are two pads against which the leaf fits when it is
drawn up out of use. The wall is recessed sufficiently to admit the clavis
rod in order to allow the leaf to lie flat to the surface of the wall. When a
wave strikes upon the leaf the force consists partly of the impact and partly,
of the weight of the water after the blow. It moves the leaf forwards towards
the wall and the rod DBQ is turned upon its axis carrying with it the counter-
weight W. The moment of the weight when it is moved but a short distance
by a light wave is very small scarcely more than sufficient to overcome the resist
"

page_text: ances of the connecting machinery and return the leaf to its initial position. But
if the force of the waves increase and move the leaf further the moment of the
counterweight is greatly increased as it approaches a horizontal position. The
effect of the counterweight thus increases with the force of the blow delivered on
the leaf. After receiving a blow the leaf moves forward until the counterweight
overbalances the momentum of the leaf and the return commences without any jar
or sudden strain. The counterweight swings backward beyond the vertical line.
As soon as this line is passed the weight comes again into operation to restrain the
velocity of the return movement. When the point of equilibrium is reached the
leaf is returned without jar to its original position where it remains slightly
oscillating until struck by the next wave. The movement can be roughly timed
to the arrival of the waves or at least it can be timed so as to avoid the leaf being
struck during the return before the weight arrives at the vertical position, by
adjusting the length the the arm SQ to suit the average force of the waves, and
the average time of their arrival. It is regulated in this respect by the same
principle as the pendulum. The motion of the rod DBQ is communicated to the
other claviger Dy ES2 and the cod E has a reciprocal rectilinear motion given to
it in a horizontal direction. This motion is carried to a place of security by a
horizontal shaft supported at the requisite distances by clavigers exactly corre-
sponding to the claviger Dy ES'. This irregular reciprocal rectilinear motion is
converted into continuous circular by means of two clavigers each attached to
a clutch, the two clutches being set in opposite directions and attached to a
revolving shaft. Several different leaves may in this manner be connected with
the same shaft. The revolutions of the shaft are then transmitted multiplied in
number by one of the methods described herein, to another shaft which is connected
to a fly wheel. When the force of the waves is too great to operate the leaf with
safety it is drawn up securely against the wall and held in that position. This can
be effected by moving back and securing the machinery at any point between the
leaf and the clutches.
This position is shewn in Fig. 6.
134. The Utilization of running water and tidal motion. The economical use of
water wheels for utilizing the motion of the water in rivers is confined within very
narrow limits.
If the velocity of the water is low the force obtained is insigni-
ficant and when the wheel is increased in size to obtain greater range the weight
of the wheel is increased in a greater ratio so that no advantage is obtained. The
force obtained from the stream by the wheel is wasted by the descending paddles
compressing the water and by the ascending ones lifting it. The roller claviger
can be adapted to utilize the force when the velocity is very low. The moving
parts are comparatively light and can be arranged to take a wide sweep without
much additional weight. The main weight of the structure is in the fixed parts.
The movement is arranged so that the moving parts have a varying velocity at
different parts of the cycle of motion and their position and velocity are arranged
in the most advantageous manner to obtain the maximum effect. Two paddles are
attached to the ends of a rod. The rod has three bearing holes, one at the centre
and one towards each end between the centre and the paddles a short distance from
the paddles. These latter bearing holes have a spindle passed through each
carrying two rollers one on each side. Two of these double paddle rods are
centred upon a crank pin of a double crank on a horizontal shaft above the water.
Two fixed guides are placed in position in parallel planes and parallel to each
other. One guide is arranged to be between the crank and one roller, the other
roller on the same spindle being between the crank and the other guide. The
double guide is U shaped. The lower part is in a horizontal direction. The rollers
of the paddle moving upward are guided until after those of the other end have
entered the guide. The two rods though pivoted on the same crank are not
directly connected together as they have a differential motion with respect to each
other during the movement. When the paddle enters the water it does not com-
press or splash the water. It enters with a uniforma velocity and at the same

page_text: angle until the paddle is submerged. It enters slowly, the velocity being about
one-fourth of the average velocity of the paddle in the water and about one-eighth
of its maximum velocity when clear of the water. The water accumulates behind
the paddle and runs up it so that the downward and forward impulse of the water
is utilized. The paddle is also lifted with the same velocity out of the water
maintaining the same angle in the opposite direction; the water accumulates behind
it giving an upward and forward impulse until it is clear of the water. The.
paddle has a long range in the water and its line of movement is a very contracted
cycloid differing but slightly from a straight line. When the crank is in a vertical
direction one paddle rod is vertical and the other horizontal. This is the only position
in which they are perpendicular to each other. Each paddle gives an impulse during
1 revolutions of the crank, after another quarter revolution the other end comes
into operation. One complete revolution of a paddle occupies the same time as
4 revolutions of the crank. Several similar arrangements may be attached to the
same shaft with the cranks set to different angles.
135: Arrangement for Propelling Boats.. A horizontal shaft passes athwart the
boat and through the opposite sides. It terminates at each end outside the boat
in a double and single crank set 180° apart. The cranks are in the same direction at
both ends. The ends of the shorter limbs of two equal sized right claviger couples,
with unequal limbs, set in the same direction, are pivoted on each double crank, the
direction of both sets being say towards the stern of the boat. Two corresponding
sets are attached to the single cranks, the direction of both sets being towards the
prow. The fixed axes of each set of two claviger couples are vertically under each
other a short distance apart. The outer ends of the two claviger couples are thus
brought further apart and are vertically under each other. The upper one is
pivoted to the upper end of a paddle and the lower one is forked out and pivoted
to a stud projecting from each side of the paddle. There are thus 8 claviger
couples carrying 4 paddles two on each side of the boat, one towards the head and
the other towards the stern.
When the shaft is rotated the 2 fore paddles nove in the same direction and
enter the water at the same time in a vertical direction. When they are at the
lowest point the stern paddles are at the highest and the two sets enter the water
alternately. The paddles are in a vertical direction at every part of the movement.
Ever at in each paddle describes a circle of the same diameter.
Two fore paddles propel the boat by direct pull upon the water and the two
ste paddles by direct thrust. When the boat is operated by manual power the
transverse shaft is dispensed with and the outer cranks and shafts terminate inside
the boat in single cranks on each side. To each of these single cranks there are
attached two hanger clavigers set in opposite directions. The two upper ones have
handles set at right angles to the clavis rods. The ends of the two lower ones are
connected by a transverse foot rod. The operator is provided with a sliding seat.
The boat is propelled by the operator pulling the handles towards him and at the
same time pushing the foot rod away from hin with his feet. The return stroke is
lighter and is effected by a push of the hands alone.
136. Chains of Claviger Couples with unequal limbs may be arranged to effect
the same work as is ordinarily accomplished by systems of toothed wheels and
axles and by combinations of pulleys. The force is perfectly transferred by this
means in any direction and the weight may have any ratio to the power. The
friction is much less than by any other method. The fixed parts are in all cases
out of the way of the moveable parts so that the range of motion is not affected
by the number of claviger couples in the system as is the case with systems
of pulleys.
137. The highest form of Claviger has the axis of the restraining arm supported
by two links of unequal lengths and not in the same plane as the claviger. The
traverse end of the clavis rod is constrained to move along a straight line in any
plane and at any inclination. The other end of the the clavis rod describes a curve
of double curvature. By this means the notion of the planets in their orbits can be

page_text: "
exactly reproduced.. It is requisite that the intensity and direction of the forces
operating should be understood and the methods of obtaining the same effects by
adjusting the proportion of the parts and the angles at which the parts of the
instrument are set.
The problems of the calculus can in this manner be solved mechanically. Curves
of all kinds representing the motion of projectiles and the forms of bodies resulting
from the operation of forces acting in different directions are exactly reproduced.
By this means theories relating to celestial physics can be put to the test of actual
experiment and those which are correct confirmed and those which are unfounded
dissipated. A study of this instrument in connection with observation of the
motions of the moon and planets shews that celestial and terrestrial mechanics are
subject to the same laws and similar dynamic effects result from the application of
similar forces.
0.
In both, the measure of the force applied in effecting a fixed amount of work is
the intensity of the force multiplied by the time it is in operation.
If the orbits of revolving bodies round a centre of force are supposed to be
circular the measure of the force of gravity is the time taken to curve the orbit to
a certain angle, when the bodies are moving with a certain fixed velocity. Thus
the intensity of the same central force acting on bodies revolving round it at
different distances is relatively
Velocity
Time
Observation shews that the velocity varies inversely according to the sq. root
of the distance. The time required by the revolving body to traverse the length
of orbit required by the fixed angle is the velocity taken inversely and multiplied
by the distance from the central force. Therefore the intensity of the force must
vary inversely according to the square of the distance.
Veloc.
Time
The relative mass of different central forces may be found in the same way by
observing any body controlled by them.
The mass =
× Distance 2. This
gives the mass relatively of the Sun, and the planets accompanied by satellites,
when the distance of the revolving bodies from the centre of force is known.
When the mass is known the distance is obtained as follows. The velocity is
equal to the length of the orbit traversed divided by the time, and as the angle is
the same in all cases the relative velocities
filling in the value of the velocity, the force =
relatively
V
= × R²
-
R³ 2 T
=
2 RT
2 RTT
T
The force
=
Velocity
Time
And
The mass of any central force
and leaving out the constant quantity which does not
affect the proportion, the mass =
R³
of
R3
T
or the
Cube of the distance
Square of the time
That is the value
T is the same for every body revolving round the same central force and the
different fractions for two bodies revolving round different central forces give
relatively the masses of the two central forces. When the revolving body moves
in an elliptical orbit, the velocity of the body varies inversely according to the
distance from the central force. The amount of controlling force exerted during
the passage of the body over small equal divisions of the orbit also varics inversely
as the distance from the central force.
Thus the controlling force has always the same ratio to the velocity whatever the
shape of the orbit.
As the velocity of bodies moving in circular orbits round the same central force
varies inversely according to the sq. root of the distance this shews that at
Aphelion the velocity is too low to be in equilibrium with the force at that
distance and that at Perihelion it is too high. Thus though the equilibrium is
disturbed the planet in its orbit is in a position of stability between the force and
the velocity. The areas covered in any given time by the radii vectores of all
bodies revolving round the same central force vary directly according to the square
root of the distance of the circular orbit of equilibrium of each from the central
:

page_text: force. In order that a body, when first drawn into a system by a central force
may have a separate existence and revolve in a closed curve round it, it is
necessary that the central force itself shall be in motion. At first the orbit is very
elliptical but the forces operating gradually bring it into a circular form at a
distance from the central force according to its velocity. The planes of motion of
the body and of the central force are also gradually assimilated to each other.
Two sets of forces each tending to cause a body to move in different planes result
in movement in a plane situated at an angle between the two, the angle varying
according to the forces. The operation is the same as previously explained for
rectilinear forces.
The test of this mechanical power applied to the theory of the tides shews that
it is founded on a misconception. It is generally stated as follows: The water
on the side under the Moon is pulled from the Earth, and piled up under the Moon,
as the Moon's action on the surface water is greater than its action on the Earth's.
centre. The Earth is also pulled away from the water on the other side by the
Moon's attraction. That part of the attraction acting at a right angle to the Earth's.
attraction, called the tangential component is the most powerful cause of the tides,
tending to close the water up under the Moon. A little consideration will shew
the fallacy of this theory and that it is mechanically impossible. A grain thrown
into one of the scales of a balance will not lift a pound weight lying in the other,
but if it be a sufficiently sensitive balance in a state of equilibrium between a
pound weight in each scale, a grain thrown into either will affect the balance. The
theory of the tides would be true if it could be supposed that the waters were
separated from the Earth and revolving round it with sufficient velocity to hold
the force of the Earth's gravity in equilibrium. As the case is every particle of
matter on the Earth is held firmly grasped by the Earth's attraction and is pulled
by it towards the centre. There is no heavenly body or combination of them able
to act upon any such particle with the same force of pull consequently it cannot be
lifted by their action against the Earth's attraction.
As a lateral movement resulting from the operation of the tangential component
of the force must have a component consisting of a lifting force acting against the
Earths gravity this movement is also impossible. Outside forces operate through
the force of gravity acting from the Earth's centre by varying the intensity of its
pull. Thus taking the attraction of the Moon for example. If the particle be
situated in a line between the centre of the Earth and Moon the action of the
attraction of the Moon is negative. The intensity of the pull on the particle
towards the Earths.centre is the difference between the two forces. On the other
hand if the Earths centre be in a line between the particle and the centre of the
Moon the action of the Moon's attraction is positive. The pull on the particle
towards the Earth's centre is the sum of the two forces. Let a particle be taken
in any position on the surface and let a line be drawn from it to the centres of
both bodies. When the angle at the particle is greater than a right angle the
action of the Moons attraction is negative, when it is less it is positive, and when
it is exactly a right angle it is nil. The effect of the force varies with the angle.
Let a straight line be drawn from the particle, perpendicular to the line from the
particle to the centre of the Earth and in the same plane as the other two lines.
Let a be the angle which the line drawn from the Moon's centre to the particle
makes, with this straight line, the effect, negative or positive, of the Moon's
'attraction is the product of the force at the point of application into the site of a.
The Sun's attraction acts in the saine manner. The pull on a particle towards the
Earth's centre at any part of the surface under the operation of these three forces
may be found as follows. The distances are taken from the particle.
Let D
دو
"
"
M.
B
R
Distance to centre of Sun.
== Mass of Sun.
=
Angle as described above made by a line from centre of Sun.
Distance to centre of Earth.

page_text: "
α = Angle described above.
The force of the Earth's gravity on any particle on its surface is
E
M
± ( sin a ± sin ß).
If it be supposed for clearnes of illustration that the three bodies are fixed at
their average distances apart and that the Earth is covered to a considerable
depth with water the surface would be adjusted by the force of gravity so that an
equal mass of water should have the same weight or be subject to the same pull.
The lengths of the radii relatively at every point and hence the amount of
variation of the surface above or below the spherical surface may be found as
follows, in all such cases as that illustrated where the variation is slight compared
with the radius. Let g = pull of gravity at any point on the surface of the
sphere under the conditions described, and let r = radius.
After the surface is adjusted to the varying force of gravity the radii will vary
as follows =
g
5236
The surface is thus depressed under the distributing body and raised on the
opposite side. The effect of the Moon's attraction is much greater than that of the
Sun but more local. The operation of the same law causes the formation of the
tails of comets and probably the spots upon the Sun and other phenomena.
Another effect of the Moons attraction may be illustrated mechanically. The
differential effect of the Sun's action and the retarding influence of the land upon
the tidal undulation, together with the time taken for the forces to effect the
movement, cause unequal protuberances of the surface on opposite sides. These
come directly under the influence of the Moon's attraction. It acts upon them in
the same manner as two equal forces acting in the same direction upon the ends of
a lever with unequal arms and rotates the Earth upon its axis.
An example of the highest forin of claviger adapted for the elucidation of
Celestial Physics has been in existence from the carliest ages of the world. It is
on a majestic scale, yet arranged with the most exact precision, and is now as
perfect for the purpose intended as when it was constructed.
It is contained in the Great Pyramid of Jeezch in Egypt, represented by
geometrical lines. The whole of the passages and markings in the Pyramid with
the exception of the two upper chambers are occupied by it. The clavis rod is two
cubits (of 20-627 British inches) wide and one cubit thick. Its lower end is at
the junction of the ascending with the descending passage and it reaches to the
south wall of the Grand Gallery and lies along the floor of the passages.
The restraining arm is along the passage to the Queens Chamber. One end is
pivoted to the clavis rod and the other is pivoted to an upright stud represented
by the niche in the Queen's Chamber.
The Queen's Chamber itself represents a cage carrying the stud and is hung
upon two links pivoted to tixed supports above in the structure.
The links are represented by channels cut in the masonry of the Pyramid.
The position represented is for the commencement of the movement.
The traverse is downward along the descending passage to a mark there
placed. The upward end of the clavis rod describes a curve of double curviture.
Minute instructions for adjusting the instrument to describe 19 different curves
are given.
The curves obtained are apparently 19 revolutions of the Moon taken at equal
intervals during the cycle known to the ancient Chaldean astronomers as "Saros."
Altogether it appears to be an exact mechanical solution of the problem of the
three bodies. The 19 curves are divided into parts each representing the move-
ment of the Moon during 24 hours, lines are drawn from the divisions to the
centre of force representing the Sun, and the incidence of each set of these lines
is marked on the ramps along each side of the floor of the Grand Gallery by holes

page_text: which are just large enough to include the lines. The two chambers called the
King's Chamber and the Antechamber contain what is practically a message or
declaration in cryptograph.
The King's Chamber by means of the geometrical lines of the normal form of
claviger exbibits a circle and sphere, and by means of a geometry bearing upon
the inter relations of the square and circle declares the dimensions of the Pyramid
and the object of building it, which latter appears to be the handing down to
future generations the exact knowledge of the ancient astronomers respecting the
Arcane of celestial physics. The King's Chamber deals with the dimensions of
the Pyramid and with two of these quantities. The King's Chamber itself is
20 cubits long by 10 cubits broad and the height is 11·1803 cubits.
geometrical figures exhibited are
A. A square with a side of 5 cubits.
B. An inscribed circle.
C. A circle of the same area as the square A.
D. A square of the same area as the inscribed circle B.
The circumference of C is equal in length to the perimeter of D.
E. A sphere with a diameter equal to the diameter of B.
F. A cube the length and breadth of which is equal to the side of D.
The
The length of each side of the base of the Pyramid was 100 times the length of
a side of the square D, and was therefore 443-11 cubits. The full height was,
100 times the diameter of the circle C and was therefore 564-18 cubits. The area
of a vertical section was 62,500 square cubits. The Pyramid was intended to
represent a semi-sphere with a radius equal to the height, the great circle of the
sphere being on the level, the circumference being equal to the sum of the four
sides at the base of the Pyramid. The other half of the sphere is to be supported
under ground. The volume of the exhibited sphere E has the same ratio to the
volume of the large sphere as the volume of the Earth to the volume of the Sun.
Under the Pyramid at the end of the descending passage is a roughly hewn
subterranean chamber of which only the ceiling is finished.
..
.
The volume of the Pyramid carried down to this level is compared with the
volume of the cube F.
The two volumes have the same ratio to each other as the mass of the Sun to the
mass of the Earth.
Dated this eighth day of October 1885.

page_text: Improved Mechanism for the Conversion, Modification,
Regulation, and Transmission of Motion.
I, WILLIAM GOLDING of Yarburgh Street, Moss Side, near Manchester, in the
County of Lancaster, Manufacturer, do hereby declare the nature of my invention
for "IMPROVED MECHANISM FOR THE CONVERSION, MODIFICATION, REGULATION AND
TRANSMISSION OF MOTION," or described more fully-A Complete Scientific Systom
of Practical Mechanics effectuated by means of a new Mechanical Power, to be called
Claviger"; and in what manner the saine is to be performed, to be particularly
described and ascertained in and by the following statement:—
"
The principle upon which this system of practical mechanics is founded is that
of the Parallelogram of Forces, and the mechanical power called “Claviger” which
is employed to carry it into effect is an exact practical counterpart of the theories
which have been established in connection with that principle.
By varying the proportion and adjustment of its parts and by combining two
or more clavigers, force in motion of any kind, acting in any direction, can be
converted or transmitted into motion of the same or of any other kind, in any
.direction and at any desired distance with mathematical precision, and without
constraint upon the part to which the motion is referred, except the actual constraint
upon it of the force applied in the direction of the motion desired.
The proportion of speed and power as between the force and the work can be
varied by it to any extent, either in length or number.
The character of the velocity can also be changed by it, as uniform velocity into
uniformly accelerated or uniformly retarded or into irregular velocity, and vice
versa.
The movements hereinafter described are for convenience divided into two classes,
namely class A and class B.
The movements belonging to class A deal with conversion, transmission and
modulation of motion by means of this mechanical power in its simplest form;
namely, that of rigid rods operating from centres. Most of the movements of
conversion and all those of transmission are mathematically exact, while those
which are not exactly so approach so nearly to it, that in practice the difference is
not important, being in most instances so small as not to be observable. In most
cases the motion is smooth, noiseless and precise, with continuous full impulse,
not needing the assistance of inertia.
Under Class B this mechanical power is dealt with in its perfect form, which
consists, in most of the movements, of more parts than in Class A. By means of
this form, force in motion is perfectly converted, varied, regulated, governed and
transmitted exactly as required.
When a movement is explained belonging to Class A if it is not a perfect
movement it will be stated in what respects it falls short of perfection.
When explaining a movement belonging to Class B it will be described as a
perfect movement. By a perfect movement, whether of conversion, transmission or
modulation or all combined, is meant a transferrence of the force with full and con-
tinuous equal impulse, delivered throughout to the receiving part of the machinery

page_text: to be moved, in a direction exactly conterminous with its motion, however long,
complicated and varied the desired resulting motion may be. An exact constant
uniformity of velocity between the power and the operating ends, or the velocity
multiplied or reduced retaining a constant ratio between them, or the velocity
exactly varied in any manner to suit the requirements of the machine. The lines
of movement to be mathematically exact, that is supposing rectilinear motion to be
changed into circular, the power end of the claviger will move in an exact straight
line while the operative end will describe an exact circle without forcible constraint.
The friction to be between parallel surfaces only, that is a hollow cylinder rotating
on a cylinder or vice versa as in pivots, fixed axes or circular bearings, or that of
blocks moving along a straight or circular slide, and the friction to be the least
possible consistent with the movement.
In addition to the perfect transferrence of the motion these mechanical move-
ments are simple in their construction and capable of application to the most
delicate machinery such as that of watches and clocks, while they can "be
constructed of enormous strength for any class of machinery with less material
and weight than that now required for the same purpose.
In addition to the description of the simple movements a few examples of their
practical application in machinery are given, in order to show how variations may
be made in the normal forms for particular purposes, and also of some of its
movements requiring the addition of subsidiary parts for particular purposes, in
order to indicate the scope of its application in machinery generally.
This description is divided into articles numbered for convenience of reference,
so as to avoid undue verbal repetition.
1. In order now to explain the principle of the movement and its practical
operation, reference is first made to Plate 1. Fig. 1. A B, B C, S x, and Sy
represent four rigid rods.
The rods A B and B C are equal in length to each other. The rods Sx and Sy
are also equal to each other and are each half the length of the rod A B or B C.
The two rods A B and B C are pivoted together at their ends B, and the two
rods S x Sy are pivoted together at their ends at S, and are each pivotted at their
other ends to the centres of the rods A B and B C respectively. The rods are
free to turn upon the pivots.
A stud or a bearing hole is made at the ends A and C for supplying means of
attachment to the connecting machinery. If the centres of the pivots A, x, B, y
C.and S are now supposed to be connected by straight lines the four rods form a
parallelogram with two of its contiguous sides extended to twice their length, and
the points A, S and C are in a straight line. Now if these rods are moved upon
their pivots this combination will be found to possess certain qualities of mobility
and rigidity which will be now explained. Whatever motion may be given to
the rods the points A, S and C are always in a straight line, and the angles A S
B and CSB are always right angles. The point S is also always in the centre of
a straight line joining the points A and C. As a result of these qualities, if force
in motion in any direction be independently impressed upon the points A and C,
the point S will remain fixed if the two forces are equal in magnitude and opposite
in direction, or it will move along a line which is the resultant of the two forces
impressed upon A and C. If the same two forces which are applied at the points A
and C be applied to a particle and represented in direction and magnitude by two
straight lines drawn from the point of application and a parallelogram be described
on these straight lines as adjacent sides the particle will move along the diagonal
of the parallelogram which passes through the point. The point S moves exactly.
in the same direction but its line of movement is half the length of the diagonal
of the parallelogram. If the diagonal of the parallelogram be divided into four
equal parts, the line described by the point S will be in most cases represented by
the two parts of the diagonal adjacent to the centre. In the case of the movement
of the particle the diagonal of the parallelogram represents the magnitude of the
resultant. With respect however to the movement of the combination of rods just

page_text: described the intensity of the resulting force is inversely as the length of the line
of motion described by S to the line of motion described by A plus the line of
motion described by C. That is the magnitude of the force of the resultant is
equal to the magnitude of the forces of the components.
2. If pressure be exerted independently upon the points A and C during a
certain interval of time and the intensity and direction of the pressure be varied
'during the interval so as to cause the points A and C to describe regular or
irregular figures of any kind and similar or dissimilar to each other, the point S
will describe a figure which is the resultant of the two figures described by the
points A and C. If it be supposed that the same forces which have operated upon
the points A and C so as to compel them to describe any such figures be made to
act upon a particle such particle will move along a course or figure of exactly the
same shape as that described by the point S but of twice the extent.
3. Let the pivot at S be fixed, still leaving the rods free to move upon it. Let
any movement be described by the point A. The point C will describe a similar
movement but opposite in direction. In Plate 1. Fig. 2 the ends A and C are
shewn connected with two cranks. If the crank at A be moved from 0 to 1 the
crank at C will be moved by the rods also from 0 to 1, but the direction is directly
opposite. If the crank A be moved from figure to figure consecutively round the
crank pin circle the crank C will move in the same order round its circle and thus
the crank C will be rotated in the same direction as the crank A. If the crank at C
be taken away the point C will still describe a perfect circle of the same diameter.
as that described by A. When the point A is moved away from or towards the
fixed point 'S by the motion of the crank the point C is correspondingly moved
away from or towards the point S to the same extent. When the point A is
depressed by the action of the crank the point C is correspondingly raised to the
same extent, when the point A is raised the point C is depressed to the same
extent. The motion of the crank A is thus perfectly transmitted to the crank C.
This transmission is effected by means of the rods acting through leverage and by
direct thrust and pull combined in the exact proportion necessary. The method
of this action will be more clearly understood when considering the conversion of
rectilinear motion into continuous circular motion. The point S bisects a line
joining the centres of the two crank shafts, it also bisects every line drawn from
any part of the circumference of the crank pin circle of A to a corresponding part
of the circumference of the crank pin circle of C, measuring the points from zero
in each in the same direction.
4. Plate 1. Fig. 3 represents rectilinear motion transmitted along the same
straight line but reversed in direction. The pivot S is fixed. The pivots A and C
are supplied with wheels or rollers. A guide F. G is fixed in position so as to
The rollers cannot be
allow the rollers A and C to run along its lower surface.
moved away from the guide. If motion be given to the point A towards or away
from S the point C moves to the same extent in an opposite direction.
5. Plate 1 Fig. 4 represents a similar movement but the lines of motion are
parallel. The motions of A and C are directed by the fixed guides F G and H K,
One guide is between one roller and the fixed point S and the other guide is outside
the other roller. This arrangement gives a reciprocal restraint allowing the
rollers freedom to run along the guides but preventing the possibility of moving
them away from their line of motion without breaking the parts.
6. In the foregoing examples the lines of motion of the points A and C are
equal, and the point S, the centre of force, is midway between them. The con-
tained parallelogram Sx By in these examples is a rhombus. Fig. 5 represents
a method of transferring any of the motions previously described and at the samé
time shortening or lengthening the line of motion. In this arrangement of the
rods the contained parallelogram is a rhomboid and two of its sides are produced
to A and C, the three points A SC being in a straight line. The necessary
vestraint is here, represented by a bearing to the connecting rod L. If the point A

page_text: be moved towards M the point C will move in a parallel and opposite direction.
the length of its line of motion bearing the same ratio to the length of the line
of motion of A that the line S C bears to the line S A. If both ends A and C are
left free to move in any direction and the point A be made to describe any figure,
the point C will describe the same figure inverted and reduced in size in the ratio
of SA to SC If each of these figures be divided into the same number of equal
parts and the corresponding division in each be connected by a straight line all
these straight lines (which are of different lengths) will pass through the point S
and it will divide each line into two parts which bear the same ratio to each other
that the line A S bears to the line S C.
'
7. In the examples given in Plate 1 Figs. 2, 3, 4 and 5, the point S is fixed
because the centre of force is a point and the forces necessary to move the points A
and C along their line of notion are for the same interval of time equal in
magnitude and opposite in direction. A different condition is represented by
Plate 1 Fig. 6. The pivots A, S and C are fixed to blocks which are placed in and
are free to move along slides D E, N M and F, D.. The centre of the slide N M
from 0 to 14 is in length and direction represented by half the diagonal of the
parallelogram of which the centre of the slides F D and D E from 0 to 14
represent two adjacent sides. If the centre of the block A be placed over the
point marked 0, the block S and the block C each take up their positions over the
point 0 in their respective slides. If the point A be now moved along the slide
towards E, the points S and C. move along their respective slides passing the
corresponding figures in each at the same instant. If power be applied at A in
the direction of the arrow it will raise a weight at C the virtual velocity being
the same for both weight and power.
If the weight or the work be attached at S the virtual velocity
P's Vel: W's Vel:: DE: NM:: W: P.
will be
The position and extent of M N may be found whatever the direction of FD
and D E by dividing the lines of motion along F D and D E into the same
number of indefinitely small equal parts. The commencement of each line of
motion is then taken as zero and the divisions numbered consecutively in the
direction of the motion. The centre point in a straight line joining each corre-
sponding point in the two lines is then marked and the locus of these centre
points is the line along which the centre pivot at S is to move. This line is
hereinafter designated the centre locus. It is always a mean in respect to
direction and form between the two lines of motion described by the power and
weight ends A and C.
8. Plate 1 Fig. 7 represents the application of the principle described in the
previous article to the conversion of continuous circular motion to reciprocal
rectilinear or vice versa. The end A is here attached to a crank. The end C is
provided with a block placed in and free to move along the straight slide E F.
The centre point of the block C moves from the point 0 to 0.
The length
between these two points is equal to half the circumference of the crank pin circle.
This line and each half of the crank pin circle are divided into the same number of
equal parts and the centre locus found as described in the previous article. This
centre locus consists of two halves of common cycloids reversed. The centre pivot S
is provided with a roller. A fixed guide M is placed in position. The profile of
its inner surface is parallel to the centre locus and is distant therefrom a length
equal to the radius of the roller on the centre pivot S. When the crank is rotated
in the direction of the arrow the centre pivot S rolls along the guide while the
point C moves along the straight line in the sense of the arrow with the same
velocity as A, until A has reached its lowest point 0. Immediately the crank has
passed 0 the point C returns along the straight line in the opposite direction.
Also the power may be applied at C.but in that case the crank must be started
to rotate in the opposite direction to that indicated by the arrow. Reciprocal
rectilinear motion is thus converted into continuous circular.

page_text: 9. It may be stated generally that whatever conversion, transmission or modu-
lation of motion is required the centre locus between the two complete lines of
motion should be found. The two ends of the rods A and C should be constrained
to move along the two lines of motion and the centre pivot along the centre locus.
This statement exhibits the application of this system in its crudest form. It is
frequently the case that a guide cannot be shaped parallel to the centre locus
without part of its bearing edges being cut away. In many cases also the direction
of the motion given by the power to the ends A or C is unsuitable-to maintaining
and moving the centre pivot S along the centre locus. These difficulties are
completely overcome, as will be explained in detail when considering the different
movements, by firstly, a system of reciprocal restraint applicable to every movement,
the application of which to rectilinear motion is illustrated in Plate 1. Figs. 3
and 4, and described in articles 4 and 5; and secondly by application of a second
arrangement of rods similar to those represented in Plate 1 Fig. (which in all
cases will have a fixed pivot either at the centre or at one end), whose office is to
hold the centre pivot and move it directly along its centre locus. In many cases
the centre locus is so nearly an arc of a circle that by slightly varying the velocity
of the power or weight end of the rods the centre locus may be made so. In that
case there is no need for fixed guides for the centre locus, as it is moved and
controlled by a link supported by a fixed pivot or stud.
It is on this modification the movements in class A are designed.
10. In order to facilitate the description of the movements to follow, names are
given to the different rods and their combinations. Plate 1, Fig. 8 represents a
claviger. The rod A B is called the clavis rod, the link or arm x S is called the
restraining arm, S is a fixed stud supporting the restraining arm and is called the
fixed axis. The pivot x is called the pivot, and is either a stud rigidly attached to
either A B or x S with the other free to revolve upon it or it is a pin not attached
to either and both are free to revolve upon it. The line described by the power
end of the clavis rod is called the traverse. When the pivot x is at the centre of
'the clavis rod and the restraining arm x S is half the length of A. B it is then a right
claviger. When the dimensions are different it is called an irregular claviger.
When two clavigers are pivoted together at one end of the clavis rods while the
fixed axes of the two restraining arms are in different positions it forms a claviger
pair. If the two clavigers are right clavigers and the distance between the two
fixed axes S S is equal to the length of one of the clavis rods then it is a right
claviger pair, see Plate 1 Fig. 9. Three or more clavigers so combined form a
claviger chain. When it is so arranged that lines joining the fixed axes form
right angles and all the clavis rods can be placed so that each shall make an angle
of 45° with such lines it is a right claviger chain. This is represented in
Plate 1 Fig. 10. Two right clavigers pivoted together at the ends of the clavis
rods and at the ends of the restraining arms form a right claviger couple, with
equal limbs, represented in Plate 1 Figs. 1, 2, 3, 4, 6 and 7.
When two irregular clavigers are coupled together so as to form a rhomboid with
two sides produced so that the points A, S, C, see Plate 1, Fig. 5, are in a straight
line and Sy is equal to y C and Sx to Ax it is a right claviger, couple with
unequal limbs. The claviger couple in its simplest form is a parallelogram, with
one side extended, formed by four rods pivotted together. A point is then taken
on one rod which lies between any two points taken on two other rods, so that the
three points shall be in a straight line. This point is the centre pivot or centre of
force, see S Plate 1 Fig. 11. Whatever motion is given to the rods these three
points are always in a straight line and the centre point maintains the same relative
position with respect to the other two. Any number of additional rods may be added
for strength forming additional parallelograms without affecting the movement.
Plate 1 Figs. 12, 13, 14, and 15 are examples of irregular claviger couples with
equal limbs. Plate 1 Figs. 16 and 17 represent irregular claviger couples with
unequal limbs.

page_text: Plate 1, Fig. 18 represents four parallelograms formed by six equal rods
pivoted at their centres and ends, this is a double claviger couple.
11. The rods of which the clavigers are composed are inflexible and may be
composed of steel or any other elastic metal, solid or hollow, and shaped propor-
tionately to withstand the strains to which they are to be subjected, so as to
economise material and lessen the weight.
In some cases the rods may be replaced by arms built up of various parts,
properly stayed, and bolted or otherwise rigidly fixed together. In the drawings
straight rods are shewn in all cases, so as to clearly represent the movements.
Supporting framework is rarely shewn, the fixed axes and guides being indi-
cated by a small cross. The pivots joints and cranks are treated somewhat con-
ventionally and small details of construction are not represented, such as bolts
washers, crank-keys &c.
Instead of cranks, single and double, and crank shafts as represented, orank
wrists attached to revolving or oscillating discs, wheels or rods are employed where
more convenient.
12. Rectilinear Motion converted to Circular Motion and vice versa.-In article 8
it has been shewn that the centre locus of a circle and a straight line equal in
length to half the circumference consists of two halves of a common cycloid
reversed. This is the case whatever the relative positions of the circle and
straight line may be. The oycloid is generated by a rolling circle of half the
circumference of the circle, the directrix being half the length of the straight
line. The generating point is taken at starting on the perpendicular line drawn
on the directrix through its point of contact with the rolling circle. If two
points be taken midway between the ends of the straight line and the centre of
the circle, the line joining these two points is the line along which the axis of the
generating circle moves. The directrix is situated on opposite sides of this line
for each half cycloid. If the straight line be longer or shorter in length than
half the circumference of the circle the half cycloids are generated by a generating
circle of half the circumference of the circle invariably connected with a rolling
circle whose circumference is the same length as the straight line. The positions
of the circle, straight line, and cycloid are also interchangeable. Thus when a
cycloid is found which is the centre locus of a given circle and a given straight
line, the circle is also a centre locus between the cycloid and the straight line,
and the straight line is a centre locus between the circle and the cycloid. Each
of them is however of half its dimensions when it is in position as centre locus.
Plate 30 Figs. 1, 2 and 3 shew a series wherein the straight line is the centre
locus, and Figs. 4, 5 and 3 show a series having a circle for the centre locus. In
each series the centre figure is the resultant of the two outer figures which are the
components. If any corresponding length be taken in Figs. 1 and 3 say from
0 to 1 and it is supposed to be sufficiently short in each to be regarded as a
straight line these two lengths will represent in direction and length the two
adjacent sides of a parallelogram of which the corresponding length in the straight
line in Fig. 2 will represent in direction the diagonal but of half its length. This
is also the case with the series Figs. 4, 5 and 3, and is true of any two figures
whatever and their centre locus. By this means curves representing the move-
ments of bodies as the result of regular forces can be analyzed and resolved into
their elements.
13. Plate 2, Fig. 1 represents a right claviger attached to a crank. A B, the
clavis rod, is five times the length of the crank. Sz, the directing arm, is half the
length of A B, and is pivoted to it at its centre. S is the fixed axis upon which
the restraining arm Sz is free to turn. O B is the crank. R is the fixed bearing
of the crank shaft. The fixed axis S.is distant from 0, the centre of the crank
shaft, twice the length of the crank, and along a line drawn from O parallel to D A.
When pressure is exerted at A through the connecting rod in the direction of
the arrow, the traverse end of the clavis rod moves along the line A D while the'
i

page_text: crank is rotated half a revolution in the sense of the arrow. The numerals indicate
the positions successively taken up by the various parts along the lines of move-
ment during one revolution of the crank. The length from 1 to 5 and from 5
to 9 along the line A D. are each equal to the diameter of the crank pin circle, and
the traverse for half a revolution is equal to two diameters. The departure of
the end A of the clavis rod during a small part of its traverse from a straight
line is so extremely small as to be practically of no moment. The crank can be
rotated in either direction. When rotated in the direction shewn the strain
upon the directing arm is tensile. When the stroke commences at the highest
point and the crank is rotated in the opposite direction the strain upon the
directing arm is compressive. The forward stroke either way is along the
straight line A D and the return is along the outward curve shewn in Fig. 2. The
forward stroke gives an impulse to the crank for two-thirds of a revolution. The
return takes place during the time the crank is making the remaining third of the
revolution. At the commencement of the stroke, starting from the point in the
crank pin circle nearest to the traverse line, the force is for an indefinitely short
time conveyed by thrust alone, the force .conveyed by leverage then commences
and uniformly increases, while that due to thrust uniformly decreases until at the
completion of a quadrant of revolution the two forces are equal. From this point
the force due to thrust diminishes, while the force due to leverage increases until
the second quadrant is completed, which for an indefinitely short movement at its
limit is effected by the leverage force alone. When the half revolution is com-
menced from the highest point, the half of the force is transmitted by direct pull
instead of by direct thrust, The proportion and direction at every point of the
two applications of the force are such that if they are regarded as being two
straight lines indefinitely small, forming two adjacent sides of a parallelogram,
then the diagonals of all the parallelograms coincide with the circumference of the
crank pin circle. It will thus be seen that the movement along the circumference
is the resultant of the two forces, but it is represented by the circumference in
direction only not in magnitude. This is owing to the two forces being in reality
one, divided in operating, so that the action of one division is complementary to
that of the other. If the traverse line be marked in a scale of equal parts
representing the magnitude of the force in units of weight, and the clavis rod
moved over a certain number of these parts, the crank end moving over a
corresponding portion of the circumference, but of less extent, exerts greater
force, the intensity of the force varying according to the inverse ratio of the
lengths covered.
The virtual velocity of the right claviger when proportioned and connected as
described in this article, for converting rectilinear motion to continuous circular is
therefore-
P's Vel: W's Vel: 4 dia ::: W: P,
(where represents the ratio of the diameter to the circumference of a circle).
The right claviger described above when attached to a crank as represented in
Plate 2 Fig. 1 is described as a hanger claviger. In all the various forms of
the hanger claviger the normal proportion is for the clavis rod to be five times
the length of crank. If any other proportion is employed the motion of the
crank is less uniform with that of the traverse end of the clavis rod. When the
banger claviger has the proportions described above, the notion of the "crank is
almost uniform with the motion of the traverse end A of the clavis rod, and
the force is transmitted throughout as a constant effort applied to the crank
pin tangentially to its circle. Half the force is transmitted through the rod by
direct thrust or pull and half by leverage upon the moveable fulcrum x, and these
two divisions of the original force are divided and recombined automatically in
the exact proportion necessary. The size of the crank is not material and the
movement will operate an eccentric equally well.

page_text: the crank starting from the position nearest the traverse line as shewn in Plate 2
Fig. 1 takes less than half the traverse and the second quadrant takes more. If
the clavis rod be less than five times the length of the crank, the reverse is the
case. The same results follow if the line of traverse slopes diagonally towards or
away from the circle. If the clavis rod be taken of any length relatively to the
size of crank and placed in position with the crank at the point nearest the
traverse line and the traverse end A of the clavis rod be placed in position so that
the line A B shall be equal to the line C D, see Plate 2 Fig. 1, and the crank
turned half round in the direction of the arrow while the traverse end A of the
clavis is moved along the line A D, some one point in every clavis rod whatever
ita length may be, will describe a curve which is almost identically the same as an
are of a circle. This point when found is the position for the pivot x. It may be
found in all cases by means of the following formula :-
Let t
"
""
= traverse for semi-circle.
T = length of the clavis rod.
* =
T:
distance to the pivot from the traverse end A of the clavis rod.
traverse for semi-circle of the normal length of clavis rod.
Then tr― } T : z
Having found and marked the position of the pivot as above, place the clavis rod
and crank in its first position as represented in Plate 2, Fig. 1 and mark the
position of x on the plane of movement of the clavis rod represented by the plane
of the paper. Next move the crank a quarter revolution forward so that it shall
be over the division marked 5 while the traverse end A of the clavis rod has its
centre on the line A D, here again mark the position of on the plane. Thirdly,
place the crank at 9 the completion of half a rotation while the end A. of the
clavis rod is on D and again mark the position of x.
Find the centre of a circle,
an arc of which will pass through these three points. This centre will be the
position for S the fixed axis.
The length of the restraining arm is the distance from S to x.
The normal form of hanger claviger is the most suitable for converting alternate
rectilinear motion into continuous circular.
For steam engines two cylinders are employed giving alternate strokes in the
same direction to two cranks set 180° apart, or alternate strokes in opposite
directions to the same crank. Each forward stroke gives full impulse forward
during gths of a revolution (or less if required).
The piston is nearly stationary during th of a revolution at the commencement
and end of the stroke. Thus one forward stroke may begin immediately the other
ceases giving half a revolution for each forward stroke or each stroke can be
lengthened and made to overlap the other, either at the commencement or finish or
both. As the movement gives a full tangential impulse a uniform motion is obtained
without a fly wheel.
This movement can also be employed for converting reciprocal rectilinear
motion into continuous circular by means of compound cylinders, the steam being
used expansively for effecting the return stroke. The amount of pressure required
to overcome the same resistances during the return stroke being less than in the
forward stroke in the direct proportion of the angular movements of the crank pin
made in the forward and backward strokes. The strain upon the crank web is
transverse throughout and is the least possible consistent with the load.
There is no strain upon the crank or crank shaft or its bearings as a result
of the conversion of the motion as this is borne by the fixed axis supporting the
directing arm.

page_text: 14. Reciprocal Rectilinear Motion in two directions at right angles to each other
converted into Continuous Circular or vice versa Class B. Plate 6, Fig. 1.-Let the
two dotted lines L M and C P, in directions at right angles to each other, represent
the travel of the ends A and C of two pistons LA and N. C. Take a point mid-
way between the centres of the lines L M and C P. It is at O the axis of a shaft,
cranked from O to S. Place the point C at the commencement of a line of travel
and the point A at the centre of the other line. Place the crank OS in position
so that the centre of its crank pin S shall be midway between the points C and A.
Connect the three points A S and C together by a right claviger couple A B C of
sufficient span for the movement. The end of one clavis rod of the couple is
pivotted to the piston at C, the end of the other clavis rod is pivoted to the other
piston at A and the centre pivot is the crank pin S. When pressure is exerted on
the pistons so as to force them to move along their lines of travel the crank is
rotated in either direction. The divisions marked along the lines CP and L M
and round the circumference of the crank pin circle are the positions taken up by
the respective parts which move along these lines, at equal intervals of time during
the movement when the motion of the crank pin is uniform. For every angular
movement of the crank pin round its circle the points C and A move a distance
along their lines of travel, the one equal to the sine and the other equal to
the versed sine of the angle moved, the radius being twice the length of the
crank O S. One piston is always half a stroke behind the other thus one is
always at the centre when the other is at the commencement and end of its stroke.
The motion of the crank pin S round its circle is the resultant of the two forces
acting along the lines L M and C S. These two forces are the components; they
are received by the arms of the claviger couple and composed at its centre pivot
into the continuous circular motion of the crank, O S. It is not necessary either
that the force applied to each end A and C of the claviger couple respectively
should vary in intensity according to the sine and versed sine of the angle, as the
claviger couple by its reciprocally complementary action takes the sum of the two
forces and automatically divides and adjusts it between the two ends A and C
in the exact proportion required. In order to insure that the points A and C shall
travel exactly along the lines L M and CP, both of the points are constrained.
The ends A and C have a roller at each end of the pivot, one running on a guide
above and the other below. These arrangements give a reciprocal restraint and
make it impossible to move the points C and A away from the straight lines
representing their travel. Any other effective method of restraint may be
employed, such for instance, as the block and slide shewn in Fig. 2, or any
modification of it.
15. Another variety of claviger for converting continuous Circular Motion into
Reciprocal Rectilinear with quick return (Class A) is the slider claviger.
It is distinguished by having a slotted clavis rod sliding along a block which is
held in position by a fixed stud upon which the block is free to turn. This stud
is the guide and fulcrum. In this form the principle of the operation of the force
is the same as in those varieties already described. With respect to the leverage
portion, the clavis rod moves along the fulcrum and thus the arms of the lever vary
in length relatively during the movement. The geometrical lines of this form are
given in Plate 3 Figs. 1 and 2.
In Fig. 1 the ratios of the parts in terms of the radius are,
o, n Radius 1.
C,
d Perpendicular 6-625.
a, b Traverse for semicircle 5 (perpendicular to c d).
o, 8 (8 is taken at the points of intersection of the lines na and m b) 1·60714.
The semicircle m d n is divided into any number of equal parts and lines equal
in length to the perpendicular line c d are drawn from the divisions to the straight
line a b. The lines touching a b divide it into parts nearly equal to each other,

page_text: and the lines very nearly pass through the point S. The widest divergence of any
line from the point S amounts to 02835 of the radius or with a traverse of
10 inches to a little over th of an inch. The resulting deflection of the ends
from the line a b when these lines are brought exactly through the point S is
still less.
70
יד
th
less than of an inch.
For all practical purposes the results may be stated as under. Let n, o be a rod
free to revolve on o as centre; na a rod pivoted to it at n; 8, a fixed stud or short
transverse rod supported at each end. The rod na is placed so as to bear against s
and is on the side of 8 nearest to m. Then if force in motion be applied to the
end a in a direction towards b so as to give it an uniform motion along the
line ab the end n of the rod a n will move along the semicircle n d m at an
uniform rate. The impulse will be a full tangential one, and the stress due to the
conversion of the motion will be borne by the stud 8. Similar results, though less
perfect are obtained when the rod a n is any length between 6 and 10 times the
radius n, o.
16. Plate 4, Fig. 1 represents the practical application of this form of claviger
for slotting, shaping and planing machines for quickly withdrawing the tool for a
new cut faster than it moves while working. A B is a slotted clavis rod attached
to the crank O B. The fixed stud S is provided with a block upon which the clavis
rod slides along the slot. The proportions represented are the same as in Plate 3
Fig. 1. The forward stroke corresponds to of a revolution of which the of a
revolution gives uniform motion to the end A of the clavis rod. It slows down at
each end during 7 of a revolution. The return is during the time taken by the
crank to make a quarter of a revolution. During the return the end A describes
an outward curve. The forward stroke in either direction according to the direction
the crank is rotated is along the straight line. The stock which carries the cutting
tool is joined to the end of the connecting rod = A. The positions occupied by
the different points, at equal intervals of time during the movement are represented
by the numerals.
tb
The shorter the clavis rod is made in proportion to the crank, the quicker is the
return in proportion to the forward movement, though the motion of the forward
movement is then less uniform. With a clavis rod times the length of the crank
the forward stroke corresponds to gths of revolution, nearly uniform during of a
revolution, slowing down during of a revolution at each end and returning
during th of a revolution. This movement is suitable for operating a pump or
other similar work. With a pedal attached to the end A it is a movement suitable
for operating a sewing or other machine to be worked by one foot.
87
th

page_text: Any ratio of velocity of the forward to the return strokes can be obtained with
the same crank and slider claviger by varying the position of the fulcrum S. If it
be moved nearer the crank the forward movement is lengthened and the return is
correspondingly hastened. If a large crank be used and the fulcrum S be moved
as near the crank pin circle as is possible after leaving sufficient clearance for the
crank pin, the time taken for return may be made to be a very small fraction of
the time taken for the forward movement. In this case the end A of the clavis
rod describes a curve during both forward and return strokes, but with a clavis
rod 8 times the length of crank, the variation of the end of the connecting rod
from uniform motion during the greater part of the forward stroke is slight. The
fulcrum S may be readily made adjustable along the line cd by using, in place of
a fixed stud, a short rod rigidly connected at each end to rectangular bushes which
slide along slotted supports placed parallel to the line c'd and fixed securely to the
framework. The bushes are clamped in the position desired.
17. This movement may be adapted for operating hammers, also for ore stampers
or pulverizers and for shears for cutting metal plates &c. In these cases the clavis
rod is a solid rod provided with a bearing piece, screwed, clamped, shrunk or keyed
on it, which projects laterally and slides along the block supported by the fixed
stud during the forward or lifting stroke. The fixed stud and its supports are
placed so as not to intersect the plane of movement of the clavis rod. At a certain
point of the movement according as the bearing piece is arranged, it moves clear
of the block leaving the clavis rod free to fall. After falling it is in position for
the next forward stroke.
18. Reciprocal Rectilinear Motion converted into Continuous Circular, half a
revolution for each single stroke, Class A.-Plate 5, Fig. 1, illustrates a third
form of claviger for this purpose, and it may be described as the roller claviger.
It has the fulcrum for the leverage half of the force rigidly fixed to the clavis
rod in the form of a stud projecting from it at a right angle. This stud is
furnished with a wheel or roller. The bearing for the fulcrum is a fixed guide G
along which the roller travels during the movement. The fixed guide not only
supplies the bearing for the fulcrum but guides the direction of the thrust and
pull. The fulcrum of the clavis rod has two distinct motions with reference to
the bearing surface of the fixed guide during the movement. One is a motion
of translation due to the part of the force acting by direct thrust or pull and a
motion of partial rotation on its axis due to the part of the force acting by leverage.
In the figure the fulcrum is represented at the centre of the clavis. rod. The
positions simultaneously occupied by the traverse end of the clavis rod, the centre
of the stud, and the crank pin respectively, at equal intervals of time during the
movement, when the motion of the crank is uniform, are indicated by the numerals.
The forward and return strokes are both along the straight line CD. The roller
and guide may be on one side of the clavis rod as represented in the figure, or the
roller and guide may be duplicated with the clavis rod between; or the clavis rod
may be double for part of its length near the fulcrum and carry the wheel between
on an axis rigidly fixed to the rod at each end, or the wheel and axis can turn
together with the bearings in the rod on either side; the double part of the rod
encloses the fixed guide. The fixed guide G represented in Fig. 1 is efficient for
rotating the crank in one direction only, that indicated by the arrow.
19. Continuous Circular Motion converted into Curvilinear.
The fixed fulcrum guides can be shaped to give any required curve to the
traverse of the operative end of the clavigers for shaping machines for finishing
up propeller blades and such work. In these cases the stock of the tool is attached
to the clavis rod direct and the latter is made with an elbow joint to allow the
tool to be returned across the surface of the work.
20. With the roller claviger as with the other forms, the ratio of the clavis rod
to the crank can be varied to any extent and the fulcrum can be placed at any
convenient part of the clavis rod, the guide being shaped accordingly. The position
and profile of the bearing surface of the guide can be readily determined in practice

page_text: by moving the traverse end of the clavis rod along the line of traverse, while the
other end of the clavis rod is being slowly rotated by the crank, and marking the
series of positions taken up consecutively by the centre of the stud during the
movement. The profile of the guide is to be parallel to the locus so obtained and
distant from it a length equal to the radius of the roller.
versa.
21. Reciprocal Rectilinear Motion converted into Continuous Circular or vice
Half a revolution for each stroke. Class B.-Plate 23. Fig. 1. The dotted
line A D represents the length of stroke. O is the crank shaft and O B the crank:
The force is delivered at an uniform velocity at the point M. It is required to
rotate the crank so that it and the point M shall have a constant velocity ratio.
The traverse line A D is divided into any number of equal parts and each division
is numbered consecutively commencing zero at the commencement of the forward
stroke. The divisions are also numbered the reverse way taking zero at the
commencement of the backward stroke. The circumference of the crank pin
circle is divided into the same number of equal parts as the traverse line. The
zero points in it are 180 degrees apart. The traverse line in the figure if
produced passes through the centre of the crank shaft. It may however be in
any direction in the plane of the crank pin circle. Whatever may be its position
the zero points should be taken on the circumference of the crank pin circle in
such a position that the first indefinitely small movement of the crank pin at the
commencement of each forward and backward stroke shall be parallel in direction
to the traverse line; that is, at the commencement of the stroke the crank should
be in a direction perpendicular to the traverse line. The divisions in the circum-
ference of the crank pin circle are also numbered the reverse way. A centre
locus is found between one rotation of the crank starting from zero and a double
reciprocal stroke along the traverse line. It consists of two half cycloids reversed:
The points in the centre locus corresponding to the divisions in the traverse line
and crank pin circle are marked with the same, figures. Another centre locus is
found and marked in the same way, between the rotation of a crank set 180°
angular distance from the other and rotated with it in the same direction, and the
same divisions in the traverse line as taken in connection with the rotation of the
first crank. This centre locus consists of two half cycloids reversed exactly similar
to the first. In the figure the traverse line produced cuts the major axes of the
two closed curves, forming the centre loci, at their middle point, and the two major
axes make the same angle with this line but in contrary directions. When the
traverse line produced does not pass through the centre O, the line which cuts the
major axes of the curves at their middle point is a line parallel to the traverse line
and midway between it and the centre O. Fixed guides G and H are provided
with their bearing edges parallel to the centre loci as previously described. They
are fixed in parallel planes. Between them in a parallel plane is a fixed straight
slide FD with a block n sliding in it. A cranked rod r kr cranked in the
middle and ends has the middle crank part passed through the block n, the
cranked ends are provided with rollers r and r which are fixed in position in
the guides G and H. A claviger couple with equal limbs B C M is centred on the
crank pin at one end and is pivoted at the other to the block N which moves
along the slide D A. Its centre pivot is the end of the cranked rod r carrying
a roller, which is then over the point in the centre locus corresponding to the points
occupied by the crank pin in its circle and the point M in the traverse line.
Reciprocal strokes given at M rotate the crank in either direction as desired.
The two fixed guides give a reciprocal constraint. The fixed rectilinear slide
restrains and directs the movement. One cycloidal guide is sufficient when the
crank is required to be rotated in one direction only. The rod r kr¹ is always
parallel to or in the same straight line with the crank O B. The centre of its
cranked ends r and are throughout the movement over. the corresponding figures
in each cycloid. They cannot be varied from this position and though the rollers 7
and are free to run along the guides in either direction they cannot be forced
away from contact with them. The guides are correctly. shaped and fixed when

page_text: the rollers press upon them the whole distance with sufficient force to turn and
run along with an even motion. The position and profile of the guides may be
readily obtained practically by the same method described in article 30. The
line of traverse A D may be of any length relatively to half the circumference
of the crank pin circle. If they differ much in length, claviger couples of unequal
limbs should be used, and the centre pivot should be at the centre of force. In
this case whatever may be the ratio between the length of the line of traverse
and half the circumference of the crank pin circle the centre loci are halves of
common cycloids reversed. Any points may be taken as zero in the circumference
of the crank pin circle, but if any points be taken other than those previously
described the two closed curves representing the two centre loci are dissimilar.
They neither of them contain exact halves of cycloids but are each composed of
portions of two adjacent half cycloids representing half a rotation of the generating
circle, and one guide will generally be considerably larger than the other. The
movement however is not affected. There is no dead point as in the ordinary way
of operating the crank. The points at which the change of motion takes place
may be called neutral points. When the claviger is on a neutral point it is in
cquilibrium between movement in either direction, but the instant it passes the
neutral point in either direction there is full tangential impulse. This movement
is a perfect movement.
22. Irregular rectilinear motion of any kind can be converted by this movement
into uniform circular and vice versa. The line of traverse is divided into lengths
inversely proportionate to the intensity of the force, while the circumference of
the crank pin circle is divided into equal parts. The centre locus is then takon
and the parts placed in position.
23. The claviger couples for effecting the movements described in article 21
may have the fixed guides at one end, while the force is exerted on the centre
pivot. The claviger couples may therefore be arranged in three different posi-
tions, depending on the position of the points of application of the power and the
work with respect to the guide. If it be taken that the power be applied in a
straight line to be converted into circular motion then when the guides are between
the traverse line and the crank, as illustrated in Plate 23. Fig. 1. it is a claviger
couple of the first kind. When the crank is between the traverse line and the
fixed guide it is a claviger couple of the second kind. When the traverse line is
between the crank and the fixed guide the claviger couple is of the third kind.
The movement is equally efficient in either of these kinds.
24. Rectilinear Motion transmitted in a parallel direction. Class A.-Plate 17,
Fig. 1.
A right claviger couple A B C.S, of which S is the fixed axis, connected
to a cranked radius rod O B, turning on a fixed stud at O. The figure is shewn
at the middle of the stroke. The proportions are A B or B C clavis rods 5 times
.length of radius rod B O. The line S B is perpendicular to the line A C. OS is
twice O B. AS and S C are each four times O B. Both ends of the claviger
couple A and C are free and move forward and backward along the dotted parallel.
lines shewn in contrary directions. They cannot be moved from the lines. The
range of the traverses must not be so long as to rotate the radius rod.
25. Fig. 3 represents a movement for transferring rectilinear motion in a
direction at right angles. Two right clavigers A B S and C BS are connected at
the ends B of the clavis rods to a radius rod B O. The proportions are the same
as for figure 1 but instead of both restraining arms being centred on the fixed
axis S, the restraining arm x S¹ of the clavis rod A B is centred on a second fixed
axis S. The line S₁O is equal to the line S O, and is perpendicular to it. See
also article 66.
26. Similar movements with free ends to the above can be arranged to transfer
the motion at any angle. Instead of the radius rod BO a short rod or a shaft
turning in a fixed bearing with a single crank at each end is used. To these
cranks are attached two hanger clavigers. The cranks can be set at any angle
apart and thus the motion is transferred in any direction in the same or parallel

page_text: planes. In these movements the velocity is exactly uniform between the two ends.
See Figs. 4, 5 and 7, Plate 17.
°
27. Rectilinear Motion transmitted in any direction uniformly multiplied or
reduced in length. The movements are similar to those described in articles 24, 25
and 26, but one claviger in each movement is larger than the other. When they
are both attached to the same radius rod it carries two projecting studs, the stud
to which the larger claviger is attached is longer than the other so that the larger
clavis rod can pass over the other during the movement. When the smaller
claviger is used for the application of the power the movement transfers the
motion at an uniformly increased velocity and when the power is applied to the
larger claviger the movement uniformly increases the efficiency of the force. See
Figs. 6 and 8.
28. Movements for Transferring Rectilinear Motion reversed in direction along
the same straight and along a parallel line, with the centre pivot fixed have
already been described in articles 4 and 5 and illustrated in Plate 1. Figs. 3 and 4.:
29. Rectilinear Motion transferred as described in the preceding article, with the
resulting line of movement increased or decreased in length. A constant ratio of
two to one may be obtained by centreing one end of the claviger couple on the
fixed stud and applying the force to either the centre pivot or to the other end of
the claviger. In the former case it is a claviger couple of the third kind. In the
latter case it is a claviger couple of the second kind. Any ratio between the power
and the weight can be obtained by employing claviger couples with one pivot
fixed, of unequal limbs of the first, second or third kind.
30. Rectilinear Motion transferred in either direction at any angle in the same
plane. Plate 1, Fig. 6 represents a movement for transferring rectilinear motion in
a direction at right angles. The movement has been already described.in article 7,
when the principle of the claviger was explained. If the guide M N be placed at
right angles to the position shewn in the figure, the centre point being kept over
the same spot the motion will be transferred in the opposite direction to that
indicated by the arrow. Thus both ends A and C will simultaneously move
towards or away from the angle D. Instead of the constraint represented in the
figure the ends of the clavis rods A and C may be pivoted to rods or shafts moving
in fixed bearings or they may be provided with rollers running along fixed guides
giving a reciprocal restraint as shewn in Figures 3 and 4, Plate 1, or any other
open effective method of constraint may be employed.
In Plate 1 Fig. 6, the lines E D and F D along which the ends A and C of the
clavis rods are constrained to move are the two sides of a right angled triangle and
both lines of traverse terminate at the same distance from the angle. The line M N
along which the centre pivot S moves is parallel to the hypotenuse and has the
same ratio to half the hypotenuse as either of the lines of traverse of A. or C has to
the sides E D or F D. The direction of the lines E D and F D may be varied so
as to make any angle at D. In fact their direction may coincide with the two
sides of any isosceles triangle, and the line along which the centre pivot noves
follows the same conditions with regard to position and length as just described
for a right angled triangle. When both ends A and C of the two clavis rods are
required to move simultaneously towards or away from the angle the centre locus
along which the centre pivot moves coincides in direction with the perpendicular
line which bisects both the angle D and the base, and has the same ratio to half of
it that each of the traverse lines of A and B has to the side of the triangle. See
Plate 18. Figs. 1, 2, 3, 4, 5 and 6.
31. Rectilinear Motion transferred in either direction, at any angle in the same
plane, and increased or reduced in length so that the operative end of the claviger
couple shall have a constant velocity ratio with the power end. Plate 18,
Figs. 7 and 8. The movements are similar to those described in article 30, but
the triangles are scalene triangles. The conditions are the same. The lines of
traverse coincide in direction with two sides of the triangle and the length from
the end of each traverse line to the angle is proportional to the length of the sides.

page_text: The motion is transferred with the constant velocity ratio that one side has to the
other.
32. Reciprocal or Alternate Rectilinear Motion transmitted into Reciprocal
Rectilinear in a direction at right angles and multiplied in number or varied in
velocity. See Plate 19..
Claviger couples are used with both ends constrained and with the centre pivot
attached to a block sliding along a fixed guide similar to those described in
articles 30 and 31.
When a line of motion in either direction, is multiplied into two or more lines
of motion the sum of whose lengths are equal to the original line, the centre locus
is a zigzag line composed of lines of equal length at right angles to each other.
The slide is made with its inner edges parallel to these lines.
'
square block is
used, and it is moved along the guide by the action of the claviger couple. The
stroke of the power end of the claviger couple is multiplied into as many strokes
at the other end as there are changes of direction in the guide, and the velocity of
the two ends is uniform.
33. When the sum of the lengths of the transmitted strokes is longer than the
original line of motion the zigzag lines of the centre locus meet each other at an
acute angle. When the sum of their lengths are less, the lines of the centre loeus
meet each other at an obtuse angle. In these cases the block is shaped to suit the
angles of the guide, two of its opposite corners being made to fit into the angle of
the guide. In both instances there is a constant velocity ratio between the power
and operating ends of the claviger couple.
34. In the same manner each return stroke of the multiplied transmitted motion
can be varied in velocity so as to move along, the line more quickly than the
forward stroke, the ratio of velocity between the two strokes being according to
the difference in the angles made by the two series of alternate lines, in the centre
locus, with a line which bisects them all.
35. Rectilinear Motion transmitted at any angle in the same plane. Two right
clavigers are pivoted together at one end with a pivot bent to the angle required.
The two restraining arms are centred on a fixed stud bent to the same angle.
Force is applied to one of the free ends towards or away from the fixed stud the
other end moves in the direction required towards or away from the fixed stud at
the same velocity as the power end:. No constraint is needed as the free ends
cannot be moved from the same plane nor diverted from the lines of movement
which if produced till they meet make the same angle with each other as the
angles in the bent pivot and stud. Plate 7, Fig. 7.
36. Rectilinear Motion transmitted at any angle in a parallel plane with uniform
velocity or with the velocity at a constant ratio. Plate 7 Fig. 6. A right
claviger abs has the ends of the clavis rod furnished with rollers which roll
along a fixed guide in shape the same as two adjacent sides of a square. The
ends a and b of the clavis rod are thus restrained. to move along the lines as
and s b. The fixed axis S is at the angle a s b. At any distance from this
cla viger another claviger a¹¹ b' 8' is fixed exactly similar in every respect to the
other and so that the centres of the fixed axes and pivots s, b, 81, b₁ are in a straight
line. The two pivots bb1 are joined by the connecting rod 6 61. If the end a of
the clavis rod ab be now moved along the line as in either direction, the end a¹
of the clavis rod a' 6' makes the same movement along the line a¹ 8'. Now if the
connecting rod be removed and the claviger a¹¹ 61 81 with its fixed guide be
turned upon the line 86 s¹ b' as an axis to any required angle and the connecting
rod adjusted and replaced the motion given to a will be transmitted to a¹ and it
will move along a straight line at the angular distance required in a parallel
plane. The direction of the motion of the end a¹ of the second claviger may be
regersed by reversing the position of the second claviger (so that the end 61 is
nearer the end b of the other claviger than is the fixed stud S), and inserting at
some point in the connecting rod a reversing tlaviger couple as illustrated in
Plate 1, Fig. 3. The length of movement of the end a¹³ of the second claviger may

page_text: be lengthened or shortened as compared with the length of movement of the
end a of the first claviger and a constant velocity ratio maintained between their
movements in the following manner. The second claviger is proportioned in size
The two clavigers are
to the first as the traverse of a¹ is to the traverse of a.
reversed in position and at some point in the connecting rod a reversing claviger
couple is inserted whose limbs are in the same proportion to each other as the two
clavigers.
37. Rectilinear Motion transmitted at any angle in any plane with uniform
velocity or with the velocity at a constant ratio. The movements are the same as
those described in the preceding article but the clavigers employed are irregular
clavigers. When the two clavigers are set as explained and joined by the con-
necting rod the corresponding ends of the two clavigers move in planes which are
not parallel.
The angle made by the intersection of the two planes is according to the
proportions of the irregular clavigers. This will be explained by reference to
Plate 5 Fig. 2; bx as is an irregular claviger, and S is the fixed axis. If the
end a of the clavis rod a b be constrained to move along the straight linery the
other end b will move along the straight line y t. In Plate 7, fig. 6 the right
claviger is shewn when it is in such a position that asb is an isosceles triangle
and the restraining arm S x bisects the angle a 8.b and the base a b. The angle as b
is a right angle. The irregular claviger in Fig. 2, Plate 5 is represented in the
same position. The angle a y b is however an obtuse angle. The size of this angle
depends upon the ratio of the restraining arm x S to the clavis rod ba.
position of the lines of traverse a y and by with respect to the fixed axis S is
determined in the following manner. A quadrant m x n is described from the
centre S at the distance S x, the length of the restraining arm. The restraining
The central line of
arın is placed on the line dividing the quadrant into octants.
The
the clavis rod ba is tangent to the arc at x and is the base of an isosceles
triangle bay. The perpendicular line y bisects the angle y and the base ba.
The position of the point y along the line as is determined by the fact that the
partye of the line y a reaching from the point y to the arc mxn or'the part y f
of the line y b are cach equal to the lines bx or x a.
38. Plate 7, Fig. 5 illustrates the manner in which the claviger couple can be
used to effect more than one motion in the same movement as well as increasing
the efficiency of the force. The figure represents a right claviger couple of the first
kind with unequal limbs. One clavis rod is shaped to form a handle. By means
of this the hook h can be lifted off its supporting stud m and placed higher up
upon the stud n.
Fig. 4 represents a similar movement with a right claviger
of the second kind. The bent end of the link l can be taken out of the slot
moved down and replaced in another slot. Any combinations of movement in the
same plane can be effected by it. The handle is moved in the contrary direction
to the desired movement when the claviger couple is of the first kind and in the
same direction when the claviger couple is of the second or third kinds.
39. Weighing and Lifting for moderately heavy goods.-Two double claviger
couples fixed parallel to each other in vertical planes at a sufficient distance apart
to allow of the package to be lifted to pass between. Two of the opposite ends of
each double claviger couple are rigidly fixed together by transverse rods which act
as pivots common to both. The fixed axes of both are in a horizontal line and are
supported at a convenient height. The package to be weighed and lifted may be
vertically under the two transverse rods and under a line joining the two fixed
axes or at any distance laterally within reach of one of the transverse rods when
the claviger couples are extended or of chains or ropes depending from it. The
package is attached to the lowermost transverse rod and weights hung upon the
uppermost one until the package to be weighed is just lifted clear of the floor.
The machine package and weights are then in equilibrium in whatever position the
machine may be placed. It can then be rotated on the fixed axes, by means of a
slight effort sufficient to overcome the resistances of inertia and friction only, until
"

page_text: the package is lifted to the requisite height and then the machine is elongated
laterally until the package is placed in the position desired.
40. The movement described above is a very suitable one for a ladle crane.
It may also be slightly varied and the lifting effected by hydraulic pressure.
The two parallel double claviger couples are then placed in horizontal planes. The
common axis of both is a vertically moving ram projecting from one end of a
hydraulic cylinder. The rods through which the rain passes have deep bearings on
the ram.
The two parallel claviger couples are stayed by four vertical rods passing
through the rods forming the four angles of the outer parallelogram of each set and
act as pivots common to both. The ladle is fixed at one of the corners and its
weight counterbalanced at the other corner. The ram lifts the whole arrangement
vertically to the requisite height. The ladle is turned round in any direction on
the ram as central axis and moved inwards or outwards radially by means of the
vertical rods. The force required for this purpose need only be sufficient to over-
come the resistances of inertia and friction. The two sets of double claviger couples
may rest upon friction rollers.
41. Weighing. The arrangement of rods for this purpose is shewn in Plate 10
Fig. 3. It is a right claviger pair described in article 10. The weights P and Q
are in scales hung at the ends of the clavis rods. The arms are joined by means of
blades. The clavis rods form the hypotenuses of two right angle triangles P & B
and QB. Let à and ẞ respectively be the angles which they make with the
lines Ps and Qs. The virtual moment of each weight is P tan a, acting upon
the point B and tending to move it along the straight line B s towards S; and Q
tan acting upon the point B and tending to move it along the straight line B s¹
towards S. When the weights are equal the claviger pair is in equilibrium as
shewn in the figure and the angles a and B are each 30°. If the weights are
unequal the rods take the exact angle at which the moments of the weights are
equal with respect to the point B. When the weights differ by the slightest
quantity it is indicated by the change of position of the point B. When the
balance is disturbed the weight which moves downwards has only a very slight
movement, the one moving upward and the point B have a greater range, but after
oscillating according to the force used they return to exactly the same position as
before they where disturbed. The weights move up and down in the same straight
lines parallel to each other. It is an extremely sensitive balance of great delicacy
and precision.
.
•
42. Plate 5, Figs. 3 and 4 represent a claviger pair for lifting weights a short
distance such as is usually performed by a jack. The object to be lifted such as
the axle of a wheel is placed in the hollow C, by moving the claviger pair into
position under it. The foot is then placed upon the pedal A and pressed down to
the bottom at S. The restraining arms Sx and Sy are double so that the clavis
rods may pass between. The position when the lifting is completed is shewn in
Fig. 4. No pressure at C can then move it back, but a slight kick or lift with
the toe at the pedal A moves it back into the position represented in Fig. 3 and
releases the weight. Very considerable weights can be lifted in this manner. If
the pressure on A is sufficient to commence the lifting it is easily continued as the
moment of the force increases the further the pedal is pressed down.
The virtual moment of the force acting at A is with respect to its application at
C as follows Let a be the angle made by the clavis rod A B with the line A s
and let ẞ be the angle made by the clavis rod B C with the line B 8¹. The virtual
moment in every position is P tan a tan B.
The length of the clavis rod CB would probably be determined by the height
of the article to be lifted. The claviger BA S may however be varied in size to
any extent. The virtual velocity in all cases varies with the angles and is-
P's Vel: W's Vel.:: sin a sin B: cos a cos B: :W: P.
The ratio of velocity to power during any definite movement is as follows
Let a and B be the angles at commencement of the movement and a¹ and ẞ' be
the angles at thẻ finish,

page_text: P's average Vel: W's av. Vel:: (sin a'—in a) (sın ẞ-sin p): (cos a'—cos α)
(cos B-cos B): : Av. W: Av. P.
For completing a stroke from any point P's av. Vel.: W's av. Vel.:: cos a cos ẞ:
covers a covers B:: Av. W: Av. P.
43. Plate 7. Fig. 1 represents the same movement adapted for punching plates &c.
One clavis rod is lengthened out to form a handle. In the same form it can be
adapted for stamping and compressing.
44. Plate S, Fig. 1 represents a similar movement. It is a claviger chain.
Clavigers of equal size are represented as pivoted together by the ends of their
clavis rods. The fixed axes are SS' and S¹ situated at the three angles of a square.
A right claviger chain consisting of three clavigers is explained in article 10, and
represented in Plate 8 Figures 3 and 4. These two chains represent the two
extremes of the movement. The moment and virtual velocity of the force are the
same as described for the pair in the preceding article. It may be shortly stated
that the pressure at d in any position of the chain is the intensity of the force
multiplied into the product of the tangents of the three angles which the power
ends of the clavis rods make with their lines of motion in the direction of their
movement. In any chain of three clavigers the force is varied by
Their angles absolutely. .
The difference of their angles relatively, and the relative positions of their
fixed axes.
This movement is adapted for pressing oil from seed and for compressing cotton,
pulp, artificial leather &c. also for pulling apart, testing the strength of materials &c.
Figs. 1 and 3 represent it at the commencement of the movement and Figs. 2 and 4
at the termination. The angle xbs is an angle of 45°. The bearing at a is to
accommodate a cross bar which is pushed along in a horizontal direction. For
compressing, the claviger chain acts upon the platen at d. The last indefinitely
small movement gives a pressure inconceivably great. No unyielding material is
strong enough to withstand it.
In the figures the restraining arms are represented double. The joints should be
well fitted and the rods built up to withstand the necessary pressure without
yielding.
The difference between the two chains represented may be more clearly shewn
by figures. In Fig. 1 let the clavis rods be each 10 feet long and the cross bar
pushed along by three or four men with a total pressure of say 400 lbs. The
length to be moved from a to s is a little over 7 feet (7·071008 ft.).
The length of the line of motion of the end d is 009543 ft. or about 1 th of
an inch.

page_text: The intensity of the pressure at d increases very rapidly as the limit of its line
of motion is nearly reached.
•
: A fourth claviger may be added to the chain fixed horizontally and might be
operated by horses.
These two examples represent the two extremes of relative dimensions for the
chain. Anything between can be arranged to suit different requirements. For
seed pressing &c when the length of movement of dis not sufficient, several
pressings can be made with the same feed by inserting each time metal plates
under the platen. No pressure at d can move it back.-
45. Curvilinear Motion converted into Rectilinear. Plate 7, Fig. 3 represents a
lever of the second kind connected to a right claviger. The radius for the claviger
is the part ob of the lever. The rectilinear motion may be varied in direction
with the lever in the same position by varying the position of the fixed axis S.
The lever may also be of the first or third kind. When of the first kind the
part forming the radius for the claviger may be bent at any angle. Fig. 2
represents the same movement with a claviger couple giving a reciprocal parallel
rectilinear motion such as is used for air pumps. In both the ends are free and
cannot be moved from the straight lines.
46. The Transmission of Circular Motion. Class A. Plate 9.-The first method
to be explained for effecting this is by means of the hanger claviger described in
article 13. Two hanger clavigers are attached to each shaft and set one net
traverse apart. The corresponding clavigers on opposite shafts are connected at
their traverse ends by transmitting rods or shafts equal in length to the distance
between the axes of the rotating shafts. The component force of the circular
motion of the power shaft is resolved by each claviger alternately and composed
into motion along a straight line. This rectilinear motion is transmitted by the
transmitting shaft to the corresponding claviger at its other end by which it is
again resolved and composed, the resultants then being circular motion given to
the receiving rotating shaft. The action of the second of the two clavigers,
attached to and operated by the rotating power shaft, begins before that of the
first has ceased, so that there is continuous impulse. The quality of the motion of
the rotating power shaft is exactly reproduced upon the receiving rotating shaft
and they move in unison. The motion is therefore perfectly transmitted. The
two clavigers on the same rotating shaft may be connected to it in different
positions, viz. both on the same side of the rotating shaft attached to two cranks
set 180° apart as shown in Fig. 1; both on the same side of the rotating shaft
attached to the same crank as shewn for a different movement in Fig. 2; on
opposite sides of the rotating shaft attached to the same crank as shewn in Fig. 4;
and on opposite sides of the rotating shaft attached to cranks set 180° apart as
shewn in Fig. 3. If the rotating shafts marked P in Figs. 1 and 2 are the power
shafts and they are rotated in the sense of the arrows the strain upon the trans-
mitting shafts is tensile only. The same is the case if the opposite rotating shafts
are the power shafts and they are rotated in the opposite direction.
When the clavigers are on opposite sides of the rotating shaft the strain on one
connecting shaft is tensile and on the other compressive. The motion is transferred
with equal perfection when the motion of the power shaft is reversed. The motion
may be reversed at any point without affecting the clavigers. The forward move-
ment in either direction is along the same straight line and the backward movement
in either direction describes the same curve. When the distance between the two
shafts is too great to allow the two clavigers to support the transmitting shaft
without sagging, each transmitting shaft is supported between by a hanger or
bangers at convenient distances. These bangers are clavigers of the same dimen-
sions and fixed in the same manner as the clavigers at the ends of the transmitting
shafts. They are attached to radius rods of the same length as the cranks and
these radius rods turn upon fixed studs. They support the transmitting shafts
and move with them in the same manner as the crank clavigers, see Fig. 1.

page_text: The two
by short
47. Circular Motion transmitted any distance. Plate 9, Fig. 2.
clavigers at each end are connected to the transmitting shafts & and
connecting rods c, c, and c¹ c¹. The clavigers and the connecting rods at both ends
are set in the same direction. The transmitting shafts are equal in length to the
distance between the axes of the rotating shafts. They move backward and
forward in a straight line. They may be supported as often as required by fixed
bearings or by friction rollers above and below. In the figure they are each
represented as supported by claviger couples A and B. The transmitting shaft d'
is attached to the claviger A by a fixed stud b¹ projecting horizontally from the
shaft and forming the pivot for the two clavis rods a¹ b₁ and b¹ c¹. The centre
pivot S¹ is the fixed axis and is attached to the framework. The ends a' and c¹ of
the clavis rods are provided with rollers which roll up and down the fixed straight
guide g. The other transmitting shaft d is attached in the same way to a
similar claviger B. These support the transmitting shafts but allow them free
movement forward and backward along the straight line.
48. Circular Motion transmitted any distance between shafts at different angles
or in different planes. The movement is the same as that described in the
preceding article, but the motion is taken from the transmitting shafts in any
direction radially. If the power shaft is a horizontal one and it is required to
transmit its circular motion to a vertical one, the short connecting rods on the
clavigers of the vertical shafts are attached to the transmitting shafts d¹ and d by
vertically projecting studs placed at the top and bottom of the ends of the trans-
mitting shafts instead of by horizontally projecting studs as represented in the
figure. As the line of forward traverse for the clavigers of the vertical shaft is in
the same direction as the line of motion of the transmitting shafts the motion is as
perfectly transferred as when transmitted to a shaft situated in a parallel plane.
During the return movement the outward curve of the claviger in a horizontal
plane has exactly the same effect, through its connecting rod upon the return
movement of the transmitting shaft as the outward curve of the claviger in a
vertical plane has through its connecting rod with it.
In the same manner the motion can be transmitted from the rotating power
shaft through the transmitting shafts to a rotating shaft the axis of which is
situated in any direction radially from the axis of the transmitting shafts d and d¹,
provided the plane of the movement of the receiving clavigers is at right angles
to the axes of the transmitting shafts. Also the motion may be transmitted to
shafts in other planes wherever a straight line common to both can be found,
which straight line is in direction perpendicular to both their axes. Where this
line cannot be found, the shafts can be connected by using in addition one of the
forms of claviger couples for changing the direction of rectilinear motion. The
motion may be also equally well transmitted direct from the horizontal shaft P
through the connecting shafts & and d¹ to another horizontal shaft in a direction
at right angles to the shaft P and parallel to the transmitting shafts and d¹.
The direction of rotation may be reversed in transmission to any shaft without
altering its position or the position of the transmitting shafts, by interposing
between the short connecting rods and the transmitting shafts at one end a
reversing claviger couple, and as one end is constrained to move with the
transmitting shaft there is no need of rollers.
The clavigers
There are some
49: Circular Motion transmitted to great distances, the line of transmission
passing through positions difficult of access. The movement is similar to that
illustrated in Plate 9 Fig. 2 and described in the preceding article.
employed have a greater ratio.of clavis rod to crank, say S to 1.
special features about this method which will shortly be described. It is designed
to transmit circular motion to great distances in the open air in order to utilize
water forces in hilly districts, the neighbourhood of which is unsuitable for the
sites of mills, or to carry force obtained from running water, tidal motion, wave
impact, &c, to places of security or to convenient positions for its utilization.
It is also intended for distributing power from a centre where it is produced

page_text: or collected to houses workshops and mills where it is required. In effecting
these objects the lines of transmitting shafts (and rectilinear transmitters where
used) will probably be at some part of their course high in the air and at
others perhaps underground and in other positions not easily accessible for oiling
and cleaning. Also at certain distances along the line of transmission it may
be necessary to reconvert the rectilinear motion of the transmitting shafts into
circular motion and back again into rectilinear motion to other shafts. To meet these
requirements; firstly the bearings of the revolving and oscillating parts of the
clavigers employed in these positions are made, by means of a new invention so as
to be absolutely free from sliding friction and hence not requiring lubrication.. In
addition, though equally as strong and certain in action as plain bearings, they are
made proof against the intrusion of rain and dust. The wear in these bearings is
extremely small resulting from rolling resistances alone, without any interfriction
of the parts, so that attention is required but seldom. As this bearing is a separate
invention and is applicable to other purposes a separate application for letters
patent will be made for it.
The second requisite is to support the transmitting shafts securely so as to
allow of their freedom of movement without needing lubrication of the bearings.
As the strain of transmission is by tension only, the transmitting shafts may
be light, even for transmitting great power. Shafts of joined lengths of weldless
steel. tubing are preferably used. A shaft of 2 inches diameter, containing in
cross section 1 circular inch in area of solid metal should be sufficient for
transmitting the greatest amount of motive power ordinarily required. A shaft
of this dimensions is capable of sustaining a steady pull of about 15 tons, without
sensible alteration, so that if it be pulled with this force endways at the rate
of 1 foot per second it will be transmitting work at the rate of 15 foot-tons
per second.
Now if the crank on the power shaft revolves at the rate of
say 120 revolutions per minute and the force be transmitted from a balanced
crank or disc with crank wrist, 4 feet from centre to centre by means of
clavigers having clavis rods 8 times the length of crank, the transmitting shafts
will be capable of transmitting 90 horse power per second with the same safety as
the 15 foot-tons were transmitted. If the traverse be made twice the length by
doubling the size of the crank and claviger, the same transmitting shafts will
transmit 180 horse power per second with the same strain and so on according to
the length of traverse and the rate of revolution of the power shaft. The supports
required for the transmitting shafts have no strain put upon them by the force
transmitted. Their sole office is to support the weight of the line of transmitting
shafts so as to prevent sagging, and side swaying from the effects of wind. For
this purpose at proper intervals along the line of transmission the transmitting
shafts pass through metal boxes which are supported and held rigidly in position.
The inside length of these boxes is half the extent of the rectilinear movement of
the shaft. The bottom of each box inside is shaped so as to consist of two planes
intersecting each other at an obtuse augle; the intersection running longitudinally
along the centre. The top of the box is moveable and forms a lid. When the
box is supported from below or from the sides, the lid fits flat upon the top and
is secured in position by bolts and nuts with adjusting set screws. When the box
is supported from above the top, the bolts of the lid pass through lugs fitting
between the upright attaching arms. The under part of this lid consists of two
planes exactly corresponding with those at the bottom but opposite in direction.
The portion of the transmitting shaft which passes along any part of the interior
of the box has brazed or otherwise suitably fixed round it a solid piece of metal
having its upper and lower sides shaped to correspond with the inside top and
bottom of the box but the planes are opposite in direction. The sides of the metal
piece and the inside sides of the box are vertical and parallel. If the shaft be now
inoved backward and forward horizontally it passes along the box without touching
any part of it. Between the metal shaping of the shaft and the box two spheres
of hard wood or metal are placed one above the shaft and one below. The shaft

page_text: rolls upon these balls, which travel backward and forward along the length of the
If there
box and keep the shaft steady against movement in any other direction.
is a likelihood of the shaft having to sustain at times great lateral pressure from
wind, the sides of the box and of the metal shaping on the shafts are made to
correspond with the top and bottom and two additional spheres are used, one at
each side. This supporting box is described as a necessary auxiliary for the
effective working of the transmitting shafts under the conditions described, but no
claim will be made in respect of it herein.
In some cases a telescoping adjustment is arranged for very long lengths of
shafting to allow for expansion and contraction due to change of temperature.
When very long lengths of shafting are used there is a temporary extension of
length due to elasticity. This is reduced and compensated for when the second
claviger of each set comes into action before the action of the first is ended. The
effect being a slight variation in the uniformity of the motion. The length and
weight of the connecting shafts can be increased within very wide limits without
their momentum injuriously affecting the motion.
When the limit of the traverse
is being approached the efficiency of the momentum is greatly decreased by the
leverage of the clavis rod and is absorbed by its means to assist the movement of
the crank. The result is the claviger and transmitting shaft slow down before
reaching the limit and then return with an outward curve, thus avoiding the shock
which would be the effect of suddenly reversing the direction of the motion. The
effect of excessive momentum in the transmitting shafts is not to waste force but
to affect the uniformity of the motion. When this occurs it is remedied by more
frequently re-converting the motion to circular thus shortening the lengths and
increasing the number of the transmitting shafts.
50. Another method of transmitting circular motion is effected by attaching to
each shaft a claviger couple in the manner represented in Plate 6, Fig. 1. The
arrangement there shewn is exactly duplicated at each end and the parts placed
in the same relative position with respect to both shafts. The end A of the clavis
rod A B is then connected by means of a claviger couple with the corresponding
end of the claviger couple on the opposite shaft. The end C of the clavis rod B Č
is also connected by a transmitting shaft with the corresponding end of the clavis
rod of the similar claviger at the other end of the transmission. The transınitting
shaft is equal in length to the distance from the axis of one shaft to the axis of
the other. By the arrangement just described the circular motion of the power
shaft is perfectly transmitted to the receiving shaft, the rotation of both being in
the opposite directions.
51. The Transmission of Circular Motion direct from one shaft to another.
Class B. The method of effecting this without first converting the circular motion
into rectilinear has been described in article 3 and is illustrated in Plate 25 Fig. 1.
It represents a right claviger couple attached by its ends to two cranks on parallel
shafts. The centre pivot is a fixed axis, situated half way between the two shafts
parallel to them, and in the same plane. More rods may be added to give
additional strength for transmitting great power. The transmission of the force is
subdivided among the rods however many may be used. In this way any desired
strength can be obtained. The movement of each pivot is only a small fraction
of a revolution and of course the total friction is not increased by multiplying
the rods and pivots as the total friction is subdivided as well as the force and in
the same proportion. All double claviger couples, however the rods may be built
together, if the fixed axis is in the centre and one half of the couple is a duplicate
of the other half reversed, are in equilibrium in every position and throughout
every movement so that no force is wasted in moving them.
Their movement when transmitting circular motion is oscillating combined with
a lengthening and shortening of the span.
52. The Transmission of Circular Motion, to the various parts of Complicated
Machinery &e round corners when framework and other parts of the machinery

page_text: intervene. The means of effecting this consists of a chain of claviger couples. A
crank at each end of the chain only is needed. One crank is attached to the power
shaft and the other to the receiving shaft. There are no guides or supports in the
chain but the fixed studs supporting the centre axes. The chains may be of any
length and placed in any direction. The claviger couples are preferably pivotted
together by coned pins with screws washers and nuts at both ends. When the
motion is transmitted horizontally, the pivot connecting the two clavis rods of each
couple is provided with a roller which runs along a support of the proper shape.
This is to obviate side strain upon the fixed studs. In constructing the chain it is
necessary to place the couples correctly in position. The centres of the circles to be
described by each end of every claviger couple must be in a line with the fixed axis,
and each claviger couple must have more than sufficient span to reach at the same
time the furthest parts of both circles. Circular motion is in this manner perfectly
transmitted to any other crank in the same plane round any intervening obstacles.
It may similarly be transmitted to a crank or cranks in any position in a parallel
plane by interposing at some point in the chain a transverse shaft of the requisite
length supported in bearings in a position perpendicular to the two planes. Tho
shaft has a single crank at each end, one of which receives the motion and the
other transmits it; or the motion may be received by a double crank on the shaft
and transmitted at both ends or from any part of its length. Other claviger
couples or chains of claviger couples may be attached to any of the pivots con-
necting the claviger couples together in the original chain to carry the motion in
other directions. These subsidiary chains can be made to vary the number of
revolutions while transmitting the motion so as to suit the requirements of the
different parts of the machinery. The means of effecting this will be explained in
its proper section.
53. Plate 11, Fig. 3 represents a claviger couple for transmitting circular motion
from one shaft to another not opposite to it, the crank pin circles being in parallel
planes. Each shaft has a single crank at the end nearest to the other shaft. The
crank pins are free to revolve in the ends of the cranks which are shaped into a
bearing for them and are each held in position by a shoulder and nut. The crank
pin is cranked at its end to a right angle, and these form studs upon which the
ends of the claviger couple are centred. The centre pivot S of the couple is a stud
projecting from a short shaft p which revolves in the fixed bearings m, n and is
held in position therein by the two shoulders shewn.
54. Plate 22, Fig. 3 represents another form of claviger couple for transmitting
circular motion in the saine direction. The ends of the clavis rods are forked and
are each centred on two studs projecting from opposite sides of a moveable crank
pin, or as shewn in the figure to two studs on a collar free to turn on a fixed crank
pin. The centre pivot a is a stud projecting from a ring or collar piece c which is
free to turn upon the tixed cylindrical rod pr and is held in place upon it by a
shoulder S and a nut n. The common pivot of the clavis rods is formed by two
studs projecting on opposite sides from a ring or collar piece & free to turn round
upon and slide up and down the rod pr. The ends of both clavis rods at y are
forked and are attached to the studs on both sides and are free to turn upon
then, or the rod pr may be free to move up and down in fixed bearings with
the two clavis rods centred on two studs projecting from it, and the collar carrying
the centre pivot loose upon it. This forin of claviger couple is suitable for com-
posing chains of claviger couples for transmitting circular motion in a horizontal
direction round obstacles &c as explained in article 52.
55. Plate 10, Fig. 1 represents two cylinders rotated in the same direction. Two
studs a and c project from the ends of the cylinders. They are connected by a
claviger couple abc having its fixed axis S supported by the framework in a line
with the line of contact of the surfaces of the two cylinders. The motion is
transmitted from the power shaft by a claviger couple connected to a crank on it
and to one of the studs a or c lengthened for the purpose. The cylinders may be
of different sizes.

page_text: 56. Plate 10 Fig. 2 represents a similar movement, but the motion of the two
cylinders is in opposite directions. The two studs a and c at the ends of the
cylinders are placed so that a line joining their centres shall coincide with or be
parallel to a line joining the centre of the ends of the fixed axes of the cylinders.
The centre pivot S and the common pivot 6 of the two clavis rods are studs
projecting from two rectangular blocks which move up and down in the fixed
straight slide m n. The centre of the slot in the slide is in the same plane as the
line of contact of the surfaces of the two cylinders and is perpendicular in direction
thereto.
57. Plate 22, Fig. 4 represents an arrangement for rotating a long line of
spindles by one movement. The claviger couple a b c is connected to two
double crauks va and vc on two vertical shafts and v' each turning in deep
bearings w. One of these vertical shafts receives circular motion from the
power shaft through a crank not shewn, below the bearing. The upper bend of
the double cranks are cranked again so as to bring the ends in a vertical direction.
The centre of these vertical ends m and n are a short distance laterally from the
axes of the vertical shafts and are in the same direction so that the upper part of
one of the double cranks is shortened and the upper part of the other is lengthened.
The two cranked ends m and thus form two short cranks m v and n v' rotating
in the same direction and parallel to each other. They are connected together
by the straight flat rod rt. At equal distances along this rod it is pierced by
holes through which are passed the crank pins of the double cranked spindles &² 8²
838&c, all placed in the same direction. The spindles turn in fixed bearings
above and below the rcd. When either shaft vor v is rotated both turn
together in unison and rotate all the spindles on the rod simultaneously. The rod
may be conveniently fixed if made in two pieces the division being longitudinally
along the centre. When placed in position the two pieces can be securely attached
by screws, or by clamps at each end r and t. The cranks on the spindles are the
same length as the short end cranks m v and n v.
58. Plate 22 Fig. 5 represents a claviger couple adapted to rotate a number of
cranked shafts situated in the samne plane, and parallel to each other. The claviger
couple is built up with parallel rods sufficient in number to furnish two for the
fixed axis S and one for each of the cranks. The cross rods are extended so as to
reach the cranks, which are of different sizes. The two outer cranks and the two
outer rods in the claviger couple regulate the position and length of the others.
The distance between the cranks may be variable in which case the lengths
and arrangement of the rods and the lengths of the cranks must correspond.
If any one of these shafts is rotated it transinits the motion to all the others and
they all rotate in the same direction simultaneously.
59. Circular Motion transmitted from one shaft to another not parallel to it,
both shafts being in the same or in different planes. Plate 11 Figs. 1 and 2
illustrate the manner of employing claviger couples to transmit circular motion
from one shaft to another shaft situated in any direction. The centre locus of the
circumference of the two crank pin circles described by equal sized cranks upon
any two shafts however situated is either a point or a straight line. The zero
points are taken on the two circumferences at the points which are nearest
together and the points which are furthest apart. Fig. 1 represents the claviger
couple connected to two cranks on two shafts in the same plane perpendicular to
cach other. The ends a and c of the claviger couple a bcs are forked and
centred on two projecting studs on the pins g h and m n which pass through
bearing holes in the forks of the forked pieces e and f. The shanks of these
forked pieces pass through bearing holes in the cranks r t and p³¿ in the position
of crank pins. This arrangement of joints allows free rotary movement of the
pivots a and c in three directions at right angles to each other. A rod m¹ n' whose
axis coincides with the line of the centre locus is free to turn and move up and
down in the fixed bearings wand w¹. The centre pivot S of the claviger couple
is a fixed stud projecting perpendicularly from the rod m n.
When the arrange-

page_text: ment is placed in position and fixed as shewn in the figure and one of the shafts
is rotated the circular motion is perfectly transmitted to the other shaft, though it
may be at any angle in any plane, and the two shafts move in unison. During
the movement the rod m' n has a motion of partial rotation on its axis and moves
endways up and down in its bearings. Fig. 2 represents an alternative method of
attaching the claviger couple to the cranks, which is effected by means of ball and
socket joints.
60. Circular Motion transmitted from one shaft to another in the same line. The
arrangement shewn in Plate 11, Fig. 4 is to avoid the great torsional strain upon
the shafting when circular motion is transmitted by a long shaft rotating on its
axis. The motion can be transmitted entirely by the arrangement shewn or it can
be alternated with lengths of rotating shafting. a b is a lever which for part of
its length at the centre may be double as shewn in plan view fig. 5. Its fulcrum
is formed by two short projecting arms o o¹ of the short shaft 8s and projecting
perpendicularly from it. The short shaft se is free to rotate in the fixed bearings
and 2 and it is held in place by the shoulders and and by the nut n.
The
lever ab is pivotted at its centro upon the arms o o. The lever at each end
passes through bearing holes in the ends of one or or two cranks as shewn in the
figure. These bearing holes are inclined at an angle to the line c d. A line passing
through the centres of these bearing holes of both sets of cranks at both ends
of the lever passes through the point of intersection of the axis of the arms of o o¹
with the axis of the shaft s s. When either crank shaft is rotated the lover a b
has two movements in a direction at right angles to each other it moves up or
down upon its pivots at o and o' and it partly rotates upou the axis of the short
shaft 8s. The crank ends turn once, at every revolution of the shaft, round the
lever ends which pass through the bearing holes in them, but there is no sliding
movement of the lever in them. The motion is thus perfectly transmitted to the
other shaft. During the movement the centre line of the lever generates a conc
of two equal nappes of which the point of intersection of the axis of o o' and 8 s
is the common vertex.
61. Circular Motion transmitted from one shaft and reversed in direction to
another shaft in the same line, and closely contiguous to it. Plate 15. Fig. 3. Two
shafts S and S' are in the same line with their ends sufficiently far apart to allow
of the passage between of the parts to be described. Two single cranks S x
and Sy are on the ends of the two shafts. Between them there is fixed a straight
slide m n.
Two clavis rods A B and C B are pivotted at their centres x and y
on the two cranks, which thus form the two restraining arms for the claviger
couple A B C. Both clavis rods are between the cranks and they are pivotted
together at B B by a short rod which allows a space between them slightly longer
than the width of the slide. The centre longitudinal line of the slide cuts a line
joining the axes of the two shafts and these two lines are perpendicular to each
other. The slide is cut through at its centre to allow passage of the rod or
pivot B B. The outer ends A and C of the clavis rods are each pivotted on a
stud projecting from a block. The studs are on opposite sides of the slide and the
blocks are arranged to pass each other in the slide during the movement. When
the power shaft, say S is rotated say in the sense of the arrow, the crank on it
during its revolution carries the centre of the clavis rod round with it, the end A
moves along the line S m while the end B moves in a straight line along B S.
When the end A has reached its limit towards m the end B is at the centre line S.
While A is returning to S the end B is moving upward beyond S in the opposite
direction. When the end A reaches the centre S, the end B is at its highest point.
While the end A is moving to its limit towards n the end B is returning towards
the centre S. Similar relative motions complete the revolution. During tho
movement the end B carries with it the end B₁ of the other clavis rod giving
throughout exactly the same motion reversed to the crank S¹ y on the other shaft
and causing it to revolve in the opposite direction. The blocks are sufficiently
long to allow their safe passage past the cut out part of the slide. The quality

page_text: of the motion of either of the cranks and of either the ends A or C and of the
end B is exactly the same as shewn in Plate 6, Fig. 1 which illustrates a different
novement.
62. Circular Motion is also equally well transmitted by the claviger couple from
a crank in a shaft turning in fixed bearings to a crank in another shaft which has
a traversing movement or any other movement of translation in addition to the
movement of rotation to be given by the claviger couple. To effect this the centre
pivot is constrained by any of the methods previously described to nove along the
centre locus between the line of motion of the shaft and the centre of the crank
pin circle of the fixed shaft. The motion of the centre pivot along this locus
does not affect the transmission of the circular motion in any way.
63. Universal Transmitter.-Plate 22 Fig. 1 represents a claviger couple a b c s
with double restraining arms, the centre pivots are two studs or wrists projecting
at right angles from a short shaft free to rotate in the fixed bearings m and m¹ and
held in position therein by the shoulder and the nuts n and n¹ or by any other
equivalent means. Any movement in any direction given to one end of the claviger
couple is exactly reproduced at the other end reversed in direction.
64. When the claviger couple has a fixed axis for its centre pivot it will transmit
motion reversed in the same plane. Thus if a pencil be fixed in each of the ends
of a claviger couple, the points of which rest upon two slates, and a message be
written upon the slate at one end, the writing is exactly reproduced at the other
end but upside down. If the message be written on the slate in vertical lines
commencing each line at the bottom, it will appear at the other end in vertical
lines with the commencement at the top and can thus be easily read.
claviger couple moving horizontally the message is transinitted correctly for
reading when the transmitter and receiver face in opposite directions. By means
of the chains of claviger couples previously explained the writing can be trans-
mitted to moderate distances, and increased or reduced in size by employing
claviger couples with unequal limbs.
With a
65. The universal transmitter described in article 90 can be similarly employed
to reproduce casts models &c. When made with unequal limbs the transmitter
will exactly reproduce models for statuary &c in any size required.
66. It was omitted to be stated in article 25 in the description of Plate 17 Fig. 3
that the arrangement of two clavigers there illustrated for transmitting rectilinear
motion along a straight line in a direction at right angles will transmit the motion
along a straight line at any angle according to the position of the fixed axis S
along the semicircular line s¹ sx¹. The angle the line of traverse of the end C
makes with the line of traverse of the end A when both are produced till they meet
is the same angle made by a line joining SO with a line joining S₁ O. The length
of the lines traversed by the ends A and C varies according to the position of S
along the are s¹s x. When the fixed axis S is in a line with S and O both lines
of traverse are nil as the length is reduced to a point only; when both the fixed
axes are at S¹ the length of each line of traverse is four times OB; this position
is shewn in Fig. 1. The length of the line of force transmitted can be varied by
lengthening the rod O B and attaching to it another stud on which the second
claviger which is of proportionate size to the lengthened radius rod is centred.
67. Continuous Circular Motion converted into Oscillating or vice versa.
Class B. Plate 26, Fig. 2.-A shaft O rotating in the fixed bearing W has a
single crank O C at one end. Closely contiguous to it and in the same line is
another shaft O¹ with a single crank O'R at its near end, or the cranked rod O'R
may be centred on a fixed axis in a line with the axis of the shaft O. Circular
motion is given to the crank OC and it is required to oscillate the rod O' R. Any
number of oscillations for one revolution of the crank may be obtained. When the
number is determined upon the circumference of the crank pin circle is divided
into the same number of equal parts. An arc e f is then described by the end R of
the oscillating rod O' R in the circumference. In the figure one. revolution of the

page_text: crank is represented as changed into four forward and four backward oscillations
of the rod. The rod O¹ R has two studs or crank wrists projecting from it, one at
its centre and the other at the end R. The wrist at z has centred upon it a
wheel or a system of rigid cross rods or any efficient equivalent arrangement for
carrying four studs upon which are centred four rollers ¹² 34. The radius
from the centre of each stud to the centre of the wrist is half the length of the
crank OC. The studs correspond in position to the four divisions in the crank
pin circle. The number of studs carrying rollers are the same as the number of
complete oscillations of the rod 01 R per revolution of the crank. A right
claviger couple R BCS of sufficient span is attached to the crank at the end C
and to the wrist R on the rod O R. Its centre pivot is one of the studs, extended
in length, which carry the rollers. A centre locus is taken between the two
complete movements of the points C and R. An outer guide mn whose inner
bearing edge is parallel to the centre locus and distant therefrom the radius of
the rollers is fixed in position round the centre locus and the four rollers.
When the crank is rotated in either direction its circular motion is perfectly
converted into the oscillating motion of the end R of the rod 01 R along the arc of
and the velocity of both is uniform. The rollers revolve round the centre at the
same rate as the crank, and the lines is always parallel to or coincident in
direction with the crank CO. The wheel and rollers run easily round the guide
and the rollers are always in contact with it.
68. Continuous Circular Motion converted into Reciprocal Rectilinear, any number
of reciprocal strokes of any length per revolution. Class B.-The traverse of the
end R of the claviger couple in the movement described in the preceding article
may be backward and forward in a straight line instead of along the arc ef. In
that case the rod O R is dispensed with. The wheel and claviger couple remain
but the centre locus is slightly changed and therefore the fixed guide is made to
correspond. The claviger couple R BC has for its centre pivot the same stud but
it is placed behind the guide instead of in front of it as represented in Fig. 2. A
second claviger couple has one end centred on the shaft O close up to the crank and
is carried down in front of the guide and the lower ends of both claviger couples
are pivotied together at R. Its centre pivot is a stud at z at the centre of the
wheel. This stud passes through a rectangular block which moves along a fixed
straight slide set parallel to the line of traverse of the end R. The length of the
line of traverse of R may be increased to any extent (without altering the crank
wheel or fixed guide) by employing claviger couples with unequal limbs. The
motion is perfectly converted.
69. The Pendulum and Works of a clock connected by direct notion. Plate 31
Fig. 1.
An axis O rotating in fixed bearings is connected with the mechanism
supplying the power. It is bent at the end into the single crank 0 C. Another
axis in a line with it is connected with the train of the clock. It is bent at
the end into a single crank OE of the same length as O C. The two cranks face
each other and are in position when set 180° angular distance apart. Between
the two axes and cranks the pendulum yz is hung, the centre of its support y
being in the line of the axes. A convenient length of the pendulum y R is taken
and at that point two studs are fixed in the pendulum on opposite sides parallel to
the line of the axes O and O. Midway between y and R a bearing hole wis
made through the pendulum; through this hole the cranked piece m wn passed.
The length of w m or wn is half the length of the crank O C or O¹ E. It has a
crank wrist at each end set in opposite directions. RBC is a claviger couple
centred at one end on the crank O C and at the other on the stud R. Its centre
pivot is the crank wrist . Another claviger couple R B E has one end centred
on the crank E and the other on the stud R¹ on the opposite side of the pen-
dulum to R. Its centre pivot is the crank wrist m. The wrists m and n are
provided with rollers. The circumference of the crank pin circle is divided
into any number of equal parts, the zero points being the two points on the
vertical diameter. The are described by the point R during the vibration of the

page_text: pendulum is marked. A parte rather less than. the whole, is taken equal
in length to half the circumference of the crank pin circle. It is divided both
ways into the same number of parts as the circumference. The divisions mark
the position of the point R at equal intervals of time during the time of oscillation,
or it may be divided into equal parts as shewn in the figure. A double centre
locus is taken as described in article 21 and two fixed parallel guides g g¹ and
h h¹ placed in position as described in that article. The ends of the fixed guides
are however left open sufficiently wide for the rollers to pass out for a certain
distance. The arc ei is now extended to and g and the lengths pe and ig are
divided in the same manner as the length e i. A double centre locus is taken
between them and the zero points in the circumference C¹ C. The fixed guides
are carried along one side of this additional double centre locus. When the cranks
are rotated in the sense of the arrow, the guides are extended on the sides shewn
in the figure. If rotated in the opposite direction they would be on the other
side of the line. The crank OC on the axis O is connected with the weight
while the crank O¹ E on the axis O' is connected with the train, and the pendulum
is between them connected to both. The weight, resistances, and pendulum are
nicely adjusted together so that the cranks make one revolution in rather less than
a second. During the time of oscillation the cranks make half a revolution and
are held motionless for a small fraction of a second before the next half revolution
during the next oscillation is made. The arc traversed by the point R is by con-
struction longer than the arc ei and it is only during the time the pendulum is
oscillating between e and that the cranks can move. During the time the small
parts of the arc between ep and ig are traversed the crank OC is held against
the pull of the weight by the rollers on the cranked piece running along the
profiles of the fixed guides parallel to the parts of the centre locus between the
points marked 0. This is effected without any stress upon the pendulum and it
is as entirely free in its swing as if unconnected with any other movement. The
crank OC by means of the claviger couple R B C exerts upon the pendulum, while
it is traversing the are ei the full pressure which it obtains from the weight while
the claviger couple R' B E transmits the power to the crank E O' to be conveyed
by the axis O¹ to the train of the clock. The pendulum is thus placed between two
equal pressures viz that of the weight and that of the resistances. The two claviger
couples in every position are in equilibrium and are equally balanced upon the
pendulum. Now if through any cause the weight slightly exceeds the resistance
the pendulum is moved more quickly along the arc and the crank O C makes half
a revolution in a correspondingly shorter period but this is compensated for by an
increased amplitude and consequently a longer interval of time during which the
cranks are at rest. On the contrary if the power is somewhat short of the exact
amount the amplitude is less and the interval the cranks are at rest corresponds.
In this way by delicate adjustment, a perfect compensation may be obtained. The
pendulum is in equilibrium between the power and the work and regulates and
controls them by compensating for a slight variation in the equilibrium by a
corresponding variation in the arc described. The action of this pendulum is
noiseless.
70. The following remarks in this article, should have been inserted in
article 51. When circular motion is transmitted between two shafts situated
a considerable distance apart by a right claviger couple of equal or unequal limbs
it is desirable that the length of the clavis rods should be in a certain fixed ratio to
the distance the shafts are apart. If the clavis rods are made only slightly longer
than is necessary to span the distance between the crank pins when they are
furthest apart the common pivot of the two clavis rods has an unnecessarily long
range of motion and has a velocity at some parts of its course considerably greater
than the velocity of the crank pin. The claviger couple is in this case propor-
tioned in the best manner when the movement of the common pivot of the clavis
rods is nearly circular and of about the same length as the circumference of
the crank pin circle. To effect this the clavis rods should be in the following

page_text: proportion. Let d =
distance between the axes of the two shafts. The length of
2
each clavis rod is v
71. To Multiply the number of revolutions. Plate 14, Figs. 1 and 2. Fig. 1
shews an clevation of the arrangement and Fig. 2 the geometrical lines of, the
movement. Two cranks AP and C W on the shafts P and W are connected.by
the claviger couple A B C S. A third shaft F is placed half way between the
shafts P and W and parallel to them with the axes of the three shafts in the
same plane. The three shafts are free to rotate in fixed bearings. The shaft F
carries at its end the straight slide m n rigidly fixed to it in a line with the
two cranks. The centre pivot S of the claviger couple A B C S is a stud pro-
jecting from a block fitted to move along the slide. The scope of the movement
of the stud S along the slide is the length of the diameter of either of the
crank pin circles, when the cranks are equal in length. If the cranks are
of unequal lengths it is half the sum of their lengths. The parts are placed
in position as shewn in Fig. 2. Let the shaft P be the power shaft. It is con-
nected with the shaft F by any of the arrangements herein described so that when
the shaft P is rotated in either direction the shaft F will be rotated with the same
velocity in the contrary direction. Now when the shaft P is rotated say in the
sense of the arrow, the crank A P carries the end A of the claviger couple round
with it in one direction while the slide m n carries round the centre pivot S in
the contrary direction with the same angular velocity. The effect upon the
crank CW through the other end C of the claviger couple is that it has an
angular velocity given to it of three times that of the crank A P. The centre
locus described by the point S during a complete movement is shewn at Fig. 2.
This represents the crank shaft F carrying the slide as being rotated twice to every
revolution of the shaft P. This gives 5 revolutions of the shaft W. The centre
locus is a symmetrical figure composed of six elongated hypocycloids with the
multiple point in a line with the axis of the shaft F. This figure may be described
by a point on the circumference of a generating circle, whose diameter is equal to
the length of the crank A P, invariably connected with another circle concentric
with it, whose diameter is one fifth the length of the crank C W, the latter circle
rolling along the concave side of the circumference of a directing circle whose
diameter is equal to the sum of the diameters of the other two.
Any uniform angular velocity may be given to the shaft F, greater or less than
the velocity of the shaft P. The shaft W and the shaft P have in all cases a
constant velocity ratio, and the locus described by the point S corresponds. In
a given time the number of revolutions of the crank C W is equal to the number of
revolutions of the crank A P plus twice the number of revolutions of the slide m n.
When the cranks are not equal in length a claviger couple of unequal limbs must
be employed. The movement represented in the figure is that of a claviger couple
of the first kind. The movement is equally effective with claviger couples of the
second and third kinds. In some cases the shaft W would require a flywheel.
72. To Double the number of revolutions. Plate 12, Figs. 1 and 2 and Plate 13,
Figs. 1, 2, 3. Plate 12 Fig. 2, shews the geometrical lines of the movement and it
will be convenient to explain it first.
From the centre b at the distance b x describe the circle c x d. From the
same centre with the distance b y, which is twice the length of b x, describe the
circle f y c.
From the centre b draw the radius line b c. Bisect the line b c at a.
From the centre a at the distance a b describe the circle c w b. Divide the
circumference cwb into any convenient number of equal parts, and the circum-
ference fye into twice the same number of equal parts, number the corresponding
points, as shewn in the figure. From each point in the circle cwb draw lines of
the same length as the radius by in a direction towards the corresponding points
in the circle f y e. When the lines are not long enough to touch the corresponding
points they must be drawn to the radius line upon which the corresponding point 5
is situated. Each of these lines is bisected by the circumference cx d. Join the
"

page_text: points in the lines made by the intersection with them of the circumference with
the centre b. Join each point of division along the circumference cwb with the
centre a.
The figure will then represent the position of the different parts of the
arrangement at equal intervals of time during the movement. At e and f the lines
touch the circumference while at y' and b' they are at their furthest point from it.
The locus of the ends of these lines is a double reversed contracted epicycloid
scarcely differing from an ellipse with e f for its major and b¹ y¹ for its minor axis.
Reference is now made to Fig. 1. The same letters of reference represent the same
positions as in Fig. 2. The centre a is the centre of a shaft and the radius ab is
the length of a single crank a a¹ upon it. The lines c b¹ and cyl in Fig. 2 are
represented in Fig. 1 by the clavis rods a¹ b¹ and a¹ y attached to the crank a a¹;
the radius lines b u and bv in Fig. 2 are the restraining arms bu and bvin
Fig. 1. The four rods thus form the right claviger couple, with equal limbs, b¹a¹
yb and the crank pin at a¹ is the common pivot of the two clavis rods. The
The centre b
centre 6 in Fig. 2 is the centre pivot or axis for the restraining arms.
is also the centre of another crank shaft B carrying at its end rigidly attached to
it the bar ef whose length is equal to the line o o¹ Fig. 2. The two shafts a and B
have their axes perpendicular to the plane of the figure and in opposite directions.
from it. The single crank and the bar are at the ends of the shafts face to face.
The ends e and fof the bar are connected to the ends b' and y¹ of the claviger
couple by the connecting rods e bland fy. The bearings of the two shafts are
marked r and s. The centre pivot b is a continuation of the shaft B, narrowed in
diameter. Now when the shaft B is rotated in either direction the motion is
transmitted to the crank a¹ a causing it to make two revolutions for every
revolution of the bar e f. The force is delivered to the crank is a full tangential
impulse all round and the motion of the crank has very nearly a constant angular
velocity ratio of two to one to the motion of the bar. The variation is so minute
There is no fixed
as to be inappreciable. This movement is a very desirable one.
part except the fixed bearings r and s of the two shafts. The movement and
consequently the friction of the joints is much less than would appear at first sight.
Half the force is transmitted by each claviger which for estimating the friction is
the same as if all the force passed through one claviger. The total movement
revolution,
of the crank end of the clavis rod upon the crank is one half of
while the crank is inaking one revolution; during the same time the movement
on the pivots b, v and y¹ are each one sixth of a revolution. But only the
half of the force due to leverage affects the friction of the pivots band v, so
that the total friction for the movement is less than the friction of one revolution
of one pivot under the full stress of the force transmitted during one revolution of
the crank a a¹. The crank shaft a may be provided at its other end with a bar
similar to that on the shaft B and the motion delivered again doubled in velocity to
a third cranked shaft and so on within a short distance the velocity can be doubled
each time and a very high velocity reached. For reducing the number of
revolutions the crank shaft is employed as the power shaft. Plate 13, Fig. 1
illustrates the perfect form of this movement. In place of the connecting rods
the claviger ends are pivotted on two studs carried by two blocks sliding in short
alots towards the ends of the bar which is lengthened for the purpose. Fig. 1
represents the movement a quarter turn of the crank further forward than in
Fig. 1, Plate 12. The angular velocity of the crank to that of the bar in the
That this is
movement represented in Fig. 1 has a constant ratio of two to one.
so may be shewn as follows. As explained in the opening article the ends of a
right claviger couple with equal limbs are always in a line with the centre pivot,
the two ends of the claviger couple represented in Fig. 2, Plate 12 are therefore
always both on the same diameter. The angle made by a line drawn from the
common pivot of the two clavis rods (in this case the crank pin a¹) to the
centre pivot b make a right angle with the diameter upon which the ends of
the claviger couple are at the instant touching, and this is the case in every
position. Let the line bo in Figs, 4 and 5 represent the radius eb of the

page_text: circle fye (Fig. 2, Plate 12) and the line o s the radius b a of the circle c w b
The axes of rotation o and s are perpendicular to the plane of the figure. Let
the lines bo and os be the initial positions of the radii and let o be the
position of the longer radius at the end of a certain interval of time. As the
angle bo m must by the construction be a right angle the position of the smaller
radius at the end of the interval will be m s. The angle m so is twice the size of
the angle bob and this is the case for any movement during the whole revolution.
The motion of the radius m 8 has therefore a constant angular velocity ratio of two
to one to the motion of the radius bo. That the angle m so is twice the angle blob
may be proved in the following manner, leaving out steps in the reasoning which
are apparent. Bisect the line mo at n, draw the perpendicular n 8 bisecting the
angle m s 8 0. The angles bo'b and mos are together equal to a right angle; and
the angles n so and mos are together equal to a right angle; therefore the
angle bob is equal to the angle m so. But the angle n so is half the angle m80;
therefore the angle bob is half the angle m s o, and the line n s is parallel to the
line bo. It is also evident from this proof that the two radii may be any length
relatively to each other. The practical effect of this is that the bar and claviger
couple may be any convenient length relatively to the length of crank. The
essential point is that the crank and shaft shall be so proportioned and placed in
position that the projection of the axis of the shaft carrying the bar shall touch
the circumference of the crank pin circle and be in direction perpendicular to
its plane.
73. To Multiply or Reduce the Number of Revolutions of a Shaft. In all the
movements of this section the axes of the two shafts are in a straight line and the
two contiguous ends terminate in single cranks facing each other with just
sufficient space between for the free passage of the rods connecting the two cranks
together. The crank pin circles are concentric with each other, or stated more
exactly the centre lines of the two crank pins describe two cylinders which have
their axes in the common projection of the axes of the two revolving shafts.
In describing the various movements in connection with this invention the method
of attaching the rods together as represented in the figures is explained for clearness
but not with the intention of limiting the movements to those exact details of
construction. The method of pivoting together may be varied and at the point
of connection either rod may revolve upon the other or any other open effective
method of connecting the rods together may be employed to carry out the principle
practically. In describing the following movements the relative lengths and
positions of the parts are those which are most advantageous for the movement
and it is to be understood they may be varied as previously explained when
describing the principle of the claviger power in connection with other move-
ments.
74. Plate 26, Fig. 1 illustrates an arrangement for multiplying or reducing the
revolutions of a shaft by means of claviger couples of the first kind. The shafts
are situated as described in article 73. The shaft 0 terminates in the single
crank OE. The 'shaft O' carries the bar D F rigidly attached to it at the end
facing the crank. The proportions designed in the figure are to multiply or reduce
in number the revolutions of one crank when transmitted to the other in the ratio
of six to one. The length of OD or O F being each half the bar is six times the
length of the crank O B. At the ends of the bar are two crank wrists D and F.
Half way between the centre and the ends are two other studs or crank wrists C
and E. On C and E are pivotted two single cranks Cx and E y, each half the
length of the crank O B. Two right claviger couples Dc B and Fe B' have their
ends B and B centred upon the crank pin of the crank O B, their other ends F
and D are each pivoted on the studs F and D at the ends of the bar. The centre
pivots of each claviger couple are respectively the crank wrists x and y. These
two crank wrists are supplied with rollers. The centre locus is a symmetrical
figure composed of- five common epicycloids, a fixed guide g g is placed in position
within it, with its outer profile parallel to the locus. Either shaft may be the.

page_text: power shaft and may be rotated in either direction and the motion is transmitted
to the other rotating it in the same direction"with a constant angular velocity
ratio of six to one or one to six as the case may be. It is a perfect movement.
When the ratio is 3 to 1, 5 to 1 or any other odd number to one, the bar is bent
to an angle so as to reach two corresponding points as nearly opposite as possible.
75. Plate 15 Figs. 1 and 2 represent another variety of this movement, more
particularly adapted for speeding up. Fig. 1 is a side elevation with one of the crank
shafts cut through, and Fig. 2 is a front elevation of the movement when both
cranks are for an instant in the same plane, the fixed guides being cut through in the
plane of the cranks and represented in section. The same letters of reference apply
to the same parts in each figure. Two shafts and O¹ are in a line and each
terminates in a single crank O Band O¹ S. A claviger couple a c be has one end b
centred upon the crank pin B, the other end a is bored out to accommodate the
rod or short shaft A' A which is partly passed through it and rigidly fixed into it
about the centre. This rod or short shaft forms the axle for two rollers r¹ and r
which are free to revolve upon it. The centre pivot of the claviger couple is the
crank pin S of the crank O' S. The fixed bearings of the shafts O and O' are
respectively marked'm and n. The restraining arms of the claviger couple are's y¹
and a r¹ and are pivoted respectively on the fixed studs y and z projecting from
the centre of the clavis rods b c and a c
The common pivot of the clavis rods is c. In Fig. 2 it is hidden by the centre.
pivot. The claviger couple is of the third kind. The shaft O' is the power
shaft and its crank O¹ S is represented three times the length of the crank O B,
giving three revolutions of the crank O B for every revolution of the crank O'S!
The crank O B is represented in the figure as being rotated in the opposite
direction to the crank O¹ S. The locus of the end a of the claviger couple is
found. As the crank pin circle of the crank O' S is the centre locus the relative
lengths of the cranks would give an angular velocity ratio of six to one with an
outer locus composed of common hypocycloids. As the ratio is taken as 'three to
one according to the lengths of the cranks the locus of the point a or A is four
contracted hypocycloids: The contraction is sufficient to allow of the outer profile
of an inner guide g¹ g! and the inner profile of an outer guide g g being made
and fixed in position, both parallel to the locus. The guides are in parallel planos
and are arranged so that each is opposite a roller as shewn in Fig 2. This
gives reciprocal restraint. When the crank 01 $ is rotated in either direction
the motion is perfectly transmitted to the crank O B which is rotated in a
contrary direction with a constant angular velocity ratio of three to one. The
crank O B may equally well be rotated in the same direction 'as the crank O'S,
and in either direction with any other constant angular velocity ratio by varying
the length of the cranks and the shape of the guides to correspond as previously
explained.
'
•
76. Plate 29 Figs. 1 and 2 represent another form of this movement more
particularly suited for speeding down. One claviger couple is used as in the
movement described in the preceding article. 'It is also a claviger couple of the
third kind, but the centre pivot is now the crank pin of the smaller crank O B.
The claviger couple A bnc has one end n centred on the crank pin N of the larger
crank O' N. The other end A is bent at a right angle for the stud A A¹ upon which
is placed the roller r. The lengths of the cranks are represented as eight to one.
This allows of an angular velocity ratio of four to one with an outer locus con-
sisting of five common hypocycloids. The guide gg is placed in position outside
the locus in the manner previously explained. A single crank u uv, twice the
length (along u¹ v) of the crank O B is pivoted upon the crank pin N outside the
claviger couple. Its pin uu' carries the roller which is free to revolve upon it.
Other rollers are provided so as to make up a number equal to the number of
revolutions made by the smaller crank while the larger is revolving once.
centre points of the axes of these rollers are an equal distance apart round the
circumference of a circle whose centre is on the centre liue of the crank pin B or
The

page_text: in that line extended.. In the movement illustrated the number of rollers.is. four,
Their axes or spindles, are held in position by a rigid piece, represented in the
figure by the. square 888.8. This gives a very strong reciprocal restraint to the
roller r. None of the rollers can be moved from the guide while the rollers are
inside it, yet they roll round the guide with a smooth and even motion, the move-
ment of each roller being composed of two motions, one motion round, the crank
pin B and the other an oscillating motion round each of the rollers in turn asya
centre. The motion is perfectly transmitted with a constant angular,,velocity ratio.
It may be varied in direction and velocity as previously, explained.
+
77. Plate 30, Figs.. 6 and 7. illustrate another variety of this movement equally
applicable for speeding up or down.. Fig. 6 represents an elevation and Fig. 7 an end
view with the crank and bar placed in the same plane.. The fixed parts representing
a vertical section through the guide, only are shaded. The two fixed bearings of
the crankshafts are marked m and n. The axes of the shafts O' and O are in
a straight line with each other. The,.shaft terminates in a single crank O B.
The shaft O' carries at its end rigidly attached to it the bar CC. The two arms C
and C are equal in length. Another bar or rod A. A equal in length to CC is
pivoted with a deep. bearing at its centre on the crank pin. B. The ends of the
bar CC and of the rod A.A are. thicker than the main part, and are bored, out
forming deep bearings for two cranked rods xy and uv. The lengths of the
cranks ¹y and.ul vl on the two rods are each equal to the length of the crank O B.
The straight part of each rod yy and.vl.v is sufficiently, long to form an axis for
a roller and ². In all measurements the length is taken from centre to centre.
The length of each. arm C,of the bar. CC is shewn in, the figure as four times the
length. of the crank, O.B. The crank O.B is to be rotated in the opposite; direction
to the bar so as to make four revolutions during the time the, bar is revolving once.
A centre locus is taken.. between the circumference of a circle, whose diameter, is
twice, the diameter. of the crank pin,circle and, the circumference of, a circle whose
diameter is twice the length, of the bar...This centre locus is a symmetrical figure
composed of five common bypocycloids... A fixed guide gg, is placed in position
outside the locus with its interior edge, parallel to the locus and distant, therefrom
the radius. of the roller. This arrangement of rods when, represented geometrically
forms an irregular claviger couple with equal limbs, and is composed of, two equal
parallelograms, the centre line being common to both.. When, the shaft O' is the
power shaft it is a claviger couple of the second kind with the fulcrum alternately
at either end. When the shaft O is the power shaft it is a claviger couple of the
third kind with the fulcrum alternately at either end. When the bar is rotated
the crank is rotated in the opposite direction with an angular velocity ratio of four
to one or any other angular velocity, ratio inversely, proportionate to the lengths of
half the bar and the.crank.. This is not a perfect movement because there is not
full and continuous´impulse. At two points during every revolution of the smaller
crank for an instant the impulse is nil.. Though this is the fact theoretically, it is
practically of little importance as the momentum of the moving parts carries them
past the neutral points. The perfect, form of this variety of the movement will
now be described.
.
78. Plate 20 Figs. 1, 2, 3 and 4 Fig. 1 shows a front view of a fixed guide
inside a centre locus composed of four., common epicycloids. This is adapted to
increase the number of revolutions in the ratio of 1 to 5. The locus is found in
the manner described in the preceding article. "Fig. 4 is a longitudinal section
through the centre of the shafts. The fixed parts only are shaded. The bar
represented in Plate 30 Figs. 6 and 7 is here replaced by the disc C C, see Figs. 3
and 4, rigidly attached to the shaft O¹. Fig. 2 represents a wheel W W. Through
the rim and projecting from both sides perpendicularly are five studs at equal
distances apart 81 to 8. Five rollers 71 to 75 are placed upon the studs on one
side. The centre of the wheel forms a hub through which is a bearing hole
sufficiently large to accommodate the crank pin B and allow it to turn round inside.
On the face of the dise C C Fig. 3 there are also fixed five studs at equal distances

page_text: apart projecting perpendicularly from it.
The distance of the centre of the fixed
studs in each case from the centre of the wheel and from the centre of the disc is
five times the length of the crank O B. On the studs projecting from the face of
the disc CC there are pivoted five links to with a bearing hole in the end of
each sufficiently large to allow the studs on the wheel W W to pass through and
turn round in them. The length of each of these links, from centre to centre is the
same as the length of the crank O B. The studs on the wheel on the opposite side
to the rollers are then passed through the bearing holes in the links on the disc.
The disc and the wheel together are then approached to the crank and fixed guide.
The wheel W W is hung upon the crank by passing the crank pin B through the
bearing in the hub. Whatever position the crank inay be in the rollers all fall in
place and are in contact with the guide. The relative positions of the rollers in
contact with the guide are shewn in Fig. 1 by the circles 1 to ³. The parts are
then fixed in position as shewn in Fig. 4. If the shaft O' be rotated the motion is
perfectly transmitted to the crank O B and it is rotated in the same direction with
a constant angular velocity ratio of five to one. The method of pivoting represented.
in Plate 30 Fig. 7 may be, adopted and the crank, rods can have a deep bearing in
the disc. Double guides, one on each, bearing n and m, may conveniently be used
where great strength is required. The ratio of revolutions should not be less than
1 to 3 with this movement otherwise, it is not a perfect movement. The ratio may
be as large as desired. The, larger the ratio the stronger the movement as all the
rollers are in contact however,uumerous they may be; but the rollers must not
exceed in number the number of revolutions the crank makes to one revolution of
the disc. The, friction is, pivotal only and it is the same in amount for the same
load per revolution of the crank however, large may be the ratio between the
angular velocity of the two shafts.
79. The guides have been fixed in all the movements described in articles 73
to 78. They may be made to revolve and some other part of the movement may
be fixed without affecting the efficiency of the movement. The ratio of the angular
velocities and the direction of the, rotation are however changed. Either of the
cranks where two are employed or the crank or the bar or disc may be dispensed
with and the guide rigidly fixed to the shaft and carried round by it. The end of
the claviger couple which had..previously been attached to the displaced crank or
bar is now pivoted on a fixed stud placed in any position along the line. of..its
former travel. The claviger couples in this position, have an oscillating. motion
instead of a rotary one. There are thus three methods of arranging the movements
according to the position of the fixed parts. The manner in which the angular
velocity ratio and the direction of the transmitted rotation are affected is shewn in
the following table.
!°
"
1
་་་
Let n represent the number of convolutions in the guide
"
i
Guide
ão,
do.
do.
Epicycloid
do.
Hypocycloid
Small crank.
D1 to n + 1
Large crank
Pivoted to fixed stud -
End of Claviger couple pre-
viously attached to large
crank or, bar
End of Claviger couple pre-
viously attached to small
crank
do.
Epicycloid
Hypocycloid
'do.
Small crauk
Guide -
do.
Small crank
Large crunk
Small crank
Guide -
+1 to 1
1
I to
Same
do.
Contrary
R-1 to 1
do.
l to.n
do.
л to 1
do.
1 to n
Same
n to l
do.'
Epicycloid
do.
Hypocycloid
do.
Large crank.
Guide
.. n + 1 to n
Large crank
n
n to n.+ 1
to n
Contrary
do.
Same
Guide
n to n. 1
do.

page_text: Figs. 1, 23 and 4 is by the intérior epicycloidal guide g. being rigidly attached
to the shaft O¹. The cranked rods x y uv &c which carry the rollers are cranked
at both ends, and the end of each crank is pivotted on fixed studs s¹ to 82 &c. The
cranked rods and rollers revolve round the fixed studs. Another method of
varying the position of the fixed parts in connection with the movement shewn
in Plate 20 Figs. 1; 2 3 and 4 is as follows The rollers may each be placed on
a separate fixed stud projecting from the framework and the guide taken from
the shaft O and hung upon the crank pin B, the latter being made to fit the
bearing hole through the guide. Studs are fixed into the face of the guide equal
in number to the rollers. The studs may be placed at any convenient part of the
guide at an equal distance from each other and from the centre of the guide.
The fixed studs on the disc C are placed in corresponding positions on the disc
and the bearing holes in the ends of the links are passed over the studs on the
face of the guide. Or the studs carrying the links as shewn in Fig. 3 may be
fixed to a framework in the vicinity of the bearing n n and the loose guide hung
upon the crank B. Fixed studs project from the back of the guide corresponding
to the fixed studs carrying the links. The studs on the back of the guide aro
then passed through the bearing holes in the links. The disc CC is dispensed
with and in its place the wheel W carrying the rollers is rigidly attached to the
shaft O¹. The wheel and shaft are then brought up to the guide and the rollers
take up their positions in contact with it. The guide in this form bas an oscillating
movement only and does not revolve, but it rotates the crank upon which it is
centred. The quality of the oscillating motion is such that during the passage of
a roller over four-fifths of each cycloid represented in Fig. 1 every point in the
guide describes a circle of the same diameter as the circle of the crank pin B and
each point at every instant is in the same relative angular position with respect
to the centre of the circle it describes as the crank and the links, which are always
parallel to each other, are in, with respect to the centres of the circles described
by them.
The
In all the movements previously explained in which a cycloidal guide is
employed the diameter of the rollers is arbitrary, and the radius of the rollers
The move-
determines the distance of the profile of the fixed guide from the locus.
ments have all the ease and smoothness of rolling contact with absolute precision.
81. To Multiply or Reduce the Revolutions of a shaft in any ratio.
principle of the movements is the same as previously described. The shafts are
in the same line. The necessary directing restraint required by the movements is
obtained by rolling wheels or rollers along circular guides upon which they are
compressed with sufficient force to prevent slipping. Plate 20, Figs. 5 and 6 shew
the geometrical lines of the movements described in article 78. The small circles
represent rollers of the same diameter as the generating circles. The radius of
each is equal to the length of the crank represented by the line o b. The directing
circles are cf g. They represent fixed circular guides. The centres of the rollers
or the axles passing through their centres are connected together and held firmly
at an equal radial distance from the centre o by a wheel or any rigid system of
rods, which is firmly attached at its centre to the shaft O¹. A stud is fixed in the
end of each roller with its centre on the edge of the periphery of the roller. The
studs are passed through corresponding holes in the rim of a wheel or in any
rigid system of rods so as to hold the studs at an equal distance from the crank
pin b. The wheel or system of rods has a bearing hole at its centre through which
is passed the crank pin b. The rollers are moved round the directing guide by
rotating the shaft O. The crank o b is rotated once for every rotation of the
rollers round their axes. The angular velocity ratio is inversely as the lengths of
mo toob. The directing guide may be made to rotate or oscillate and some
other part of the movement may be fixed as previously described.
represents in detail some varieties of the movement described in this article.
82. Plate:21 Figs. 1 and 2 represent one variety of the movement described in
the preceding article. The fixed part is the rigid piece carrying the studs which
Plate 21

page_text: support the rollers. The rollers may be as numerous as desired provided they do
not touch each other. The more numerous they are the less pressure is required
to prevent them from slipping. Fig. 1 is an elevation of the movement looking
along the crank shaft. Fig. 2 is a section along the line a' O' B c. The fixed parts
only are shaded. Two shafts O' and O are placed with their axes in a straight line.
The shaft O terminates in the single crank O B. The shaft O¹ carries at its end
rigidly fixed to it the wheel or cylindrical disc C C the periphery of which is
covered with leather. The six rods a a, which connect together the studs on the
rollers form a double claviger couple with the two inner, eross rods extended.
If they are pivoted. together and the rods are free to turn upon the pivots the
four parallelograms will nevertheless remain squares and the pivots are rigid and
immovable when in position on the rollers as the distance from joint to joint is
invariable during the movement; the joints may therefore preferably be riveted.
Or the studs on the rollers may be connected together by a ring forming the rim
of a wheel connected by radial supports to a central hub which is hung upon and
supported by the crank pin B. The bearings of the shafts are respectively m m
and n n.
.
AA is a portion of the fixed supporting framework of wood or metal.
The part of each stud 8' to 88 which projects beyond the rollers is rectangular in
section. A groove is cut in the fixed framework A A in the proper position for
each stud. These grooves are open towards the outside and ends allowing the stud
carrying the roller to be readily placed in them. They are shaped to the studs so
as to allow no lateral movement but they allow an adjustment of the stud in a
radial direction. At the bottom the groove is widened out somewhat at each side
to accommodate a rubber pad v, vl, &c. The rubber pads are smaller than the
recesses provided for them so that when the thickness of the pads is required to be
reduced by pressure there may be room to accommodate their increased length
and breadth. Outside each groove rigidly attached to the framework is a metal
bracket tt &c., each bracket is tapped and threaded, with two internal or concave
screws through which two solid screws w w pass and act upon a metal plate u u
which is the same shape as the outer rectangular surface of the stud and rests upon
it. The screws may be conveniently finished with square or polygonal flat bolt
heads. By the aid of this arrangement the, studs are held firmly, in position and
the rollers are one by one easily compressed upon the leather covered wheel C C
with sufficient force to prevent slipping under any load, as one roller cannot slip
without all the others slipping too. When the rollers are compressed with sufficient
force the wheel or other arrangement of rods a a &c is then fitted on the crank
pin B and on the studs y¹, y² &c so that the latter may easily revolve in the
bearings. Either shaft may be the power shaft. If the shaft O¹ be taken as the
power shaft and rotated in either direction, the motion is perfectly transmitted to
the shaft O and it is rotated in the opposite direction. The angular velocity ratio
of the shafts is inversely as the radius of the disc C C is to the radius of the roller.
The studs y¹ to y which project from the ends of the rollers may be in any position
between the perimeter of the roller and the stud upon which it revolves without
affecting the ratio of the velocities. The crank O B must however in all cases be
equal in length to the distance between the centres of the stud s and the stud y.
83. Plate 21 Figs. 3 and 4 represent the movement described in article 81 with
the circular directing guide fixed. Both figures represent longitudinal sections
through the centres of the shafts when all the parts of the movement are in one
plane. The fixed parts only are sliaded. Fig. 3 represents the movement with an
interior fixed guide and Fig. 4 with an exterior one. Both movements have
a device for compressing the rollers on the fixed guide to prevent slip and each
movement has an additional loose wheel which bears the strain due to the com-
pression of the rollers and prevents it falling upon the bearings. The two shafts O
and O see Fig. 3 have their axes in a straight line. The shaft O¹ carries at the
end rigidly attached to it the wheel u ai u. It has deep bearings.u u in the rim
at equal distances apart, one for each roller. It is connected by radial arms to a
central hub ii which is keyed upon the shaft O¹. Another wheel exactly similar.

page_text: pressure.
"is centred at the hub upon the crank pin B of the crank O B. The rollers have
'each a cylindrical recess in one end. The projection of the interior circular
surface of the recess is concentric with the projection of the periphery of the roller.
A stud 8 of sufficient length is firmly fixed into the recess of each roller. The
stud is of smaller diameter than the recess and it is fixed with its centre line
'coinciding with the axis of the roller. There is thus left in the end of each roller
a symmetrical annular recess. The bearings of the shafts are m m and n n.
The
periphery of the cylindrical part of the fixed guide A. A is covered with a leather
ring. It is made by stamping out of the hides, rings or portions of rings of the
width of the intended thickness' of the covering. The interior or concave diameter
of the rings is rather less than the diameter of the circular guide. Sufficient rings
are stamped out so that when they are placed side by side with their edges
outwards and inwards they will build up a ring of leather rather wider than the
length of the rollers. The ring of leather so built up is made pliable and placed
upon a slightly coned drum. The smaller diameter of the drum is arranged to
allow the ring to be readily placed upon it. The larger diameter is at the opposite
end of the drum and it is equal in diameter to the diameter of the cylindrical
guide A A. The drum is then brought up to the guide, and the built up leather
ring is forced along it on to the guide. When it is in position on the guide as
'shewn in section at e'e its exterior surface is rolled down with considerable
The effect of these two processes is to make the built up leather ring thinner and
wider. The rollers, as numerous as desired; are then placed on the leather ring
and temporarily held firmly in place at equal distances apart. A loose annular
wheel ww is then 'fitted to pass over the rollers. An annular disc cc is held to the
'face of the fixed guide by the bolts and nuts zz which pass through the disc and
the fixed guide. The outer edge' of the disc is bent to accommodate and hold the
leather ring. When the bolts are tightened up by turning the nuts the leather
ring is compressed in the width and increased in thickness so as to assume very
nearly its original dimensions. By' this means the rollers can be compressed
between the fixed 'guide and' the loose annular wheel with sufficient force to
prevent slip under any load. At equal' distances round the projecting edge c¹ of the
annular disc c c holes have been previously punched opposite the centre of the
thickness of the ring and corresponding holes are now bored through the leather
'ring and into the fixed backing. Nails made of round wire, clinched up at one end
for a head are passed through the holes. By this means the leather ring is held
firmly in place. The hub of the wheel a a is then placed upon the shaft O¹ and
the bearing holes uu in its rim are passed over the studs s on the rollers. The
'wheel is then keyed or otherwise rigidly fixed to the shaft O. A cranky equal
in length to the crank O B is keyed shrunk or otherwise rigidly fixed to the end of
each of the studs s which' project from the rollers. The roller stud and crank then
revolve together as one solid piece. The 'crank pins y are placed through the
corresponding bearing holes in the rim of the wheel x b b x. The crank shaft O is
then brought forward and the pin B of its crank O B is passed through the bearing
in the hub ff. Either shaft may be the power shaft. If the shaft O be the power
shaft and it is 'rotated in either direction the shaft O B is rotated in the same
direction with a constant angular velocity ratio. The number of revolutions made
by the shaft O while the shaft O¹ is revolving once is equal to
Diameter of fixed guide
+ 1,
Diameter of roller
Fig. 4 represents the same movement with an exterior annular fixed guide.
The same letters of reference refer to the corresponding parts in each figure. In
Fig. 4 the wheel aa has a stud a¹ projecting at right angles from the rim for.
every roller. These form the supports upon which the rollers revolve. The
wheel W. W is a loose wheel riding upon an extension of the shaft O¹. The loose
wheel is surrounded by the leather ring and it also carries two annular discs one
an each side with the bolts and nuts for compressing the leather ring as previously

page_text: described. The single cranked rods hy are rigidly attached to, the ends of the
rollers. The two shafts rotate in opposite directions. The number of revolutions
made by the shaft O while the shaft O¹ is revolving once is equal to
The interior diameter of the fixed guide
Diameter of roller
−1.
!!
In both movements the loose wheel is carried round in the same direction as the
shaft O
.
+
•
84. Fractional Variation of the number of Revolutions by means of hypo-
cycloidal and epicycloidal curves. The method to be explained in this article has
for its object the transferrence of rotary motion from one shaft to another, the
velocity being varied in transmission so that the angular velocity ratio of the
two shafts shall be as 1 to 1 and any fraction, or as 1 to any fraction greater than
a half, without employing the method of frictional rolling explained in articles'81,
82. and 83. Reference is made to Plate 16 Fig. 2. Let the circumference CC
represent the interior of a rim on a disc of which the point, is, the fixed centre.
B is a circular disc represented in the figure of a radius th the radius of C C. Let
the point o on the disc B be taken as a generating point., If the disc B be rolled
along the interior surface of the rim, say in the direction indicated by the large
arrow, until it has made one revolution round the centre x.and returned again to its
original position, the point o will have generated six common, hypocycloids, see Fig. 1.
Let it be supposed that the point o carried a pencil during the movement and
described these curves, on the inner face of the disc. Let D represent a rod pivoted
at one end on the fixed centre, at and with the other, end bent, to a right angle
and passed through the centre z of the, disc B. A circle uy is described on the
disc from the centre x with the radius 2 b. Any point y is taken in a plane*
parallel to the disc on the projection of the circumference uy, this point represents
a fixed stud, supported from the direction opposite to the disc. A fixed stud wis
placed in the same position on the disc B. A rod E of the same length as the
rod D is pivotted at its two ends on the studs wand y. It is assumed that the
disc B presses upon the rim with sufficient force to prevent slipping. The rod D
is revolved round its centre x say in the sense of the arrow with an uniform
velocity, carrying round with it the disc B. The two rods D and E with the two.
lines z wand x y form a parallelogram of which the side x y is immoveable. The
radius zw of the disc B must therefore remain parallel to the line x y during the
movement. The point w describes a circle round the point y and every point i
the circle w b' describes a circle round the corresponding point in the circle uy.
The disc B presses upon the rim and carries round with it the disc CC. At the
end of one revolution of the rod D the disc B is again in its original position as
shewn in the figure and the disc C has been moved round in the same direction as
the rod D one revolution minus a length of its circumference equal to the circumn-
ference of the disc B. And as the radius zx plus the radius zb is equal to the
radius C any given point on the circumference C C has been moved round a
distance equal to the circumference described by the point z (the centre of the
disc B) that is the angular velocity of the rod D and of the disc Care inversely,
as the radii. During the movements the pencil at o has exactly traced over 5 out
of the 6 curves which were described by it when the disc B was rolled round the
rim of the then fixed disc CC. The disc B has not actually rotated but with respect
to its pivot z and the centre x it has apparently rotated once backward in the sense
of the small arrow. Its effect upon the rotation of the disc C is precisely the same as
if it had actually rotated backward once on its axis. The same results follow if the
rod E be.rotated instead of the rod D. Fig. 3 represents the disc B on the exterior
surface of the disc C. If the disc B be released from the rods and rolled round the
disc CC (which is four times the radius of the disc B) the generating point o will
generate four common epicycloids. Let the disc B be connected with the rods D
and E as described in connection with Fig. 2. It is carried round by revolving
either of the rods D or E on the axis x or y as just explained. When it has made
in

page_text: +
one revolution and again regained its original position it has rotated the disc C_C
one rotation plus a length of circumference equal to the circumference of B;
that is the angular velocities of the rod D and of the disc C C are inversely as
the radii. During the movement the point o will have passed over the four
curves and in addition will have passed over the first curve a second time. The
application is as follows. Plate 16. Fig. 4 represents a longitudinal section of
the movement. An internal wheel with curved teeth outside and parallel
to the hypocycloids described by the point o in Fig. 2 is rigidly fixed to the
end of a shaft O.
The position of the axis of the shaft corresponds to
the point in Fig. 2. A front view of the wheel is similar to the fixed
guide G G Plate 16 Fig. 1. Another shaft O¹ is fixed in the same plane as
the shaft O but not in a line with it. The position of its axis corresponds
to the point y in Fig. 2. The shaft O¹ has the disc d d rigidly fixed to the
end facing the wheel. Five pins or studs p, p, see Fig. 5 are firmly fixed into
the disc at equal distances apart. The number of pins is always
# Y
Bee Fig. 2.
The distance of the centre line of each pin from the centre of O³ is equal to the
line wy.
Each pin is supplied with a roller rr free to turn upon it. The radius
of the rollers, is equal to the distance of the profile of the curved teeth from the
hypocycloidal curves. When the shaft O¹ with the disc is brought up to the
wheel w the rollers fall into the curves and are all in contact with them. See Fig. 1.
If either shaft be rotated the other shaft will be rotated in the same direction.
The motion of the shaft O has a constant angular velocity ratio to that of the
shaft O¹ as 5 to 6. While the shaft O is making one revolution the shaft O makes
a fraction of a revolution which may be expressed as follows for any dimensions
N° of teeth-1
No of teeth
A similar movement may be constructed with the teeth inside and parallel to
the epicycloidal curves generated by the point o in Fig. 3. The front view of the
toothed wheel so constructed is represented in Plate 20 Fig. 1. The position of
the rollers on the disc attached to the other shaft. O¹ are represented in the same
figure by the circles to . The angular velocity ratio of the shaft to the
shaft O is as 5 to 4 and may for any dimensions be expressed as follows-
No of teeth + 1
No of teeth
Fig. 6 represents the same movement as Fig. 1 but the centre locus consists of
elongated hypocycloids.
The motion is smooth and even. There is no slip, wedging or backlash. Half
the number of teeth drive or are driven at every instant throughout the movement.
Both movements are the counterparts of the geometrical diagrams Figs. 2 and 3
just explained. In all cases, whatever the number of teeth, the radius of the
generating circle must be equal to the difference between the radius of the directing
circle and the arm D or E, and the eccentricity of the axes of the two shafts when
projected on the same plane must be equal to the radius of the generating circle.
The movement represented in Fig. 4 is to be preferred to the other. By means of
either of these movements the angular velocity ratio may be varied in the following
manner 2 to 3, 3 to 4, 4 to 5, 5 to 6, 6 to 7, and so on in the same sequence.
Other ratios are best, obtained by making two changes. Say 3 to 5 is required.
The changes are 3 to 6, and 6 to 5, or say 5 to 7 is required. The changes are
5 to 6 and 6 to 7.
Any ratio may be obtained in one movement as follows. Suppose the ratio
required, is as 3 to 5, the centre locus is taken as described for Fig. 1 between the
two motions during a complete cycle. The centre locus in this case is the series of
curves which would be obtained by rolling the generating circle twice round the
directing circle. These curves intersect each other. This increases the number of
teeth and part of the profile of the curves is consequently. cut away, but this is

page_text: compensated for by twice the number of rollers being allowed upon the disc d d.
Plates 27 and 28 illustrate other arrangements of the niovement for multiplying
the revolutions of a shaft described in articles 75 and 76. See also article 95 for
further particulars of the movement described in this article.
85. Plate 22 Figs. 2 and 6 illustrate a method of safely propelling a bicycle for
those riders who might possibly prefer the rotary motion of the foot. The pedal is
connected with the crank by a claviger couple of unequal limbs. That represented
in Fig. 2 is a claviger couple of the first kind and that in Fig. 6 of the second
kind.
There is only one fixed point viz. the fixed axis S. The pedal P is attached
to the free end of the claviger couple, the centre of its spindle describes a circle
and cannot be moved in any other direction. The arrangement must be duplicated
on the other side of the wheel. The position of the circle described by the pedal
may be located in any direction round the axle by varying the position of the
fixed axis S and it may be any distance away from the axle by increasing the size
of the claviger couple. The size of the circle described by the pedal may be varied
as desired by making the position of the fixed axis S adjustable along the line
joining the centres of the two circles. It may be rigidly attached to a rectangular
bush supported in a slot in the fixed framework and clamped in position. A very,
slight movement of the fixed axis S makes a considerable difference in the move-
ment of the pedal.
Plate 25 Fig. 2 illustrates the adaptation for velocipedes of the clutch movement
described herein. As it is there represented it will only drive in one direction.
A clutch for a velocipede should not only allow the wheel to outrun it and thus
move faster than the corresponding movement of the pedals for turning &c but it
should be efficient for driving the machine backwards and for restraining it
when back pressure is applied to the pedals. The driving wheels are not con-
nected by a through axle, and the machine is therefore left open between tho
wheels. The clutch in this adaptation is a-claviger pair. A disc d is rigidly
fixed by a short shaft to the hub of the inner side of the driving wheel; this
disc has a wide circumferential rim or flange f having a smooth circular interior
surface. A fixed pin or stud S projects from the centre of the disc. This pin is
the fixed common axis of the two clavigers abs and cyes, set in opposite
directions. The extreme length of each clavis rod ab and c ye is slightly greater
than the radius of the interior surface of the rim. The restraining arms x 8 and
ys are quite distinct from each other and are both centred at their ends upon the
common fixed axis S. The clavis rods are widened out at their outer ends into
the feet or clutch pieces bb¹ and e e¹. The outer bearing profile of of these pieces is
an arc of a circle shaped to fit the interior of the rim when the clutch is in action.
The fixed axis S is extended outwards into a pin z of smaller diameter. The end a
of the clavis rod ab has two fixed pins projecting from opposite sides giving it
aT shaped end. The end c of the clavis rod ce has a fixed pin projecting, towards
the disc. The two corresponding pins on the side adjacent to the disc are con-
nected by a short rod ac slotted for a short distance at its centre and pivoted at
each end on the pins. This rod connects the two clavis rods together, and its
length regulates the extent of the clearance for the recoil. The slot is passed over
the pin upon which it slides. A T shaped rod Ca is pivoted at the end' upou the
pin a. The short arm of this rod adjacent to the disc carries the roller r. The
length of the stém Ca of the rod plus the radius of the roller must be slightly
longer than the radius of the inner surface of the rim. On the outer short arm of
the T shaped rod the end C of a claviger couple A B C S is pivoted. The other
end A of the claviger couple is pivoted upon the crank pin A of the single,
crank A O on the subsidiary axle O. The length of the crank. A O must be equal
to the radius of the inner surface of the rim minus the radius of the roller 7. The
arrangement is repeated in connection with the other wheel. The power is com-
municated to the subsidiary axle O by means of a crank at its centre, operated
1:
'
hú the nod vods The beerinde fox the driving whould as
fitted on the short

page_text: 1
shafts connecting the discs with the hubs. "These bearings are connected and
carried by a U shaped framing passing downwards towards the ground with
branches for supporting the fixed' axis'S, the bearings of the subsidiary shaft O,
the steering wheel &c. The driving wheels may be before or behind the rider.
When the crank A O is rotated in the sense of the arrow the roller r rolls a
short distance along 'the inner surface of the rim and forces the point a towards the
fixed axis S," this brings 'the 'clutch piece b b into contact with the rim and it
presses upon it directly in a radial direction all along the surface of contact with
great force. With the relative positions shewn in the figure the virtual moment of
the outward pressure of the clutch piece on the rim is forty-eight times that of the
force acting through the claviger couple AB CS at C. The virtual 'moment of the
pressure can be varied to any extent in accordance with the explanations previously
given in article 42 when dealing with the principles of movements composed of
claviger pairs. The clutch disc and wheel are now practically one piece and the
driving wheel is rotated synchronously with the subsidiary axle.. The other clutch
piece e e has been carried by the same movement quite clear of the disc. Should
either wheel outrun the motion of the subsidiary axle as in turning corners the
disc flange throws off the clutch piece leaving both clutch pieces clear to the extent
allowed by the clearance. Two or three powerful and rapid strokes may be given
to the pedals and then they may be held stationary by the feet while the machine
runs freely forward until the force of the impulse is exhausted. When, running
down inclines by the force of gravity the driving wheels run free and the pedals
are held stationary and used as foot rests. Suppose now the velocity of the
machine, is too great and it is desirable to restrain it, the pedals are pressed back-
ward by the feet, the roller C rolls backward along the rim and brings the clutch
piece e e¹ into contact with the rim with great pressure. The parts are immediately
locked together as one piece, and they so remain while the back pressure upon the
pedals is continued. The subsidiary axle is then driven by the driving wheels and
their velocity is reduced by increasing the load by the back pressure upon the
ascending pedals. When the machine is at rest it can be driven backwards by
operating the pedals in the reverse direction. The roller cannot in any case be
removed from contact with the interior of the rim during the movement.
1
Plate 5 Fig. 5 represents an arrangement of mechanism with the claviger
movement for operating the steering wheel of velocipedes. A steering handle is
attached to a spindle c which for about half its length from the junction with the
handle is threaded with an exterior screw of coarse pitch. The threaded part of
the spindle passes through a fixed tubular stud S which is rigidly attached to the
framework. The stud is threaded with a corresponding interior screw. The lower
part of the spindle carries the tubular collar e within which the spindle is free to
turn: The tubular collar is held in place by the ring r above it which is screwed
or rigidly fixed in any way to the spindle and by the flat annular nut n which is
screwed on the lower end of the spindle. On opposite sides of the loose collar e
are two fixed pins upon which are pivoted the two forked ends of a clavis rod A x B.
The restraining arm x y bas its fixed axis y vertically under the fixed tubular
stud S. A connecting rod A z is pivoted to the end A and is connected at the
other end with 'the steering wheel. When the steering handle is very slightly
screwed down the claviger moves the rod Az a much longer distance horizontally
towards z, the reverse is the case when the handle is screwed, up. The sensitive-
ness of the movement may be varied to any extent by varying the size of the
claviger relatively to the distance s'y.
Plate 30, Fig. 8 represents a claviger adapted as a safety brake for tricycles
operated as at present by chains and chain wheels, with balance gear inside a
tubular axle. It is more particularly suitable for those tricycles with driving
wheels before the rider. They are generally restrained by a band brake acting
upon the periphery of a drum fixed upon the axle and this is operated by a
lever. The centre of gravity of the rider is nearly vertically above the axle
and when the brake is applied- with any force the re-action upon the frame
{

page_text: work of the machine causes the rear part of the machine with the rider to revolve
upon the axle.
In Fig. 8 the axles are represented in cross section; O is the solid
axle and a the tubular one. The disc d with the circumferential rim or flange f is
fitted upon the tubular axle. A claviger bx d¹¹o has the axle a for the axis of its
restraining arm z o. The sum of the lengths of ox and x d is rather longer than
the radius of the interior surface of the rim. The clavis rod b x d is broadened
out into the foot or brake piece dd. The outer profile of this is an arc of a circle
of the same radius as the interior surface of the rim and it is made so as to fit the
interior surface of the rim when the brake is in action. The clavis rod "x b is
extended in length to 'n and is bent upwards into a curve at b so as to avoid coming
in contact with the axle. A fixed stud S supports and holds the rod n b d in a
convenient position by means of the slotted piece m which slides down and up
against the stud when the brake is applied and released. The brake piece d¹¹ d' d
is held away from the rim when not in action by a light coiled spring attached to
This holds the rod nd firmly against
the stud S and to the top of the slot in m.
the stud. The bearing edge of the brake piece should preferably be covered with
leather. The brake is applied by pressure of the foot or feet upon the end of the
rod towards n which is shaped to accommodate the foot and act as a foot rest
while descending hills. Very delicate and gradual application of the brake can be
effected in this manner as well as an extremely powerful pressure when desired
without any danger of the machine being thrown over as the only reaction upon
the machine is through the restraining arm co upon the axle which has no effect
whatever upon the stability of the machine. This brake may also be conveniently.
fitted upon the short axle carrying the lower chain wheel.
86. Clutch Motion for operating Drill Braces &c. Plate 30 Figs. 9, 10 and 11
represent three variations of the claviger clutch previously described for turning
Drills or for other tools requiring a step by step movement with free return of the
handle. Fig. 9 is similar to the clutch shewn in Plate 25, Fig. 2. The disc !
having the circumferential flange is attached to the spindle or stock of the tool.
The handle H B is pivoted at B on the common pivot of the claviger couple
forming the clutch. At p on the inner side of the handle there is a fixed pin
carrying the roller r, which rolls along the inner surface of the rim. The handle
roller and guide then form a roller claviger. The distance of the pin from the
end B is arranged so that when the clutch is in action, with the full pressure the
line B makes an angle with the line B s¹. The larger the angle the greater
the pressure. A similar arrangement is illustrated in Fig. 10. It is intended for
transmitting great force and the bearing surfaces are made correspondingly large
The ends a
to prevent the surface of the rim being crushed or worn uneven.
and c of the claviger couple are pivoted upon strong pins fixed to the segmental
pieces m and n. The handle is similar to that shewn in Fig. 9 but it is pivoted
at e on a pin fixed in another segmental piece p. The convex edges of these
pieces are finished to fit the inner surface of the rim. The grip can be arranged
to have any ratio to the force applied to the handle. The length of movement at
the release is very slight and it is regulated by the space which intervenes between
the two pieces m and p. The arrangement represented in Fig. 11 is similar to the
preceding. The segmental piece p is omitted and the handle is obtained by
extending the clavis rod bc. In all three examples the clutches are shewn in action.
When the handle is pulled in the direction indicated by the arrow the clutch
instantaneously grips the disc, the force of the grip varying with the force applied
to the handle but very greatly increased and is more than sufficient to overcome
any resistances. The length of clearance at the release for the clutches shewn in
Figs. 9 and 11 may be regulated by connecting the centres of S and B or b by a
small wire double link.
87. Arrangements for operating Brakes for Restraining and Stopping Railway
Trains.
A claviger couple is supported by a horizontal bar carried by the axle trees at
mirent of the

page_text: two clavis rods is a short distance above it. Two brake blocks formed of. tw
equal segments are bolted to the ends of the clavis rods.
block, in, the vicinity of the bolt, is recessed to accommodate a rectangular block
The centre of each brak
through which the bolt is passed. The two rectangular blocks slide for a shor
distance along grooves in the upper surface of the bar. The length of the clavis
rods is arranged so that when the brake is applied, the common pivot of the
claviger couple is at a slightly higher level than the fixed axis. The brake is
operated by the common pivot being forced vertically downward causing the brake
blocks to press against the periphery of the wheels. This is effected by a claviger
pair, one end of which is pivoted on the cominon pivot. The claviger pair passes
through a slit in the bottom of the van.
a horizontal line between the two fixed axes.
The common pivot of the pair travels in
the top of the van and its line of travel is vertical.
The free end of the pair is towards
repeated on the other side. The two upper ends of the claviger pairs on opposite
The same arrangement is
šides are pivoted at the end of a transverse rod which passes across the van.
When the brake is to be applied the guard seizes the transverse rod and applying
his weight pulls it down in a vertical direction. When the brake is taken off the
transverse rod is pushed back until caught and held in position by a spring catch.
Any amount of pressure may in this manner be applied to the wheels.
All the carriages in the train are fitted with the bar, claviger couple, and brake
blocks, and they are all brought under the control of one guard by the following
arrangement. A smaller claviger is pivoted at one end on the common pivot of
the claviger couple carrying the brakes. The fixed axis is just under the carriage
floor and the vertical motion of the common pivot of the claviger couple of the
first brake applied is transferred by it into horizontal motion which is transmitted
from carriage to carriage by a horizontal rod moving backwards and forwards in
bearings and operating clavigers of the same size set to the same angle and
attached to the common pivots of the other block carrying claviger couples. If the
carriages are supposed to be equally loaded so that the heights of the frames are
the same throughout and the distances between the carriages are supposed to be
invariably the same then all the brakes could be simultaneously applied by a rigid
horizontal rod running from end to end. But these conditions never obtain. The
arrangement shewn in the skeleton diagram in Plate 24 Fig. 1 is for the purpose
of connecting the horizontal rods between each carriage. With this connection the
carriage frames may be on different levels, the distances between the carriages may
vary within the limits allowed by the couplings and buffers, and the carriages of
the train may at the moment be moving at different velocities without these
conditions in the slightest degree affecting the application of the brakes. They
are applied and taken off under any or all of these conditions simultaneously
throughout the train, and each horizontal rod has the same range and quality of
motion. A double claviger couple a bs 81 composed of six rods of equal length
is pivoted at S on a fixed stud or pin in the frame of one carriage and at S¹ on a
fixed stud or pin in the frame of the next carriage. The two cross
together at o by a loose pin. The fixed pins S and S¹ are on the same level as the
rods are pivoted
fixed axes of the clavigers connected with the claviger couple carrying the brake 4
blocks. The claviger mg d s is connected with the horizontal rod m t at m, the
fixed axis is at S, and the claviger is below it. A similar claviger set to the same
angle, with the fixed axis at S', but situated above it is connected at n with the
horizontal rod nr. The two ends c and d'of the two clavis rods c n and m d are
connected by the claviger couple cedo which has its centre pivot on the pin at o. 5
Horizontal motion given to either of the rods t mor nr is exactly reproduced in
the other in the opposite direction notwithstanding that each set of the fixed
points S and S" and the bearings of the horizontal rods may have an independent
differential motion.
The skeleton diagram Plate 24 Fig. 2 represents arrangements of clavigers for 5.
utilizing a, part of the momentum of the train itself to generate the retarding force
for destroying the remainder. Fio 2 represents the

page_text: described. The claviger previously described which is connected to the common
pivot b is represented by the lines axbs, it is pivoted at a to the horizontal rod a j
which passes through the bearing y fixed to the framework of the carriage. The
rod af is tubular at the end for the length d f. A strong coiled spring de is
placed in the tubular end of the rod a f. The rod eg which carries the buffer r
is carried through the fixed bearing z and into the tubular end of the rod af where
it acts upon the spring as a plunger. It is held in place against being drawn out
too far by a fixed collar and nut. There is a fixed collar c on the rod af between
the end a and the bearing y. A light spiral spring is coiled round the rod and
fixed at the ends to the fixed collar c and, the end of the fixed bearing y. The
claviger a zb 8 is duplicated on the opposite side of the fixed axis S forming the
claviger couple a b a' s. The horizontal rod springs buffer &c. are also duplicated
in connection with it. Its operation is as follows. When a retardation has been
caused in front by the application of the brake or by the reversal of the engine, the
buffer r strikes against the buffer 1 of the preceding carriage and brings the brake
blocks into use by means of the clavigers. A very small pressure at the buffers,
will put on the brakes with great force. The force can be varied according to the
angles at which the clavigers are set and according to the length and strength of
the spring. If, after the application of the brake to its full extent, the carriage
through possessing greater momentum should move faster than the preceding
carriage, the further pressure on the buffers is expended in compressing the coiled
spring de. These buffers do not supersede the main buffers. When the pressure
is relieved the brake blocks are brought away from the wheels by the action of the
light coiled spring at c. To prevent the application of the brake during shunting
a bar is pivoted at the centre on the fixed pin S. It has a short circular shaped
recess towards each end which when placed in position fit over the pins forming
the pivots at a and a² and is held in position by a spring or a pin inserted through
it. The pressure on the buffer r is then expended entirely upon the spring.
Plate 23, Fig. 2 represents a somewhat similar arrangement to the preceding
but the force obtained by the pressure on the buffers is used to lift the carriage
bodily from the rails and place the weight upon a sledge. The sledge slides along
the rails until the momentum is expended, and thus the wheels, are saved from
being worn. The lines db indicate the sledge. A strong curved bar oy &
881 is supported by the axle-trees O, and O¹ and grasps them above and
below. At ss and 811 are three strong pius forming at s' and 8 the fixed axes
for two clavigers cx d's' and a x b 8 having rods of sufficient strength for the
purpose. The two ends c and d are connected by the claviger couple ceas, the
fixed axis of which is S. Two fixed bearings m and n vertically above the axle
trees are supported from them. The rods carrying the buffers pass through these
bearings. These rods, with the springs &c in connection though not shewn in the
figure are precisely similar to those previously described and represented in Fig. 2
Plate 24, though the details are not indicated in this figure. If either of the
buffers be struck with sufficient force both clavigers will be operated, the ends a
and c will move to 8" and s¹ and, both clavigers assume the appearance of rigid
vertical supports bearing upon the sledge which rests upon the rails. During
the movement the fixed pins a and 8 and the curved bar to which they are
attached have been moved upwards a short distance and as the curved bar is
attached to the axle trees the whole carriage is lifted with it. If the coiled
spring represented at c Fig. 2 'Plate 24 were not used it would remain in
this manner supported by the sledge until one of the buffers were pulled out-
wards. A very slight pull on the buffer or buffer rods is sufficient. The operation
of the forces when the carriage is lifted on the sledge by the recoil of the
buffer caused by a retardation in front is as follows, lengths and weights being,
given for additional clearness. A low velocity is taken as the momentum and
consequently the force available for lifting is then less. Let the lines c d or a b
represent a length of 30 inches, c s' or as a 'length' of 7 inches, the lower sur-
face of the sledge being about four-fifths of an inch from the rail, Suppose the
.
+4
A

page_text: arrangement is attached to a truck and that the, truck and load weigh 20 tons.
The truck moving on a level with a velocity of 4 feet per second. The preceding
truck has been lifted, upon the sledge, and its velocity at the moment of contact of
the two brake buffers has been reduced to say 3 feet per second. Its rear brake
buffers are withdrawn 7 inches. The truck under consideration moves forward
11 inches, before the sledge attached to it touches the rail. During a further
forward movement, of 31 inches the truck is lifted up one-fifth of an inch, and, its
weight. is supported by the sledges. If the pressure be sufficient to commence the
lifting it must go on to the full height allowed by the clavigers as the moment. of
the force very rapidly increases.
W
g
Vz
"
To lift. 20 tons one-fifth of an inch requires about 676 units of work.. The units
of work, conserved in a body weighing W lbs moving with a velocity of V feet a
second is equal to
where is 32, the measure of the force of gravity.
The effective velocity is the excess of the velocity of the truck over the preceding
one whieli excess is taken at 1 foot per second. This worked out gives 700 units
of work. This force acts through a length of 3 inches, at the commencement
with a virtual velocity of 8 to 1, and with a mean virtual velocity throughout
of 17 to 1. Its efficiency to lift the truck is then at least 700 x 85600 units
being more than 8 times the force required for the purpose. Part of the momentum
to be destroyed is thus used to destroy the remainder.
1. 4*
88. Safety-valve Mechanism for locomotive, marine and stationary engine boilers.
Plate 31, Fig. 2. This arrangement of a claviger is for the purpose of preventing
the pressure of the steam whilst blowing off through the safety-valve from rising
beyond the limit to which the valve is adjusted, through the extra extension of the
spring and consequent increase of pressure upon the valve. A claviger abcs is
employed. The rods are double. The two clavis rods are connected by the studs
a, b and c which pass through both. The two restraining arins are supported from
the sides by the fixed framework at the fixed axes S and S. A roller is placed
upon each end of the stud c. The lower stud a passes through the safety valve
and the lower end a of each clavis rod is pivoted upon it on opposite sides. A
straight guide g is placed in position as shewn in the figure, its lower surface is
in a direction' at right angles to a line joining the two points a and S. It is
arranged relatively to the diameter of the rollers so that the line along which the
point C moves when the roller rolls along the guide if produced will pass through
the point S. A coiled spring P is connected at one end to the stud c between the
rollers and at the other to a fixed stud x, supported by the framework. The
upward pressure of the steam upon the valve varies in its pull upon the spring
according to the angle of the clavis rod a b c as previously explained herein. In
the position shewn in the figure the force tending to extend the spring is one-third
the pressure of the steam upon the valve. Supposing the valve to be lifted by the
pressure, the stud 'c with the rollers move in the direction of z. The movement in
this direction increases the force of the pull upon the spring at the same time the
spring is being extended and its force, of recoil is increased. In this manner the
spring and claviger may be constructed and adjusted so that the two movements
and consequent variations of force may exactly neutralize each other so that the
pressure of the spring upon the valve through the action of the claviger remains the
same in any position. Or they may be arranged so that the pressure of the spring
is less when the valve is blowing off strongly than when the valve is shut, in order
to compensate for the effect of the friction of the large quantity of steam passing
in that case through the narrow opening of the valve. Instead of adjusting the
force of the spring to the claviger, the claviger may be adapted to any spring of any
strength and length to obtain a given unvarying pressure according to the length
of the clavis rod a c in proportion to the distance from S to a when the valve is
closed by placing the fixed guide g at an angle instead of horizontally and by
lengthening the restraining arms S6 by placing the fixed axis S higher up along a
line drawn upward from S at an angle of 135 degrees to the line S c as described in

page_text: connection with Fig. 2 Plate 5. The exact dimensions and positions may be
calculated by means of the formulæ explained herein...
89. Direct Acting Pressure Steam-Guage. Plate, 31. Fig. 3 represents the same
movement as that described in the preceding article adapted for a pressure guage.
In this case it is preferably made with double clavis rods joined by the studs as
described in the preceding article, but with two rollers carried on the stud c
between the clavis rods. The restraining arm is single and is continued beyond
the fixed axis S and is shaped into the hand or indicator i which can move over
the face of an arc shaped guage marked with figures representing the various
pressures. A weight W is pivoted at a. The rod cm of a piston in which works
in a small cylinder is pivotted to the stud c, between. the rollers. The small
cylinder has a communication w with the steam in the boiler. When the boiler is
void of steam the piston m is nearly close up to the end o of the cylinder and the
restraining arm,S b is at an angle of 45° to a vertical line. As the pressure of the
steam acts upon the piston m it moves it along the cylinder towards the end
pulling the stud,c with the roller r along the guide in the same direction. This
movement causes the weight W to be lifted vertically. The moment of the weight
increases as it rises and it rises until it counterbalances the pressure of the steam.
As it rises it turns the restraining arın S 6 upon its axis at S and the hand upon
it indicates the pressure of the steam upon the guage. Any range of pressure can
be indicated by this apparatus.
90. Continuous, Circular motion in opposite directions converted into reciprocal
rectilinear motion. Plate 31. Fig. 4 represents two spur wheels m and n (attached
to parallel shafts O and O¹) in direct gear with each other.
A stud or crank wrist is fixed in the face of one wheel, in any position.
Another stud is correspondingly fixed in the other wheel in any position radially
but so that the radial line S o' is half the radial line a o. The two studs or crank
wrists are then connected by a claviger couple of equal or unequal limbs: In the
figure a right claviger couple a bcs with, equal limbs is shewn. One end a is
pivoted upon the stud a,, while the other stud S is the centre pivot of the claviger
couple. When the spur wheels are rotated the end c has a traversing movement
to and fro exactly along a straight line cd the forward and backward motions
being exactly the same in quality as that represented along either of the lines in
Fig. 1, Plate 6. The line of traverse may be turned in any direction in the same
plane by differentially changing the position of the fixed studs or crank wrists a S,
while maintaining them at the same distances respectively from their fixed
centres O and O¹. With a right claviger couple with equal limbs as represented
in the figure the length of traverse at each semi revolution of the wheels is equal
to four times the length of the radius line O a. The length of the traverse may
be varied with the same wheels and crank wrists by using claviger couples with
unequal limbs. The line c d is the line of motion described by a particle which is
revolving with uniform velocity round another particle at a distance equal to O a,
the latter particle itself, revolving with the samne velocity in the opposite direction
at an equal distance from a fixed point.
91. An Improved Ellipsograph.-If the first particle revolves round the other,
particle at a greater or less distance than the distance at which the second'
particle revolves round the fixed point, both, particles revolving with the same
angular velocity round their respective central points and in opposite directions,
the first particle will describe an ellipse of symmetrical shape, bisected by either
the major or minor axes such as is drawn by a carpenters trammel, the direction
of motion of the particle, in the ellipse being in the same direction as the motion
of the particle revolving at the greater distance from its central point. This
ellipse is thus shewn to be an elongated hypocycloid. This principle may be prac-
tically employed in the manner shewn in Fig. 4 Plate 31 just, described to. form an
ellipsograph for drawing ellipses by the stud S or the stud a or both being made
adjustable by being placed in a radial slot and fixed in any position by a nut or set
screw. The pencil for drawing the ellipse is placed at c. The motions of planets

page_text: revolving in elliptical orbits may be exactly reproduced by this arrangement with
an additional claviger movement attached to give a variable motion of rotation
to either of the wheels corresponding to certain laws and varying according to the
relative lengths of the major and minor axes of the 'ellipse.
92. Plate 34, Fig. 2 représents à similar movement to those described in the two
preceding articles. It is adapted for drawing epicycloidal and hypocycloidal
curves of every description. The pencil is placed at a at one end of the claviger
couple the other end of the claviger couple and the centre pivot are centred
respectively in the slotted cranks O' n and O'm. These cranks are rigidly connected
to two short shafts O¹ and O revolving in fixed bearings. Rotary motion is given
to the shafts in either direction at different velocities. Plate 34, Fig. 5 represents
another arrangement of claviger couples for drawing common epicycloids and
hypocycloids. They are described by the points a'and b. The fixed points are S, S¹
and S. The motion given to the rod m'S is exactly reproduced in the rod Sun;
and the motion of rotation given to the rod c d round its centre S' is exactly
reproduced in the rod ab round its centre n. The motions given to either set of
corresponding rods has no effect whatever upon the motion of the other set, but
the resulting motion of the two sets is shewn by the motion of the points b and a
which describe figures exactly alike but in a direction at right angles to each other.
93. Plate 34, Figs. 3 and 4 represent claviger couples adapted for reproducing
drawings maps, &c on the same scale or on a larger or smaller scale. Very great
differences in scale can be obtained by these arrangements with perfect accuracy.
The fixed point in each is the stud S which is attached to a flat board m m
which is secured to the drawing board by pins. The pencils are placed at p and p¹.
The ratio in size of the two drawings is as p S to S pl. The essential point is that
the adjustable pencils p and p' and the fixed axis S should be in a straight line.
Plate 34 Fig. 1. represents a claviger couple in connection with a pair of com-
passes. The claviger couple holds the pencil pp which is kept clear of the paper
by a slight coiled spring not shewn. It is intended for readily marking the centre
locus. The points of the compasses are each placed upon the corresponding position
in the two outer figures and upon the pencil being pressed down with the finger it
marks the centre between the two points.
94. Apparatus for trisecting any angle. Plate 34 Figs. 6 and 7 are skeleton
diagrams representing arrangements of double claviger couples for trisecting angles
The common pivot of the rods a and b and of the rods a¹ and b' are studs upon
short sleeves which slide along the rods c and d respectively. The rods mon are
fitted to the angle; the rods y and z then trisect it. Some of the rods may be left
out and a much simpler instrument remains equally efficient for the purpose. This
is represented in Plate 34 Fig. 8. It consists of the four central rods of the
arrangement represented in Fig. 7. It is composed of two right clavigers pivoted
together at one end of the clavis rods. The two restraining arms are crossed and
the free ends which terminate with a fixed pin set at right angles to the rod are
inserted by means of the pin in slots in the free ends of the clavis rods. Let a¹
b₁ c¹ be the given angle to be trisected. Bisect it by the line b'x. The lower
edges a bc of the rods a n and cm are fitted to the angle. The instrument is then
moved lower down so that the angle e b₁f made by the interior edges of the two
clavis rods falls upon the angle a b c and the angle a b c which has previously
been fitted to the angle a¹ b c falls upon the line b₁x. A line drawn down the
interior edges of the clavis rods from 1 to m and n respectively trisects the
angle ab c. That it will equally well trisect any angle may be seen on reference
to Fig. 9, which represents the geometrical lines of the instrument. Join ef. It is
required to shew that the angle eb fis three times the angle e'blf. By construction
the lines b¹ m, b¹n, m f and ne are equal to each other and the triangles b¹ m fand
bine are similar. "The angles e b¹ f, b₁ fm and b¹ e n are therefore equal to each
other. The angles e b₁f, b₁fe and b₁e'f are together equal to the angles e bf, bef
and b fe
But it is apparent that the angle bfe is less than the angle b¹fe by the
angle b¹ fm and that the angle bef is less than the angle b¹ ef by the angle b¹e n.

page_text: Therefore the angle e bf is greater than the angle e bf by the two angles b'e n
and 6 fm and as these angles are each equal to the angle e b₁f the angle e bf is
three times the angle e b¹ f
95. Fractional multiplication or reduction of the number of revolutions of a
shaft by means of the guide and roller wheel being both revolved. This has been
previously described in article 84 but it was shewn therein that the difference was
as 3 to 4, 4 to 5, 5 to 6 and so on. Any ratio of difference may however be
obtained as follows. See Plate 32 Figs. 1 and 2. The two shafts are represented
by x and y. The shaft x carries keyed or otherwise rigidly fixed to it the roller
wheel ww and the shaft y carries in the same way the cycloidal guide wheel g g.
The guiding circles are shewn by the dotted lines. Their radii are as 1 to 4. From
these the centre locus giving the correct profile for the teeth may be obtained in
the manner previously described herein. The guide wheel in Plate 32 Fig. 1 has
10 teeth. These are obtained by taking two centre loci between the guiding circles,
the zero points being taken 180° apart on the smaller guiding circle. There are
thus two sets of 5 hypocycloids crossing each other and forming a syminetrical
figure. The centre of each hypocycloid within the points where the curves cut each
other is then disregarded and the curved teeth made parallel to the outer curves of
the centre locus in the manner previously described. Now the same guide wheel
with the curved teeth may be employed to give any ratio according to the number
of teeth it possesses by changing the roller wheel and placing it in different
positions along the line y z. In Fig. 1 the ratio of the revolutions is as 4 to 1, the
line yx is one-fifth part of the line y z, the roller wheel has 8 rollers and the guide
wheel 10 teeth. The ratio of revolutions between the two wheels, the number of
rollers of the roller wheel, and the position of the shaft x along the line y z and
consequently the radius of the roller wheel is as follows:-
x Y =
x y =
x y =
Zy 2,
yz, 8 rollers, 10 teeth, revs of x: revs of y :: 5 : 4 :: y z : x 2.
6 rollers, 10 teeth reve of x: revs of y 5:3::y 2:02.
4 rollers, 10 teeth rev³ of x: rev" of y :: 5 : 2 :: yz: xz.
¾ y 2,
x y = yz, 2 rollers, 10 teeth reve of : revª of y:: 5 : 1 :: 32: x z..
Guide wheels with epicycloidal teeth may be used the rollers running outside the
teeth. The revolutions then vary as previously explained in article 84. The
curves for the teeth may be defined exactly by mechanical means as follows
referring to Fig. 1. A spur wheel with interior teeth to be placed against the .
disc g g and concentric with it and both fixed so that they cannot revolve.
A spur wheel with exterior teeth to be held in gear with it by a radius rod
turning on the common centre. A cutting tool is fixed into the inner face of the
small wheel at right angles to it and bent so that the point shall be opposite to the
pitch circle of the teeth. The small wheel is then revolved round the centre in
gear with the fixed wheel with interior teeth, it then defines on the disc the
hypocycloidal curves required. For epicycloidal curves the fixed spur wheel has
exterior teeth. To obtain the same curves as are obtained by the centre locus the
diameter of the pitch circles of the wheels are not the same as the dotted guide
circles shewn. They are as follows When the guiding circles are as x to y.
x representing the smaller and y the larger, the rolling circle for the hypocycloids
is and the directrix 3+, and the rolling circle for the epicycloids is and the
directrix 3-*
Plate 32, Fig. 2 represents the manner in which ratios in different series to that
just described are obtained. This represents ratios as follows 5 to 3, 5 to 4, 5 to 6
5 to 7 and 5 to 8. One zero point only is taken in the circumference of each
guiding circle. They are then each divided into parts of equal length and the
centre locus taken between 5 revolutions of the inner and 3 revolutions of the
outer circle, the superfluous parts of the curves being eliminated, as previously.
described. The movement is sweet in either direction the two wheels working
I

page_text: together by rolling contact alone, half the rollers receive or give impulse throughout
as the case may be, and as no clearance is needed there is no backlash.
96. To double the number of revolutions of a shaft. Plate 33, Fig. 1, is an
adaptation of the movement described in the preceding article in accordance with
the principles described in article 95. The guide wheel has two slots forming a
cross. The rollers are slightly smaller in diameter than the width of the slot,
allowing a slight clearance in this form. The sum of the impulses received by the
two rollers during each revolution is exactly equal throughout the movement to an
equal continuous tangential impulse given to either of the points a or b on the
.bar a b.
↑
97. Plate 33, Fig. 2, represents the application of this movement to a safety
bicycle. A portion of the framework or fork of the wheel is represented by f
which supports in a bearing the axle a which is rigidly fixed to the hub h.
A bracket b springs out from the fork f and terminates in a bearing supporting
the spindle of the guide wheel g. To the end of this spindle outside the bracket
the crank c is keyed or otherwise rigidly attached. The roller wheel w is rigidly
attached to the outer end of the axle a and the whole arrangement is fitted so that
the rollers of the wheel w traverse the slots in the guide wheel g.
When rotary
motion is communicated to the crank c by any of the pedal motions described
herein for giving half a revolution at each downward stroke of the foot, the wheel
belonging to the hub h makes one revolution for each downward stroke of
the foot.
W
98. Double Roller Claviger. Plate 35 represents the geometrical lines of a double
roller claviger. The line ab represents a straight rod. At the centre d is a fixed
pin passing through the rod perpendicular to the plane of the paper. It carries at
cach end a roller, one of which runs along a fixed guide above and one along a
fixed guide below, or any other effective method of constraint may be used such
as a block and slide, so as to constrain the point d to move along the straight
line e.f which produced passes through the centre point o.
The line o c represents
a crank or radius rod free to revolve upon a centre at o. It is pivoted at c to the
rod a b. The radius rod or crank oc may be pivoted to the rod at any point
between the ends a and b and the pivot d may be at any point along the same rod,
the radius rod co and the centre o being altered in length and position to corre-
spond. When the rods and points are relatively of the lengths and in the positions
represented in the figure, if the radius rod o c be uniformly rotated in either
direction, the positions occupied by the different points at the same-instant of time
is represented by the same figure in each case. Suppose the power be applied to
the points a and b by alternate downward strokes the crank or radius rod is
revolved round the centre o. The force is transmitted by leverage upon the
moveable fulcrum d and by direct thrust, the point & acting as guide.
The vertical element of the motion in the curve is effected by leverage and the
horizontal by direct thrust. The rod thus acts from a to c as a roller claviger of
the first kind and from d to b as a roller claviger of the second kind. The ends a
and b are a full stroke apart and the point & is in time between the other two and
half a stroke behind and before the ends respectively. .
99. Double Bent Roller Claviger. It was stated in the provisional specification
that the clavis rod might be bent as well as straight. Plate 36 represents the
geometrical lines of a double bent roller claviger. The same letters and description
relating to the movement and geometrical figure described in the preceding article
equally apply to this figure, but instead of the points a, c and being in a straight
line the point c may be any distance along a line c d which bisects the line a bat
any point and at any angle. In the figure the four points a, d, b and c are
represented as rigidly connected by an L shaped rod. They may be rigidly con-
nected by a rod or rigid arrangement of rods of any shape. When as in the
figure the lines a d, d b and b c are each equal in length, the angle a dc
a right angle, and the line along which the point d is constrained to move when

page_text: produced passes through the centre o the arrangement is a right double bent
claviger. If either half of the rod a b be omitted the movement is then a right
bent roller claviger of the first kind. As described in the preceding article
any other effective method of constraint for constraining the point d to move
along the line fe may be used instead of the roller and guides. . Alternate
or reciprocal motion may be given to the points a and b and they move up
and down along the lemniscata curves shewn by the dotted lines. The radius
rod oc then revolves upon its centre o and the point d moves up and down along
the straight line fe, or if the radius rod o c be revolved round the centre o the
The conversion and
points a and b have a reciprocal movement given to them.
transmission of the motion is effected by a combination of leverage with direct
thrust or pull. The way in which this is effected may be explained by examining
a complete movement of the point a. Supposing the power is applied to the
point a in a direction downwards following the line of figures. The radius rod co is
turned in the direction of the arrow. The commencement of its revolution is at o.
From 0 to 4 its movement is effected by leverage alone, the rod and stud turning
inside the roller or block at d as the case may be, the latter acting as fulcrum.
From 12 to 0, the corresponding distance towards the termination of the stroke,
the power is transmitted by direct thrust, the roller or block acting as guide.
During the centre of the stroke from 4 to 12 these two methods by which the force
is transmitted are combined in the exact proportions required. The commencement
of the stroke for the end commences at the point marked 8 in the circle, and
when the radius rod is turned in the sense of the arrow, the force is transmitted in
the reverse manner to that just described commencing by pull and finishing by
leverage. During a complete revolution of the radius rod the roller or block moves
up and down in the guide a distance each way equal to the diameter of the crank
pin circle. The directions of the motion of the points a, d and b do not coincide
as to time, the points a and b being half a stroke apart and the point d being a
quarter of a stroke apart from each of the other two.
The length of the stroke from a to i is exactly equal to the two sides of the
square inscribed within the crank pin circle. The length of the traverse from a
to 4 is equal in length to half the side of the square minus zs, from 4 to 8 the
same length plus zs, from 8 to 12 the same length plus wm, from 12 to 0 the same
length minus w m, from 0 to 4 upwards the same length as A to 4 downwards
from 4 to 8 upwards the same length as 4 to 8 downwards from 8 to 12 and from
12 to a upwards the same lengths as from 8 to 12 and from 12 to i downwards.
For convenience of description when the movement as shewn in plate 36 is
pivoted at d to rollers running along fixed guides it is called a double bent roller
claviger and when it is pivoted to a block moving in a fixed slide it is called a
O double bent slider claviger.
and 39 represent
The same letters
Where only one
100. Pedal Mechanism for Velocipedes, lathes &c. Plates 37, 38
the application of the movements described in articles 98 and 99.
of reference apply to the same parts in each as in those articles.
guide is used it is desirable to employ a wire or similar arrangement fixed just
clear of the roller to prevent the momentum at the end of the stroke from sending
the roller away from the guide and perhaps rotating the claviger round the crank
pin. The rollers are preferably covered by a rubber tyre. In those movements
with one pedal the stress of the pressure of the roller is against the guide both
during the downward and upward movement. In the latter case when the pedal is
brought up by the action of the crank the pressure is against the guide because
the pedal end is the heavier. In those movements with two pedals and one
roller the roller rolls along one guide and just clears the other. At part of the
stroke the stresses upon the roller are in opposite directions and they may just
counterbalance each other. In such case the roller touches neither side, rolling at
the other times against the guide towards which the pressure is greatest. In each
figure the circles P represent the end view of the pedals. The crank is slotted so
as to allow the clavigers to be adjusted in it to shorten or lengthen stroke. Any

page_text: other form of pedals may of course be used to suit different requirements. The
fixed guides are marked g g.
Plate 37, Fig. 4 represents a roller claviger of the second kind adapted to operate
the front wheel of a large wheeled safety bicycle running even.
Plate 37, Fig. 2 represents a double roller claviger for operating a velocipede
driven by two riders one behind the other.
Plate 37, Fig. 1 represents a double bent roller claviger for operating a velocipede
driven by two riders one sitting behind the other.
Plate 37, Fig. 3 represents a bent roller claviger suitable for operating a medium
sized front wheel of a safety bicycle.
Plate 38 Fig. 1 represents a roller claviger suitable for operating the front wheel
of a safety bicycle. Lines joining the points c d and b make an acute angle at d
and the line of traverse of the point d does not pass through the centre o. The
rod cx is rigidly attached to a sleeve .m which can be adjusted along the rod a b
and fixed in position by a set screw x, thus varying the length of stroke.
Plate 38, Fig. 4 represents a bent roller claviger similar to that shewn in Fig. 3
Plate 37 but lines joining the points ad and c form an equilateral triangle. The
geometrical lines of this movement are shown in Fig. 3.
Plate 38 Figs. 2 and 5 represent bent hanger clavigers.
Plate 39 represents a double bent roller claviger, adapted to operate a velocipede
driven by two riders riding one behind the other. Instead of placing the roller
at d, the point of intersection of the rods, it is placed lower down on a con-
tinuation of the rod c d. In the figure the rod a b is represented rigidly fixed to
a sleeve m n which slides upon the rod c d and can be moved up and down upon
it and fixed in position by the set screw d.
101. The Transmission of Circular Motion. Plate 40, Figs. 1 and 2 represent
very suitable forms of claviger couples for transmitting circular motion to short or
moderate distances. Fig. 1 represents a claviger couple with equal limbs and Fig. 2
a claviger couple with unequal limbs. The fixed axes are marked S and S.
102. Plate 40 Figs. 3, 4, and 5 represent a method of transmitting circular
motion by connecting together by rods the corresponding parts of two bent roller
slider or hanger clavigers each one of the two being of the same size and shape and
placed in the same position at the required distance apart. The same letters of
reference refer to the same parts described in articles 98, 99 and 100 and to the
figures referred to therein.
Fig. 3 represents two bent hanger clavigers so connected by the rods d d
and b b.
Fig. 4 represents two double bent slider clavigers so connected by the rods & b
and a u
Fig. 5 represents two bent slider clavigers so connected by the rods d d
and a .
103. The Claviger Clutch. Plate 40. Figs. 6 and 6^. A disc having a projecting
flange or rim is rigidly attached to a shaft S which in the position represented
in Fig. 6 is extended on the opposite side of the disc and revolves in fixed bearings.
A centre part of the shaft S or of the disc is extended upwards beyond the face
of the disc and forms the axis S¹ for the restraining arm S¹ x which is connected
with the clavis rod A. B thus forming a claviger. The end A of the clavis rod is
branched out into the foot or bearing piece A. m, which is in one rigid piece with
the clavis rod. The profile of the outer edge of the bearing piece is an arc of the
circle described by the inner surface of the rin l. The total length of the clavis
rod from a point in the bearing edge f along a straight line through to. B must
be slightly longer than the radius Sf. At the end B there is a stud projecting
inwards from the clavis rod in a direction parallel to the stud St. On this stud the
link Bis pivotted. This link carries at the end r on a stud set outwards, in the
sane direction as the stud S', the roller ². The length of the link plus the radius
of the roller, i.e. the length of the line B f¹ is slightly greater than the part B f"
of the radius S₁". The axis S¹ is extended sufficiently far to form the axis for

page_text: another disc L which is free to turn upon it and moves inside the rim of the
other disc. The stud is of sufficient length to pass through a bearing hole in
the disc L. The power may be applied to the disc L by a rotating shaft or by a
crank. In the former case the axis S¹ is lengthened so as to extend through and
beyond the disc L. A shaft or axle moving in fixed bearings is rigidly attached
to the disc L round the axis S¹. The shaft or axle is hollow as far as the nearest
crank in it and the lengthened axis S' passes along the centre and is secured by a
nut and washer at the other end leaving it free to rotate inside the shaft or axle
when the movement requires it. When the motion is delivered to the disc L by a
claviger couple a crank wrist R is fixed at any convenient point on the disc.
When the disc L is rotated in the sense of the arrow, the stud r is carried round
in the same direction, the roller running along the interior surface of the rim.
This presses the point B towards the centre S' and causes the bearing piece A m to
press against the interior of the rim of the disc with much greater force and carry
it and the shaft to which it is attached round with it. This position is shown in
Fig. 6. When the forward movement of the disc L is relaxed, stopped or reversed
so that the disc is moving with greater velocity than the disc L, the bearing
piece m immediately moves away from the rim and allows the disc free movement.
A wire or light chain may be attached between the points S¹ and B, to limit the
scope of the recoil which may be very slight.
104. Valve Expansion and Reversing Gear for Steam engines. Plates 41, 42
43, 44 and 45. In all these examples of the application of claviger movements for
this purpose a slot link formed out of a right double bent slider claviger is
employed and the motion is taken from the cross head, from any part of the
connecting rod or from the crank pin. The principle and action of the right
double bent slider claviger has been explained in article 99.. The lines marked 4. 4,
and 4. 4 in Plate 36 represent the lead lines. The effect of the movement is
exactly the same as the ordinary link motion with two eccentrics, and it is much
simpler in construction and more powerful in operation. For convenience of
explanation the right double bent slider claviger in its application for the purpose
described at the head of this article will be called "the slot link." When the slot
in the link is curved it does not affect the accuracy of the motion. In the case of
a curved slot link for operating the valve direct the block carrying the connecting
link attached to the valve rod moves away from the straight line a db Plate 36
either towards a and b or at the centre d but that this does not affect the time and
length of the movement may be seen on reference to Plate 39. The movements aro
without error and perfect in every respect.
Plate 41 represents a direct acting valve gear. The motion is communicated to
the slot link from the connecting rod. The slot link, c d a b, may be situated in
any convenient position, but it.is desirable that the centre Jine of the guide g g
should be in the same line as the line of motion of the valve rod. The slot link is
curved to the arc of a circle having a radius equal to the length of the connecting
link vb, the radial action of the latter is thus corrected by the curvature of the
slot link. The motion is taken from the point C in the connecting rod D'B and
transmitted to the slot link by the claviger couple with unequal limbs C mc S m¹
of which S is the fixed axis. The line c d in the slot link corresponds to the line
CD in the connecting rod but it is reversed in direction. The line cd has the
same ratio to the line CD that the distance between the lead lines in the travel of
the valve has to the diameter of the crank pin circle. The limb C S of the claviger
couple has the same ratio to the limb s c. The result is that the motion of the
point C on the connecting rod is communicated to and exactly reproduced at
the point c on the slot link. The pivot d upon which the slot link oscillates
corresponds to the cross head D but it moves in a contrary direction to it being in
time one stroke apart from it. The block b to which the valve rod connecting link
is pivoted is arranged to slide up and down in the slot link so as to obtain different
degrees of port opening and cut off. For reversing, the block b is moved to the
other end of the slot link. A method of effecting this by a claviger couple with

page_text: unequal limbs bn e s¹ n¹ is represented in the figure. The direction of the slot
link is reversed so as to give equal grades of expansion. Fig. 2, Plate 43 represents
the application of this movement to an ordinary marine engine.
Plate 42 represents another form of the same movement.
The slot link is
placed in the opposite direction to that shewn in Plate 41. A straight slot link
a bed is used and it is connected to the connecting rod at C by the claviger
couple with unequal limbs Cm e S of which S is the fixed axis. The block b which
slides along the slot link is connected with the valve rod v v by the claviger
couple with unequal limbs b n¹ v S¹ of which S¹ is the fixed axis. The latter is a
stud upon a screw pinion which is moved up and down the fixed screw by operating
the handle wheel. The reduction in the length of the movement required for the
valve travel is effected by both the claviger couples. When the fixed axis S¹ is
moved up or down by the reversing wheel the movement of the block b in the slot
link corresponds.
Plate 43. Fig. 1. represents. the motion for the slot link taken from the cross
head. The direction of the slot link is reversed for direct acting as explained in
connection with Plate 41. The motion may be transmitted to the slot link from
the cross head by a claviger couple but as the motion of the cross head is in a
straight line it may be transmitted as shewn by a telescopic lever.
The slot link is here pivoted at C to a crank wrist on a disc O which revolves
upon a fixed stud or it is rigidly attached to a short shaft free to revolve in fixed
bearings. The fixed pin in the slot link at d which passes through the block
sliding along the fixed slide g g carries on the other side another block which is
held between the forked ends of the telescopic lever ds L. The lever is connected
at the other end to the cross, head at L. The fulcrum of the lever is s and it and
the fixed guide gg and the bearings of the disc O are attached to the common
framework. The slot link carries upon its back another slot at a higher level for
operating a separate expansion slide. The radius co has to the length of the main
crank and the line c d has to the length of the connecting rod the same ratio that
the travel of the valve from lead line to lead line has to the diameter of the crank
pin circle. The arins of the lever are in the same ratio. No claim is intended to
be made for the telescopic lever herein. The disc may be made heavy enough to
give momentum sufficient to carry the disc over the dead centres. The expansion
rod link a vis pivoted upon a stud in the block m which is free to slide along
the slot ef. The controlling rod x a' is pivoted upon the same stud and may be
operated by a governor or by any other means. The main valve. rod link a vis
pivoted upon the block n which is free to slide up and down the slot n b and is
controlled by the reversing rod ra which is pivoted upon the same stud. This
valve gear may be applied to the cross head of any piston rod such as those
operating beam engines and direct acting pumps.
Plate 44 Fig. 2 represents a similar valve gear double for operating the valves of
two cylinders placed at right angles to each other.. The motion is taken from an
elongation of the crank pin on the main crank and is transmitted by a claviger
couple. The method of attaching the claviger couple to the crank and disc and
the position of the parts are shewn separately in Fig. 3 of the saine plate.
105. Plate 44 Fig. 1 illustrates the practical application to the steam engine of
the movement represented in Fig. 1 Plate 6 and described in article 14. The two
cross leads of two pistons working in two cylinders set at right angles to each
other are connected by a right claviger couple the centre pivot being the crank pin.
The movement of the pistons is exactly the same forwards and backwards as
though each were connected to the crank by a connecting rod of infinite length.
The motion of the pistons is transmitted to the crank pin as a constant effort
applied in the direction of its motion. There is thus no dead point and no need
for a fly wheel. The power so applied is the sum of the two pressures upon the
pistons. The force is thus equalized. There is no stress thrown upon the crank 5
shaft or its bearings as a result of the conversion of the motion. There is no
sudden change in the direction of the stress so that even if the bearings upon the
L

page_text: crank pin should be loose there is no thumping or noise. The strains move with
regular velocity all round the crank pin bearings. The same is the case with the
joints of the claviger couple. Their movement is also slight and as the force is
divided amongst them the total friction is comparatively slight
106. Plate 45, Fig. 1 represents the practical application to a beam movement
for a steam engine of the double bent slider claviger described in article 99 and
illustrated in Plate 36 and the valve gear shewn in the figure is the same as just
described in article 104.
Three cylinders are employed on the compound system, the centre one being
used to expand the steam previously used by the other two. The used steam is
conveyed from the top and bottom of the small cylinders alternately to the top
and bottom of the large cylinder by crossed pipes the outlet of the steam from the
small cylinders being controlled by the same valve gear which operates their
valves. No steam is admitted into either small cylinder at lead for cushioning but
the outlet of the used steam into the large cylinder is cut off at lead and the
piston cushions against what is left. At port opening for the small cylinder the
outlet of the used steam is opened. The position of the crank and pistons, the
condition of the steam in the cylinders and the movement of the used steam to
the large cylinder at eight equal intervals of time during the revolution of the
crank is shewn by the figures in Plate 46.
The horizontal lines indicate the live steam, the vertical lines indicate the
steam being used expansively. The narrow vertical lines indicate the used steam
which has been employed for cushioning.
Plate 45 Figs. 2 and 3 represent in skeleton another arrangement of the beam
motion illustrated in Fig. so as to bring the crank lower down for operating
screw propellers. Fig. 2 is an elevation and Fig. 3 is a plan view.
107. Plates 47, 48 and 49 illustrate the practical application of the hanger
claviger herein before described to operate the ram of a shaping machine, with
quick return. It allows of any length of stroke and any ratio of return to forward
stroke as previously explained herein.
Plate 47 represents an elevation, Plate 48 an end view, and Plate 49 a plan view
of the movement and attached parts.
Having now particulary described and ascertained the nature of my said
invention and in what manner the same is to be performed, I declare that what
I claim is
1. The mechanisms hereinbefore described as hanger clavigers and their appli-
cation as mechanical movements in machinery generally for converting rectilinear
motion into circular motion and vice versa substantially as hereinbefore describėd
in article 13 and illustrated by Figs. 1 and 2 Plate 2 of the accompanying
drawings.
2. The use of the above mechanism referred to in Claim 1 for the purpose of
communicating the piston motion to the power shaft of steam or other engines
substantially as herein before described in article 13.
3. The mechanism herein before described as a claviger couple and the method of
employing it for converting two reciprical rectilinear motions acting at right angles
to each other into continuous circular motion and vice versa substantially as
hereinbefore described in articule 14, and illustrated by Fig. 1, Plate of the
accompanying drawings, and its use as a mechanical movement generally in
machinery.
4. The mechanisms hereinbefore described as slider clavigers and their appli-
cation as mechanical movements in machinery generally for converting circular
motion into reciprocal rectilinear motion, with quick return, and vice versa,
substantially as hereinbefore described in articles 15, 16 and 17, and illustrated
by Figs. 1 and 2, Plate 3; and by Fig. 1, Plate 4, of the accompanying drawings.
5. The use for the purposes herein before mentioned in article 17 of the
mechanisms described in claim 4.

page_text: 6. The mechanisms hereinbefore described as roller clavigers and their appli
cation as mechanical movements in machinery generally for converting rectilinea
motion into circular motion, and vice versa, substantially as hereinbefore described
in articles 18, 19 and 20 and illustrated in Fig. 1, Plate 5 of the accompanying
drawings.
7. The arrangement of Claviger mechanisms and its application as a mechanical
movement in machinery generally for converting rectilinear motion into circular
motion, and vice versa, with constant velocity ratio, substantially as herein before
described in articles 8, 12, 21, 22, and 23, and illustrated by Fig. 7, Plate 1, and
by Fig. 1, Plate 23 of the accompanying drawings.
8. The arrangements of claviger mechanisms and their application as mechanical
movements in machinery generally for transmitting rectilinear motion in any
direction with constant velocity ratio, varying the same in transmission in number
direction and velocity, substantially as hereinbefore described in articles 4, 5, 6, 7,
9, 10, 11, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 and 66, and illustrated by
Plates 1, 17 18, and 19 of the accompanying drawings.
9. The arrangements of Claviger mechanisms and their application as mechanical
movements in machinery generally for transmitting rectilinear motion at any angle
in any plane, with uniform velocity or with velocity at a constant ratio substan-
tially as herein before described in articles 36 and 37, and illustrated by Fig. 2,
Plate 5, and by Figs. 6 and 7, Plate 7 of the accompanying drawings.
10. The arrangements of the mechanism herein before described as a claviger
couple for effecting motion in two directions and varying the efficiency of the force
during transmission for use for similar purposes to those referred to in the
description substantially as herein before described in article 38, and illustrated by
Figs. 4 and 5 Plate 7 of the accompanying drawings.
11. The use for the purposes of weighing and lifting of the mechanism herein-
before described as a double claviger couple substantially as hereinbefore described
in articles 39 and 40.
12. The use for the purposes of weighing of the mechanism hereinbefore described
as a claviger pair substantially as herein before described in article 41, and illustrated
by Figs. 3 and 4, Plate 10.
13. The use for the purposes of lifting stamping punching, restraining velocipedes
&c of the mechanism herein before described as a claviger, singly or two in com-
bination, substantially as herein before described in articles 42, 43, and 85, and
illustrated by Figs. 3 and 4, Plate 5, by Fig. 1 Plate 7, and by Fig. 8, Plate 30, of
the accompanying drawings.
14. The use for the purpose of compressing &e of the mechanism he.einbefore
described as a chain of claviger pairs substantially as hereinbefore described in
article 44 and illustrated by Figs. 1 and 3, Plate 8 of the accompanying drawings. 4
15. The arrangement of the mechanism herein before described as a hanger
claviger and its combination with levers for effecting a transinission in a rectilinear
direction of the force applied to the lever, varying it in intensity during transmission;
and its use as a mechanical movement in machinery generally, substantially as
described in article 45 and illustrated by Figs. 2 and 3, Plate 7 of the accom- 4
panying drawings.
16. The arrangements and combinations of the mechanisms hereinbefore described
as hanger clavigers and their application as mechanical movements in machinery
generally, for transmitting circular motion from one part of the machinery to
another substantially as hereinbefore described in articles 46, 47, 48 and 50, and
and illustrated by Plate 9 of the accompanying drawings.
17. The arrangements and combinations of the mechanisms herein before described
as hanger clavigers for transmitting power to a distance in the form of continuous
circular motion substantially as hereinbefore described in article 49.
18. The mechanism herein before described as a claviger couple and its application 5.
as a mechanical movement in machinery generally for transmitting circular motion.
from one part to another substantially as herein before described in articles 3, 6, 9,*

page_text: 10, 11, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 70 and 101, and illustrated by:
Plate 1; Figs. 1 and 2, Plate 10; Figs. 1, 2, 3 and 5, Plate 11; Fig. 3, Plate 15;.
Figs. 3, 4 and 5 Plate 22; Fig. 1, Plate 25; and Figs. 1 and 2, Plate 40.
19. The use in machinery generally of the improved apparatus for transmitting.
circular motion substantially as herein before described in article 60 and illustrated
by Fig. 4, Plate 11, of the accompanying drawings..
20. The use for the purposes herein before referred to of the mechanism for
transmitting and reproducing motion in any direction in any plane, substantially
as herein before described in articles 63, 64 and 65, and illustrated by Fig. 1
Plate 22, of the accompanying drawings.
21. The mechanismo far converting oscillating motion into continuous circular
motion, and vice versa, varying the motion and modifying it during transmission,
and its application as a mechanical movement in machinery generally substantially
as herein before described in article 67 and illustrated by Fig. 2 Plate 26 of the
accompanying drawings.
22. The mechanism for converting continuous circular motion into reciprocal
rectilinear, any number of traverses per revolution, and vice versa, and its applica-
tion as a mechanical movement in machinery generally, substantially as herein-
before described in article 68.
23. The improved mechanism for connecting the weight and works of a clock
and regulating its movements in combination with a pendulum by direct motion,
hereinbefore
instead of by the intervention of escapements, substantially as
described in article 69 and illustrated by Fig. 1, Plate 31 of the accompanying
drawings.
24. The mechanism for multiplying or reducing the number of revolutions of a
shaft in transmission from one shaft to another, and its application as a mechanical
movement in machinery generally, substantially as herein before described in
article 71, and illustrated by Figs. 1 and 2, Plate 14 of the accompanying
drawings.
25. The mechanism for doubling or halving the number of revolutions of a
shaft in transmission from one shaft to another, and its application as a mechanical
movement in machinery generally, substantially as herein before described in
article 72, and illustrated by Plate 12 and 13 of the accompanying drawings.
26. The mechanism herein before described as a claviger couple in combination
with fixed or revolving or oscillating guides for multiplying or reducing the number
of revolutions of a shaft, in transmission from one shaft to another contiguous to
each other and in the same line, and its application in machinery generally,
substantially as herein before described in articles 73, 74, 75, 76, 77 and 79, and
illustrated by Figs. 1 and 2, Plate 15; Fig. 1, Plate 26; Figs. 1 and 2, Plate 29;
Figs. 6 and 7, Plate 30; and by Plates 27 and 28.
27. The arrangements of Claviger mechanisms containing a circular arrangement
of rollers for rolling on a fixed revolving or oscillating cycloidal guide for multi-
plying or reducing the number of revolutions of a shaft in transmission from one
shaft to another contiguous to each other and in the same line; and their applica-
tion in machinery generally, substantially as described in articles 78, 79, 80
and 81, and illustrated by Figs. 1, 23 and 4, Plate 20, of the accompanying
drawings.
28. The arrangements of mechanism for multiplying or reducing the number of
revolutions of a shaft in transmission from one shaft to another, contiguous to each
other and in the same line, by rolling contact of rollers on fixed or moveable
cylindrical guides, and their application in machinery generally, substantially as
described in articles 79, 81, 82, and S3 and illustrated by Figs. 5 and 6, Plate 20
and by Figs. 1, 2, 3, and 4, Plate 21.
29. The arrangements of mechanism and their application as mechanical move-
5 inents in machinery generally for the fractional multiplication or reduction of
the number of revolutions of one shaft in transmission to another shaft by means
of revolving cycloidal guides and rollers substantially as hereinbefore described in

page_text: rvices of and ɔ and illustrated by Plate 16, Figs. 1, 2, 3, 4, 5 and 6 and Plate 32,
Figs. 1 and 2 of the accompanying drawings.
30. The mechanism hereinbefore described as a claviger couple applied for
operating a bicycle by pedal action substantially as hereinbefore described in
article 85 and illustrated by Figs. 2 and 6 Plate 22, of the accompanying drawings.
I claim all forms of claviger couples for this purpose except the particular form
which is a right claviger couple of the second kind with the common pivot of the
two restraining arms midway between the power end and the fixed axis.
31. The mechanism consisting of a claviger couple and a claviger pair forming a
transmitter of circular motion with clutch action; and its application to velocipedes
substantially as hereinbefore. described in article 85 and illustrated by Fig. 2,
Plate 25, of the accompanying drawings.
32. The mechanism herein before described as a claviger in connection with a
handle and screw for operating the steering of a velocipede substantially as hercin-
before described in article 85 and illustrated by Fig. 5, Plate 5, of the accompanying
drawings.
33. The Claviger movements forming clutch motions for operating drill braces,
substantially as hereinbefore described in article 86, and illustrated in Figs. 9. 10.
and 11 Plate 30.
34. The combination and arrangement of claviger movements in connection with
brake blocks, and their use for the purpose of restraining and stopping railway
engines and trains substantially as herein before described in article 87, and
illustrated in Fig. 1 and 2, Plate 24, and in Fig. 2, Plate 23, of the accompanying
drawings.
35. The safety valve mechanism substantially as herein before described in
article 88 and illustrated by Plate 31, Fig. 2, of the accompanying drawings.
36 The direct acting pressure steam guage substantially as herein before described
in article 89, and illustrated by Plate 31, Fig. 3, of the accompanying drawings.
37. The mechanism for converting continuous circular motion in opposite
directions into reciprocal rectilinear motion and its application as a mechanical
movement in machinery generally, substantially as hereinbefore described in
article 90, and illustrated by Plate 31, Fig. 4, of the accompanying drawings.
38. An improved ellipsograph substantially as herein before described in article 91.
39. The adaptations of the mechanism hereinbefore described as a claviger couple
for drawing curves, trisecting angles, and reproducing drawings, maps &c sub-
stantially as herein before described in articles 92, 93 and 94, and illustrated by
Plate 34, Figs. 1, 2, 3, 4, 5, 6, 7, 8, and 9.
40. The mechanism for doubling the revolution of a shaft, and its application
as a mechanical movement .in machinery generally substantially as herein before
described in article 96 and illustrated by Plate 33, Fig. 1, of the accompanying
drawings.
41. The application of the mechanism referred to in the preceding claim to the
driving of velocipedes, substantially as herein before described in article 97, and
illustrated by Plate 33, Fig. 2, of the accompanying drawings.
42. The mechanism herein before described as a double roller claviger, and its
application as a mechanical movement in machinery generally, for converting
alternate or reciprocal rectilinear motion into continuous circular, and vice versa,
substantially as hereinbefore described in article 98, and illustrated by Plate 35 of
the accompanying drawings.
43. The mechanisins hereinbefore described as bent roller clavigers, double bent
roller clavigers and double bent slider clavigers, and their application as mechanical
movements in machinery generally, for converting reciprocal and alternate
rectilinear motion into continuous circular motion, and vice versa, substantially as
herein before described in article 99, and illustrated by Plate 36, of the accompanying
drawings.
44. The adaptation and application for pedal mechanism for operating velocipedes,
lathes &e of the mechanisms described in claims 42 and 43, substantially as herein-

page_text: before described in article 100, and illustrated by Plates 37, 38 and 39 of the
accompanying drawings.
45. The adaptation of the mechanisms hereinbefore described in articles 98, 99
and 100, and their application as mechanical movements in machinery generally
for transmitting circular motion substantially as hereinbefore described in
article 102 and illustrated by Plate 40, Figs. 3, 4 and 5, of the accompanying
drawings.
46. The mechanism herein before described as the claviger clutch and its
application as a mechanical movement in machinery generally for clutch motions,
substantially as hereinbefore described in article 103, and illustrated by Plate 40,
Figs. 6, and 64, of the accompanying drawings.
47. The mechanism herein before described in article 99 as a double bent slider
claviger, arranged and applied for operating the valves for steam and other engines,
substantially as hereinbefore described in article 104, and illustrated by Plates 41,
42, 43, 44, and 45, of the accompanying drawings.
48. The mechanism hereinbefore described in article 99 as a double bent slider
claviger, in combination with the mechanism herein before described as a claviger
couple and alternatively, when the motion is taken from the cross-head, in com-
bination with its mechanical equivalent, a telescopic lever, and the application of
such combinations for operating the valves of steam and other engines, substantially
as herein before described in article 104, and illustrated by Plates 41, 42, 43, 44,
and 45 of the accompanying drawings.
49. The application of the mechanism herein before described as a claviger couple
for reversing gear for steam and other engines substantially as herein before
described in article 104, and illustrated by Plates 41 and 42 of the accompanying
drawings.
50. The application of valve gear such as herein before described and claimed
to all engines where hitherto the "eccentric and link" motion has served like
purposes, substantially as herein before described.
51. The application of the mechanism hereinbefore described as a claviger couple
for transmitting the motion from two pistons operating in two cylinders set at
right angles to each other, to the crank shaft and rotating it, substantially as
hereinbefore described in article 105, and illustrated by Plate 44, Fig. 1, of the
accompanying drawings.
52. The application of the mechanisın hereinbefore described in article 99 as a
double bent slider claviger as a beam for transmitting and converting the reciprocal
rectilinear motion of the pistons of three cylinders into the continuous circular
motion of the crank shaft, substantially as hereinbefore described in article 106,
and illustrated by Plate 45 of the accompanying drawings.
53. The application of the mechanism herein before described as a hanger
claviger, for operating a ram holding a tool, with quick return stroke for shaping
planing and slotting machines, substantially as hereinbefore described in article 107,
and illustrated by Plates 47 48 49 of the accompanying drawings.
Dated this ninth day or
Witness,
I. & J. SHOOLBRED.
1st 1880.
WILLIAM GOLDING.