APPARATUS WHEREBY THE RELATIVE MOTION OF TWO OR MORE BODIES MAY EITHER BE VARIED IN ANY REQUIRED MANNER INDEPENDENTLY OF THEIR ACTUAL MOTIONS, OR MAY BE DETERMINED
Year: 1884

page_text: I, HENRY SELBY HELE SHAW, of University College, Bristol, Professor of
Engineering do hereby declare the nature of the said invention for "APPARATUS
WHEREBY THE RELATIVE MOTION OF TWO OR MORE BODIES MAY EITHER BE
VARIED IN ANY REQUIRED MANNER INDEPENDENTLY OF THEIR ACTUAL MOTIONS,
OR MAY BE DETERMINED;" to be as follows:
This invention consists of a mechanical device, which, in its fundamental form,
is composed of a sphere having two sets of rollers in frictional contact therewith.
In applying the said invention the following conditions are to be observed:-
1st; Rolling motion only of the surfaces in contact must, with certain definite
exceptions, be ensured. 2nd; Each set of rollers is to be always in contact with a
great circle of the sphere, and the imaginary diametral planes which form the
two temporary great circles of the sphere, by their intersection with the spherical
surface, must be always perpendicular to each other. 3rd; The plane of rotation
of each of the rollers should, in general, but need not in all cases, contain the
centre of the sphere and must be perpendicular to the diametral plane of its great
circle of contact.
Each set of rollers is carried in a separate frame, the frames having such motion
with respect to each other as to ensure the relatively perpendicular position of the
planes of the great circles. The conditions above set forth being observed, cach
frame can have motion only about an axis lying in the plane of its own great
circle and perpendicular to the plane of the great circle of the other frame at its
centre.
If, for convenience, one frame is fixed with its great circle of contact horizontal,
the other frame must be so supported as to be enabled to rotate about a vertical
axis. The former may be designated the fixed frame, and the latter, the movable
frame. On the exertion of a force tending to turn one of the rollers in the fixed
frame, the said roller will, by frictional contact, tend to turn the sphere about an
imaginary axis in the diametral plane of that frame, as the axes of rotation of the
sphere and roller will then intersect. All the other rollers in the said frame will,
except in a case hereinafter more particularly referred to, freely rotate on the
19

page_text: sphere when it is turning about an axis in the said diametral plane, but not other-
wise. The effect of the movable frame is to determine the particular axis about
which the sphere, as aforesaid, tends to be turned. Inasmuch as the rollers of the
movable frame are subject to similar conditions to those to which the rollers of the
fixed frame are subject, the axis about which the sphere must revolve in order that
the required conditions may be fulfilled, is that coinciding with the line common
to both the great circles of contact, that is with the intersection of the perpendicular
diametral planes. Of the rollers, two only in each frame can roll at once round
great circles of the sphere the said two rollers being each equidistant from the
points of intersection of the two great circles and directly opposite to each other.
The other rollers, rolling on small circles of the sphere, have different relative
motion or angular velocitios according to the circles on which they roll. The
actual velocity of any of these said other rollers is dependent, first, upon the actual
motion or angular velocity of the roller which turns the sphero and, secondly, upon
the relative position of the driving roller and that driven with respect to the axis.
of rotation of the sphere.
..
As the force exerted on the driving roller practically produces only an effect
parallel to the plane of the great circle of contact of the movable fraine, no
tendency to turn the said frane bodily about its vertical axis of rotation is created,
and the motion of the frame is, consequently, independent of the motion imparted
to the driving roller, and vice versa.
Thus the relative motions of the driving roller and any other may be varied by
changing the position of the frame without affecting the actual motion or angular
velocity of the driving roller which latter may be simultaneously and independently
varied in any required manner.
Conversely, by means berdinafter more particularly described, whatever relative
motions or velocities two separate rollers may have they may be made to always
tend to adjust the position of the frame so as to roll upon circles of the sphere
corresponding to their respective motions. Thus the position of the frame
determines their relative motion or velocity ratio.
Whilst the conditions horeinbefore set forth are fulfilled, the distribution of the
rollers in their respective frames does not affect the position of the axis of rotation
of the sphere, depending, as it does, upon the position of the planes of rotation of
the sets of rollers relatively to each other and not to their angular distance apart.
By preserving a sufficient distance, on each side, between the rollers in the
movable frame and the great circle of contact of the fixed frame, the movable
frame may be turned round through any angle without causing contact to occur
between the rollers in the two frames. Should the frictional contact on the sphere
of two opposite rollers of either frame coincide with the point of intersection of
the two great circles of contact, through which point the axis of rotation of the
sphere passes, the points of contact aforesaid, then serve as temporary centres of
rotation of the sphere and do not, themselves, turn. It is only when the movable
frame assumos a limited number of certain definite positions that the aforesaid
effect is produced upon two opposite rollers of the fixed frame, and the velocity
ratio then has an extreme value. But when the said effect is produced upon two
opposite rollers of the movable fraino, the said rollers always act as the centres of
rotation of the sphere and the travel of their frame is limited by them to thọ
distance apart of two rollers of the fixed frame. Thus the said rollers of the
movable frame constituto movable centres.
For the transmission of varying motion the rollers in the fixed frame are
generally to be employed. One or more of the rollers of the movable frame which
support the sphere may also be used for the same purpose.
Any desired number of rollers may be carried in the frames.
The said invention will be more clearly understood by reference to the accom-
panying sheets of illustrative drawings.
Fig 1 represents a plan, and Fig 2 an elevation, of a sphere G and accompanying

page_text: D. D are the rollers of the movable frame (not shown). The arrangement of
the rollers in the movable frame is such that motion of the movable frame does not
cause their contact with those of the fixed frame. The rollers A. A' and B. B¹ are
respectively in contact with the sphere G at the points a. a' and b. b' upon tho
great circle formed by the intersection of the horizontal diametral plane with the
sphere. The rollers C. C₁ and D. D' are in contact with the sphere Gat
the points c. and d. upon the great circle formed by the intersection of a
vertical diametral plane.
In turning the roller A, the axis of consequent rotation of the sphere G passes
through the intersection of the great circles, that is through k. k, Fig 2. The
roller A rotates on the circle represented by the dotted line a. p. q, Fig 1. Tho
motion of the roller A' is similar to that of.the roller A. The rollers B. B' having
similar motion to each other, that of the roller B only requires to be considered.
The circle on which the roller B rotates is represented by the dotted lines b, r, 8,
Fig 1. The ratio of the two radii a, p. and b, r gives the relative motion or
velocity ratio of the rollers A and B.
By moving the frame carrying the roller C. C¹ and D. D¹ about a vertical axis,
the radii a. p and b. r, and the relative motion of the rollers A and B, are altered.
One limiting case is when, by the coincidence of the axes k. k¹ and b. b², tho
velocity of the roller B is nil. The other limiting case is when the axes k. k¹
and a. a' coincide, immediately before which the velocity of the roller B would
have its extreme possible relative speed.
Figs 3 and 4 illustrate in plan and elevation a different method of disposing the
rollers. The rollers C. C₁ of the movable frame, (not shewn) being always in
contact with the intersection of the great circles of the sphere, constitute movable
centres. The rollers D. D' form the centres of rotation of the frame, the vertical
axis of the sphere passing through their points of contact therewith. Under this
arrangement the range of relative motion or velocity ratio is limited to the ratio
of the square. of the maxima and minima values of the radii a. p and b. r
determined by the degree of proximity which the rollers C. C¹ can respectively
assume to the rollers A. B' and A' B.
Figs 5 and 6, which represent diagramatic plans of the apparatus, demonstrate
modes of obtaining numerical results. In Fig. 5, N represents the centre of the
roller A, and . k the temporary axis of revolution of the sphero G. O. M. is a
perpendicular at the centre O of the sphere G meeting the axis of the roller A,
produced, in M.
Taking M. N. as a variable force and the wheel A to be thereby turned through
the distance through which the said force overcomes a resistance, the turning of
the wheel B gives the product of the said two quantities, in other words, the work
done by the force.
Since M. N. varies as the tangent of the angle through which the frame is turned;
the method of computation above set forth may be conveniently termed the tangent
method of computation.
In the plan of the sphere shown at Figure 6 M. N. is perpendicular to the
line O. M. The rollers D or D' of the movable frame may, in this case, be turned..
The rotation of the roller B varies conjointly as the value of M. N. and the rotation
of D. or D¹ Since M. N. varies as the sine of the angle of inclination of the
frame, the method of application, by which work may be measured, may be con-
veniently termed the sine method of computation.
Conversely, if, in either of the above cases, motion by one body had been
imparted to the roller B, the roller A would tend to turn by means of the sphere.
If the axis of the roller A be in the form of a screw freely working in the roller A
as a nut and be driven by another body, should the relative motion or velocity.
ratio of the roller A and its axis not be the same, the position of M and, therefore,
of the frame, will, by the action of the scrow, be so adjusted that the velocity ratio
of the roller A and its axis becomes the same. Hence the position of M indicates
ar.determines the relative motion or velocity ratio of the two bodies.

page_text: If, instead of the actual quantity, the trigonometrical ratio of an angle were given
as one of the variable quantities, the methods set forth with reference to Figs 5
and 6 allow this to be obtained by a suitable arrangement in connection with the
angle (a) of the frame, that is, of the axis of revolution k. k¹.
Figs: 7, 8, 9 and 10 represent different views of parts of the sphere and roller
mechanism and illustrate its application-wherein the rollers in the movable frame
are upon the great circle of the rollers of the other frame.
This application is adapted for the mechanical integration of areas. By the
addition of one more set of spheres and rollers it is adapted for the determination,
simultaneously, of the statical moment of an area. With two additional sets of
sphere and rollers it is adapted to the determination simultaneously of the moment
of inertia of the area about a given line. The elevation of the movable frame F is,
with its supporting bracket I, shown apart, at Fig: 10, from the rest of the
mechanism. The frame F is free to rotate bodily about the vertical axis on the
centres E. E¹. In the integration of areas, the paper upon which is represented the
area to be integrated is wound about the drum or cylinder H, (Figs: 7.8 and 9.)
and the roller Ä bears upon it. As the drum or cylinder H is caused to rotate
by turning the milled wheel J, (Fig 8) the roller A revolves and motion is thereby
imparted to the sphere G and transmitted to the roller B the motion of which for
a given movement of the roller A, depends upon the position of the axis of rotation
of the sphere G, that is, upon the position of the movable frame. The line k. k'
(Fig: 7) corresponds to the said axis which depends upon the position of M,
corresponding, when the movable frame is in its place, to the position of the
pointer P. The pointer P is made to continuously coincide with the boundary of
the area to be integrated, and, by the combined effect of the position of the frame,
regulated by the pointer P, and the motion of the roller A across the curve, the area
is directly given by the distance turned through by the roller Band measured by the
hand or pointer K upon the dial L. The pressure exerted by the rollers A. A¹ and
B. B' upon the sphere is adjusted by means of the springs S. S. (Figs: 7, 8, and 9)
The adjustment of the rollers C. C and D. D' of the movable frame is effected
by means of the sliding bearings U. U and V and the corresponding springs ✗Y
and Z seen at Fig: 10. By a modification of this mechanism the continuous
product of any two quantitios, one increasing in value according to the rotation of
the roller A, the abscissa, and the other proportional to the distance or corresponding
ordinate M. N, may be obtained, whether the product be work done (f. F. d. a) or
any other quantity.
Conversely, by causing M to be moved by a Screw, turned instead of the roller A
through which it passes as a nut, while the roller B is being turned independently
by another moving body, the relative motion of A and B or their velocity ratio is
given by the position of the pointer P or the point M shown on a suitablo scale.
The relative value or quotient of any two quantities may thus be obtained.
By means of the arrangement above described of the sphere and rollers a range
of relative motion or velocity ratio sufficient for a variety of purposes may be
obtained. The sphere must be of such a nature that the edges of the discs C. C'
may twist upon the surface to which they act as centres of revolution. The
rollers D. D' have the same relative motion.
In Figs: 11 and 12, which represent the more general form of arrangement of
the mechanism, the rollers of which more than the four shown may, if required,
be employed, are so disposed as to avoid twisting of the surface of the sphere in
contact with them, so that only rolling of the sphere and rollers occurs. Under this
arrangement, in which the principle of action is the same as that of the arrangement
berein before described, extreme range of relative motion or velocity ratio is possiblo-
At Fig 11 is shown the elevation of the frame F working on the centres E. E
about a vertical axis and in such a position that the motion or velocity of the
roller B is infinitely small compared with that of the roller A. At Fig 12 is shown
the frame F, in plan, and its supporting bracket L. The dotted lines indicate the
position of the frame which causes a relative motion of the rollers A and B measured

page_text: by the distance M. N. By varying the position of the point M the axis N.Q. may
be made to transmit any required motion to the axis O. P. Conversely, if, N. Q
be the axis in the form of a Screw passing through the roller A as a nut, the
position of the point M may be made to indicate the relative motion or angular
velocities of the body the motion of which corresponds with the motion of the
scrow, and the body the motion of which corresponds with the motion of the
roller B.
By this invention the relative motion or velocity ratio of two bodies in motion
may be varied in any desired manner without requiring the surfaces, through which
the motion is transmitted, to slip over each other, as required, for instance, in the
case of the disk and roller mechanism.
Thus, since nothing but rolling motion is required, the normal pressure of the
surfaces in contact may be considerably reduced, since the edge of the disks, rollers
or wheels may be milled, serrated or furnished with teeth so as to impress tem-
porarily a corresponding toothed envelope upon the surface of the sphere which
may be made of suitable material for this purpose.
The mechanism is, therefore, suitable for employment in such appliances as
dynamometers, continuous indicators, governors, horse power and efficiencý
indicators, and for transmitting force.
Again, since there is no motion not coinciding with the plane of rotation of the
rollers, one source of error, in devices of an analogous kind, is avoided. The
mechanism is, therefore, suitable for mathematical purposes of the greatest accuracy,
both for processes of summation and differentiation.
The symmetrical disposition of the moving parts enables the normal pressure of
the rollers transmitting power to be balanced by, the opposite rollers. Therefore;
the pressure due to this cause is taken off instead of acting, as it otherwise would,
upon the system which serves as a bearing upon which the sphero rotates.
These opposite rollers may, if desired, be employed simultaneously to transmit or
receive motion.

page_text: TATTOO
DIECITATIO
I, HENRY SELBY HELE SHAW, of University College, Bristol, Professor of
Engineering do hereby declare the nature of my said invention for "APPARATUS
WHEREBY THE RELATIVE MOTION OF TWO OR MORE BODIES MAY EITHER BE VARIED
IN ANY REQUIRED MANNER INDEPENDENTLY OF THEIR ACTUAL MOTIONS OR MAY BE
DETERMINED," and in what manner the same is to be performed, to be particularly
described and ascertained in and by the following statement:-
My said invention consists of a mechanical device which, in its fundamental
form, is composed of a sphere having two sets of rollers in frictional contact
therewith In applying the said invention the following conditions are to be
observed-1st, Rolling motion only of the surfaces in contact must, with certain
definite exceptions, be ensured-2nd, Each set of rollers is to be always in contact
with a great circle of the sphere, and the imaginary diametral planes which form
the two temporary great circles of the sphore, by their intersection with the
spherical surface, must be always perpendicular to each other. 3rd, The plane of
rotation of each of the rollers should, in general, but need not in all cases, contain
the centre of the sphere and must be perpendicular to the diametral plane of its
great circle of contact.
Each set of rollers is carried in a separate frame, the frames having such motion
with respect to each other as to ensure the relatively perpendicular position of the
planes of the great circles. The conditions above set forth being observed, each
frame can have motion only about an axis lying in the plane of its own great circle
and perpendicular to the plane of the great circle of the other frame at its centre.
If, for convenience, one frame is fixed with its great circle of contact horizontal,
the other frame must be so supported as to be enabled to rotate about a vertical
axis The former may be designated the fixed frame, and the latter, the moveable
frame. On the exertion of a force tending to turn one of the rollers in the fixed
frame, the said roller will, by frictional contact, tend to turn the sphere about an
imaginary axis in the diametral plane of that frame, as the axes of rotation of the
sphere and roller will then intersect. All the other rollers in the said frame will,
excopt in a case hereinafter more particularly referred to, partly rotate on the sphere
when it is turning about an axis in the said diametral plane, but not otherwise.
The effect of the movable frame is to determine the particular axis about which
the sphere, as aforesaid, tends to be turned-Inasinuch as the roller or rollers of
the movable frame are subject to similar conditions to those to which the rollers of
the fixed frame are subject, the axis about which the sphere must revolve in order
that the required conditions may be fulfilled, is that coinciding with the_line
common to both the great circles of contact, that is with the intersection of the
perpendicular diametral planes. Of the rollers, two only in each frame can roll at
once round great circles of the sphere the said two rollers being each equidistant
from the points of intersection of the two great circles and directly opposite to

page_text: each other. The other rollers, rolling on small circles of the sphere, have different
relative motion or angular velocities according to the circles on which they roll.
The actual velocity of any of these is dependent, first, upon the actual motion or
angular velocity of the roller which turns the sphere, and, secondly, upon the
relative position of the driving roller and that driven with respect to the axis of
rotation of the sphere. As the force exerted on the driving roller practically
produces only an effect parallel to the plane of the great circle of contact of the
movable frame, no tendency to turn the said frame bodily about its vertical axis of
rotation is created, and the motion of the frame is, consequently, independent of
the motion imparted to the driving roller, and vice versa.
Thus the relative motions of the driving roller and any other may be varied by
changing the position of the frame without affecting the actual motion or angular
velocity of the driving roller which latter may be simultaneously and independently
varied in any required manner.
Conversely, by means hereinafter more particularly described whatever relativo
motions or velocities two separate rollers may have, they may be made to always
tend to adjust the position of the frame so as to roll upon circles of the sphero
corresponding to their respective motions. Thus the position of the frame
determines their relative motion or velocity ratio.
Whilst the conditions herein before set forth are fulfilled, the distribution of the
rollers in their respective frames does not affect the position of the axis of rotation
of the sphere, depending as it does upon the position of the planes of rotation
of the sets of rollers relatively to each other and not to their angular distance
apart.
By preserving a sufficient distance, on cach side, between the roller or rollers in
the movable frame and the great circle of contact of the fixed frame, the movable
frane may be turned round through any angle without causing contact to occur
between the rollers in the two frames Should the points of frictional contact on
the sphere of two opposite rollers of either frame when two opposite rollers are
used or of one when the opposite one is removed coincide with the point of
intersection of the two great circles of contact, through which point the axis of
rotation of the sphere passes the point or points of contact aforesaid thon serve as
temporary centre or centres of rotation of the sphere and do not themselves turn.
It is only when the movable frame assumes a limited number of certain definite
positions that the aforesaid effect is produced upon two opposite rollers of the fixed
frame, and the velocity ratio then has an extreme value. But when the said effect
is produced upon two opposite rollers of the movable frame if two be used, which
is not always the case, the said rollers always act as the centres of rotation of the
sphere and the travel of their frame is limited by them to the distance apart of two
rollers of the fixed frame. Thus the said rollers of the movable framo constitute
movable centres. This is the special case forming part of the invention comprised
in my former application for Letters Patent N° 6206 dated 10th April 1884.
For the transmission of varying motion the rollers in the fixed frame are
generally to be employed. One or more of the rollers of the movable frame which
support the sphere may also be used for the same purpose.
Any desired number of rollers may be carried in the frames.
My said invention will be more clearly understood by reference to the
accompanying sheet of illustrative drawings.
Fig. 1, represents a plan, and Fig: 2 an elevation of a sphere G and accompanying
rollers. A, A and B, B' are the rollers of the fixed frame (not shewn). C, C and
D, D' are the rollers of the moveable frame (not shown) The arrangement of the
rollers in the moveable frame is such that the motion of the movable frame does
not cause their contact with those of the fixed frame. The rollers A, A' and B, B'
are respectively in contact with the sphere G at the points a, a and b, b' upon the
great circle formed by the intersection of the horizontal diametral plane with
the sphere. The rollers C, C and D, D' are in contact with the sphere Gat

page_text: the points c. c' and 'd, d upon the great circle formed by the intersection of a
vertical diametral plane.
In turning the roller A the axis of consequent rotation of the sphere G passes
through the intersection of the great circles, that is through k, Fig 1. The
roller A rotates on the circle represented by the dotted line a. p. q. Fig 1 The
motion of the roller A is similar to that of the roller A¹. The rollers B, B' having
similar motion to each other, that of the roller B only requires to be considered.
The circle on which the roller B rotates is represented by the dotted line b, r, 8,
Fig 1. The ratio of the two radii a p and b. r gives the relative motion or
velocity ratio of the rollers A and B.
By moving the frathe carrying the rollers C, C, and D, D' about a vertical axis,
the radii a,p and b, r, and the relative motion of the rollers A and B are altered.
One limiting case is when by the coincidence of the axes k. k¹ and b. b, the velocity
of the roller B is nil-The other limiting case is when the axes k. ' and a, a
coincide immediately before which the velocity of the roller B would have its
extreme possible relative speed.
Figs 3 and 4 illustrate in plan and elevation the special method of disposition of
rollers in the movable frame herein before referred to as forming part of the invention
comprised in my said former application for Letters Patent N° 6206 of 1884
already alluded to as forming part of the subject matter-The rollers C, C' of the
movable frame (not shown) being always in contact with the intersection of the
great circles of the sphere constitute movable centres-The rollers D. D' form
the centres of rotation of the frame the vertical axis of the sphere passing through
their points of contact therewith.
Under this arrangement the range of relative motion or velocity ratio is limited
to the ratio of the maxima and minima values of the radii a. p and b, r determined
by the degree of proximity which the rollers C, C' can respectively assume to the
rollers A, B and A', B.
Figs 5 and 6 which represent diagramatic plans of the apparatus, demonstrate
modes of obtaining numerical results. In Fig 5 N represents the centre of the
roller A, and K. K the temporary axis of revolution of the sphere G.
oM is a perpendicular at the centre o of the sphero G meeting the axis of the
roller A produced in M.
Taking M N. as a variable force and the wheel A to be thereby turned through
the distance through which the said force overcomes a resistanco the turning of the
wheel B gives the product of the said two quantities in other words the work done
by the force.
Since M. N. varies as the tangent of the angle through which the frame is turned,
the method of computation above set forth may be conveniently termed the tangent
method of computation.
In the plan of the sphere shown at Fig 6 M. N. is perpendicular to the line O M.
The rollers D or D' of the movable frame may, in this case be turned. The rotation
of the roller B varies conjointly as the value of ML N. and the rotation of D or D¹.
Since MN, varies as the sine of the angle of inclination of the frame the method of
application by which work may be measured may be conveniently termed the sine
method of computation.
Conversely, if, in either of the above cases, motion by one body had been
imparted to the roller B the roller A would tend to turn by means of the spherc.
If the axis of the roller A be in the form of a screw freely working in the roller A as
a nut and be driven by another body, should the relative motion or velocity ratio
of the reller A and its axis not be the same, the position of M and, therefore, of
the frame, will, by the action of the screw, be so adjusted that the velocity ratio of
the roller A and its axis becomes the same. Hence the position of M. indicates or
determines the relative motion or velocity ratio of the two bodies.
In place of the arrangement of which the screw forms a part a connection may !
bo made by wheel work or by Levers or by any other suitable means.

page_text: If, instead of the actual quantity the trigonometrical ratio of an angle were given
as one of the variable quantities the methods set forth with reference to Figs 5 and 6
allow this to be obtained by a suitable arrangement in connection with the angle (a)
of the frame, that is, of the axis of revolution k. kl.
An arrangement of sphere and rollers comprised in my invention forming the
subject of my said former application made by me for Letters Patent numbered 6206
dated 10th April 1884 and described in the complete specification of the said
application as adapted for the mechanical integration of areas, is also described
in the Provisional Specification of this present application for Letters Patent
numbered 8391 dated 29th 1884. It is introduced in the Provisional Specification
for the purpose of enabling the features of improvement comprised in the invention
herein being described to be better understood.
In Figs 7 and 8 which represent the more general form of arrangement of the
mechanism, the rollers of which more than the four shewn may, if required, be
employed are so disposed as to avoid twisting of the surface of the sphere in contact
with them so that only rolling of the sphere and rollers occurs. Under this
arrangement extreme range of relative motion or velocity ratio is possible. At
Fig 7 is shewn the elevation of the frame F working on the centres E E about a
vertical axis and in such a position that the motion or velocity of the roller B is
infinitely small compared with that of the roller A. At Fig 8 is shown the frame F
in plan and its supporting bracket I The dotted lines indicate the position of the
frame which causes a relative motion of the rollers A and B measured by the
distanco M N. By varying the position of the point M the axis NQ may be made
to transmit any required motion to the axis O. P. Conversely, if N. Q be the axis
in the form of a screw passing through the roller A as a nut the position of the
point M may be made to indicate the relative motion or angular velocities of the
bodies the motion of one of which corresponds with the motion of the screw,
the motion of the other of which corresponds with the motion of the roller B.
Figs 9. 10. & 11 represent respectively different elevations and a plan of amplified
arrangement of sphere and rollers wherein two rollers are disposed in a fixed framo
(not shown in the drawing) and one roller in a movable frame. A and B tho
rollers of the fixed frame, are in contact with the sphere G at the points indicated
by a and b-D the roller supported in the movable frame F is in contact with the
sphere at the point indicated by d-The sphere G is thus supported by the rollers
at the points a. b. and d. The diametral planes d. k. k' and a. k b. k. intersect in
the line k. k which is the axis of rotation of the sphere G when turned by either
of the rollers A B D. If turned by either of the rollers A or B the result obtained
corresponds to the tangent or cotangent of the angle through which the frame F is
moved If turned by the roller D the result corresponds to the sine or cosine of
the said angle.
Fig 12 represents a sectional elevation and Fig 13 a plan of the simplified
arrangement of sphere and rollers last described adapted for operation to ascertain
the product of two variable quantities. The rollers A and B in contact with the
sphero G at the points a and b are carried upon the spindles and m free to rotate
in bearings attached to or forming part of the fixed frame L The frame I is
tilted or inclined to a degree sufficient to cause the sphero G to rest upon the
rollers A and B aforesaid and upon the roller D carried below the sphere in the
movable frame F. The frame F is free to rotate in bearings f. and g formed in
the bracket R. If the frame F be turned in its bearings ƒ and g through any angle
the tangent of which is proportional to the quantity being measured while tho
axis m of the roller A is turned at a known rate or to a known extent the axis of
the roller B will rotate proportionally to the product of the aforesaid quantities
and the circumferential motion of the roller A.
By these means the presence of a fluid electric energy or force the power being
transmitted through any piece of mechanism or any other variable or constant
quantity may be measured in amount, it being understood that the arrangements.

page_text: are such that the tangent of the angle through which the frane F is turned is, as
aforesaid, proportional to the quantity being measured.
If desired one or more rollers A¹ B' D' C, C¹ reprosented in the drawing in
dotted lines may be employed in addition to the rollers A. B and D without
affecting the results obtained by use of the latter.
•
The product may be indicated by means of a hand or pointer turning on the
face of the graduated dial L, or by the counter T.
As represented at Figs 12 and 13 the apparatus is arranged for obtaining tho
product of two constant quantities one of which is indicated upon the scale t, u an
index v being set at the required point and assuring the correct position of the
pointer P. The index v being set the other quantity is measured on the dial L¹ by
turning the hand belonging thereto to the required graduation on the face of the
dial. The product is thon read from the dial L or counter T.
1
Fig 14 represents in sectional elevation and Fig: 15 in Plan the application
to a plain meter of the sine arrangement of the sphere and rollers herein before
referred to.
The point Z being fixed in the paper or on a fixed stand bearing the figure of an
area to be measured the pointer P is moved in conformity with the configuration
of the said figure-The roller D is thus made to roll upon the surface of the paper
and motion is imparted by it to the Sphere G which is thus caused to turn about
an axis formed by the intersection of the diametral planes which pass through the
points 6 and d and which, when produced, contain the Axes of the Rollers B and D
respectively.
The Roller B is consequently rotated and the result is recorded upon the dial L
by means of the hand K.
The Sphere G is maintained in position by the Rollers Q and R carried in the
frame.S which is rigidly connected by the pin N to the dial Case and to the Polar
arm M-The pin N freely fits in the boss of the radius arm O. Hence when the
pointer is moved radially about the pin N the dial case, the Rollers B. R and Q
and the Sphere Gare made to turn together and the axis about which the Sphere G
turns is altered to obtain the desired end-For the purpose of ascertaining the
moment of area and moment of inertia of any figure the Rollers B. R. Q the
Sphere G and dial L are moved through respectively two or three times the anglo
described by the polar arm M about the pin N during the operation of tracing
the figure by the pointer P. In order to effect this a train of wheels or their
equivalent is employed and is arranged accordingly on the relatively moving parts
of the Instrument at the same time the end of the frame O instead of being fixed
at Z runs upon Rollers in a groove or otherwise parallel to the line about which
the movement is required to be known. If desired, the lower roller D may be
removed and the Sphere allowed to roll on the surface of the diagram The same
result will be obtained but the Roller in contact with the Sphere is now replaced
by the surface with which the latter is in contact, that is by a Roller which has
practically an infinite radius.
I would have it understood that I do not hereby claim the use of movable centres
in connection with a sphere which forms the subject of my former application for
Letters Patent N° 6206 of 1884 and which embraces only a special case of the
more general form of the Sphere and Roller mechanisin hereinbefore described.
Having now particularly 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 use of a sphero and rollers in frictional contact therewith arranged and
acting substantially as hereinbefore described and illustrated for the purpose of
enabling the relative motion of two or more bodies either to be determined or to
be varied in any required manner independently of their actual motion.
8. The combination of parts constituting the apparatus constructed arranged
and operating eitlier according to the sine or tangent method of computation for.

page_text: application to calculations, integration of areas or inoments; obtaining the record
of work done by machines electrical or otherwise and for the transmission and
regulation of motion and force by means of the mechanical combination of sphere
and rollers herein before set forth.
3. The use of a sphere and roller mechanism in connection with a screw as
hereinbefore set forth or analogous device for the measurement of efficiency or the
rate of work or motion or for regulating motion or force.
4. The combination of any number of sets of sphere and roller, mechanism so as
to obtain the resultant effect of any required number of variable quantities.
Dated this 2nd day of March 1885
W. LLOYD WISE,
Applicant's Agent.