APPARATUS WHEREBY ANY REQUIRED VARIABLE VELOCITY RATIO BETWEEN TWO OR MORE DISCS, ROLLERS, OR OTHER ROTATING PIECES MAY RITHER BE OBTAINED OR ITS MAGNITUDE BE DETERMINED to be as follows:
Year: 1884

page_text: I, HENRY SELBY HELE SHAW, of University College City of Bristol, Professor
of Engineering in the said University College, do hereby declare the nature of
said invention for "APPARATUS WHEREBY ANY REQUIRED VARIABLE VELOCITY
RATIO BETWEEN TWO OR MORE DISCS, ROLLERS, OR OTHER ROTATING PIECES MAY
RITHER BE OBTAINED OR ITS MAGNITUDE BE DETERMINED to be as follows:-
وو
-
General description of invention. This invention consists in the employment of
moveable centres in connection with a rotating piece so that the velocity ratio of
two or more surfaces of revolution in contact with the rotating piece can be altered
in any degree by moving the axis about which the aforesaid pièce tends to rotate
without moving the piece itself.
Under one arrangement these centres consist of rollers so placed that their
motion in connection with the rotating piece involves a minimum of resistance.
The centres may however consist of fixed points or pieces of metal or other
material.
Disadvantages which the Invention is designed to obviate. The conflicting
requirements which are usually involved in devices for changing the velocity ratio
of the surfaces of revolution by altering their position relatively to the axis of the
rotating piece are as follows:-
This
The surfaces have to roll upon each other and no circumferential slipping
must take place. At the same time to alter the velocity ratio axial motion is
necessary. In existing mechanical arrangements this axial motion takes place by
moving the surface or surfaces of revolution, in contact with the rotating piece,
bodily over the latter. For example, in disc and roller integrators.
necessitates either slipping of parts otherwise designed to roll without slipping
or requires intricate combinations of mechanism. The former in addition to the
evil effects of undue wearing of the surfaces in contact is known to result in the
introduction of an error when the combined slipping and rolling takes place. The
present invention effects the same result by changing the position of the temporary
axis about which the rotating piece turns.
Advantages derived. This device allows the surfaces of revolution; such as the
roller in the disc and roller integrator; to be of such material as to cause necessary.

page_text: and sufficient friction for rolling without slipping in contact with the rotating
piece; which piece corresponds to the disc in the above-mentioned combination of
the disc and roller; while the rotating piece as also the centres may be of such
material as to allow them to pass easily over each other. Loss of accuracy is thus
provided against and the possibility of transmitting appreciable forces without
undue wear due to slipping of the surfaces in contact is thus made apparent.
Description of apparatus whereby the objects of the invention are attained.
The rotating piece above alluded to is in the fundamental form which is the one
about to be described a sphere. The surfaces of revolution are discs or rollers the
peripheries of which are in contact with it. The sphere is enclosed by two frames
which support it by a number of rollers, generally four in each frame.
Each set of rollers is in contact with the sphere on one of its great circles formed
by the intersection of a diametral plane with the spherical surface. The frames
are capable of relative motion in such a way that the above diametral planes are
always perpendicular to each other. The rollers are arranged in the same manner
in each frame and rotate in planes perpendicular to their diametral planes of
contact.
The two above diametral planes intersect in a diameter at the extremities of
which two rollers in one frame, or their equivalents are always in contact with the
sphere, these rollers forming the centres of rotation of the sphere.
At the same time the other two rollers which are placed equi-distant from the
two first and from each other and are therefore at the extremities of a diameter
perpendicular to the aforesaid diameter, act as centres about which the frame
freely turns round the sphere. This frame may therefore be called the moveable
frame. The first two rollers always keep in the diametral plane of the other frame
which may be called the fixed frame. It will be seen that, inasmuch as the sphere
always turns on centres which are in the plane of contact of the fixed frame, the
rollers of the fixed frame can always freely turn on circles of larger or smaller size
on the sphere, independently of the change of position of the centres. Thus as the
rollers in the fixed frame are not required to slip in contact with the sphere when
their relative velocity ratio is changed in any required manner their surfaces, as
already pointed out, may be made of suitable frictional material to transinit with
accuracy any required motion.
Mode of operation. One mode of obtaining the required velocity ratio is as
follows:
If turning motion be imparted to one of the rollers or discs in the fixed frame
then the sphere and consequently all the other rollers or discs in that frame as well
as the two rollers which act as centres of the moveable frame will revolve. The
two other rollers which act as the centres of the sphere alone do not turn.
The rollers that turn will do so with a velocity depending on two things. 1st the
velocity of the driving disc or roller. 2ndly the size of the rolling circles on the
sphere against which they are in contact which depends upon their position with
respect to the temporary axis.
By turning the first mentioned disc or roller at a known rate and altering the
position of the moveable frame, a variable motion may be given to any of the
revolving rollers except that one which is exactly opposite to the driving roller.
This always rotates at the same rate as the driving ruller and may also be used as
a driver simultaneously with the other. This arrangement has a range of variation
which corresponds to the tangent or co-tangent of the angle of inclination which the
plane of the moveable frame makes with the plane of the driving discs or rollers in
fixed frame. It may therefore be called the tangent arrangement.
Another mode is to impart known motion to one or both of the rollers which act
as centres to the frame (in contra distinction to those acting as centres to the
sphere) in the moveable frame. These rollers always rotate in contact with a great
circle of the sphere, and by altering the position of the frame any required motion
may be obtained from any of the other rollers. The range of variation is in this

page_text: case more limited and now corresponds to the sine or cosine of the angle which
the moveable frame turns through. This may be therefore called the sine
arrangement.
There are two modes of determining what is the velocity ratio of two moving
bodies corresponding to the two foregoing modes of procedure. In the 1st case one
roller in the fixed frame turns the sphere and other rollers as before at a rate
corresponding to that of one moving body. The axis of one of these latter is now
a screw, the roller upon it forming a freely fitting nut. This axis is turned at a
rate proportionally with that of the second moving body. If the axis and disc or
roller does not rotate at the same speed the position of the moveable centres will,
by the action of the screw, be altered in one direction or the other until the screw
and disc are moving uniformly. A pointer attached to the moveable frame will
indicate by its position the velocity ratio of the two rollers and therefore of the
two moving bodies. In the 2nd case by employing a similar arrangement the two
rollers in the moveable frame which act as centres to this frame and rll on great
circles of the sphere may be turned at a rate proportional to one moving body and
the screwed axis in the above mechanism may pass through one of the rollers in
the fixed frame.
Mode of arranging the mechanism in order to obtain desired quantitative results.
To obtain the correct position of the moveable frame in order to ensure the
required velocity ratio of the rollers or discs in the 1st case or to determine the
value of the velocity ratio in the 2nd case according to the position of the frame
various devices may be employed. Two only will be described corresponding
respectively to the tangent and sine arrangement above mentioned.
With the former, i.e the tangent form, the driving roller in the fixed frame is
turned at a known rate. Perpendicular to the axis of this and at a constant
distance from the centre sphere is a straight guide. Sliding on this guide is a
piece through a swivel on which passes and slides a bar or pointer rigidly connected
with the moveable frame and either perpendicular to, or coinciding with, the
temporary axis of the sphere i.e. with the intersection of the two above mentioned
diametral planes. The distance along the guide at which the centre of the sliding
bar intersects it, is a direct measure of the velocity at which the driven disc or
roller turns. For since the distance of the guide from the sphere is constant this
length is a measure of the tangent of the angle of inclination of the moveable
frame.
For the sine arrangement the sliding bar or pointer passes through a sliding
block on the guide which does not swivel so that the bar and guide are always
perpendicular to each other. The extremity of the guide, i.e. where it intersects
the perpendicular from the sphere upon it in the former arrangement, is now
provided with a swivelling joint. Thus the constant distance from the centre of
the sphere to this point is now the hypotheneuse of a right angled triangle and the
distance, along the guide of the intersection of the bar is one of the sides. This
distance is as before the measure of the velocity of the driven roller and corresponds
to the sine of the angle turned through by the moveable frame.
Although the velocity of the moving discs or rollers has been mentioned
throughout it is quite clear that the space turned through by the driven roller
is a measure of that turned through by the driving one taken in conjunction with
the position of the moveable frame-without special reference to the time in which
it is performed the time being the same for the motion of both rollers also a com-
bination of two or more sets of frames and spheres may be employed so that the
resultant effect of any number of variable velocities or quantities may be obtained.
Applications. The following are some of the applications of this invention.
(1) The integration of areas-In this case the driving roller is turned at a
velocity corresponding to the rate of increase of the abscissa, the distance along the
guide i.e. the position of the moveable frame always corresponding to the ordinate.

page_text: Then the velocity of the driven roller or distance turned through in a given
time corresponds to the product of the two variables, i.e. gives the area of the
figure.
The mechanism may be arranged either to move over the area or may remain
fixed whilst the area passes over the rollers in contact with them.
(2) Work of any prime movers being a product of force exerted by space passed
through may likewise be integrated-The force may be either the pull of a spring
in a dynamometer or the pressure of a fluid in a motor of any kind.
This invention is applicable to rotary as well as reciprocating motors or
machines.
.
(3) For measuring the work done by an electric current, the one variable may be
the electro-motive force, the other the current passing-Their product is given by
the turning of the driven roller.
(4) This invention may replace combinations of wheel work in cases where
moderate forces have to be transmitted and changes of velocity ratio are requred
rapidly, as for example in light screw cutting lathes.
(5) For Measuring velocity.-The velocity ratio of space passed over to the time
occupied in doing it is required. The driving roller in this case may be moved at
a velocity proportional to the body whose velocity is required to be known, the
axis of the driven roller by a clock. The position of the moveable frame indicates
at once the required velocity. If desired the screw may be driven instead by the
moving body.
(6) The Horsepower or rate of working may be indicated by using one sphere
and frames to give work and a second sphere and frames to divide work by the
time of doing it as in the foregoing application.
(7) The efficiency of any machines whatever may be similarly obtained.
(8) By a combination of two spheres and sets of frames and rollers various
problems may be solved such as obtaining the statical moment of an area, while by
a combination of three spheres and rollers the moment of inertia of an area about
a given line may be calculated.
The volume of solids of revolution or solids formed by ruled surfaces may like-
wise be obtained by suitable combination of the fundainental form of mechanism
of sphere and roller frames.

page_text: I, HENRY SELBY HELE SHAW of University College, Bristol, Professor of
Engineering in the said University College, do hereby declare the nature of my
said invention for "APPARATUS WHEREBY ANY REQUIRED VARIABLE VELOCITY
RATIO BETWEEN TWO OR MORE DISCS, ROLLERS OR OTHER ROTATING PIECES MAY
EITHER BE OBTAINED, OR ITS MAGNITUDE DETERMINED," and in what manner the
same is to be performed, to be particularly described and ascertained in and by
the following statement :-
This invention consists in the employment of movable centres in connection with
a rotating piece so that the velocity ratio of two or inore surfaces of revolution in
contact with the rotating piece can be altered in any degree by moving the axis
about which the aforesaid piece tends to rotate without moving the piece itself.
Under one arrangement these centres consist of rollers, so placed that their
motion about the rotating piece involves a minimum of resistance. The centres
may, however, consist of fixed points or pieces of metal or other material.
The conflicting requirements which are usually involved in devices for changing
the velocity ratio of the surfaces of revolution by altering their position relatively
to the axis of the rotating piece are as follows:-The surfaces have to roll upon
each other and no circumferential slipping must take place. At the same time, to
alter the velocity ratio, axial motion is necessary. In existing mechanical arrange-
ments this axial motion takes place by moving the surface or surfaces of revolution
in contact with the rotating piece bodily over the latter. For example, in disc and
roller integrators. This necessitates either slipping of parts otherwise designed to
roll without slipping, or requires intricate combinations of mechanism. The former,
in addition to the evil effects of undue wearing of the surfaces in contact, is known
to result in the introduction of an error when the combined slipping and rolling
takes place. The present invention effects the same result by changing the position
of the temporary axis about which the rotating piece turns.
This device allows the surfaces of revolution such as the roller in the disc and
roller integrator to be of such material as to cause necessary and sufficient friction
for rolling without slipping in contact with the rotating piece which piece cor-
responds to the disc in the above mentioned combination of the disc and roller,
while the rotating piece, as also the centres, may be of such material as to allow
them to pass easily over each other. Loss of accuracy is thus provided against and
the possibility of transmitting appreciable forces without undue wear, due to
slipping of the surfaces in contact, is thus made apparent.
The rotating piece above alluded to is, in the fundamental form which is the one
about to be described, a sphere. The surfaces of revolution are discs or rollers the
peripheries of which are in contact with it. The sphere is enclosed by two frames
which support it by a number of rollers, generally four in each frame.
Each set of rollers is in contact with the sphere on one of its great circles formed
by the intersection of a diametral plane with the spherical surface. The frames aro
capable of relative motion in such a way that the above diametral planes are always
perpendicular to each other.
The rollers are arranged in the same manner in each frame and rotate in planes
perpendicular to their diametral planes of contact.
The two above diametral planes intersect in a diameter at the extremities of
which two rollers in one frame, or their equivalents, are always in contact with the
sphere, these rollers forming the centres of rotation of the sphere.

page_text: At the same time the other two rollers which are placed equidistant from the two
first and from each other and are, therefore, at the extremities of a diameter
perpendicular to the aforesaid diameter, act as centres about which the frame freely
turns round the sphere. This frame may therefore be called the movable frame.
The first two rollers always keep in the diametral plane of the other frame which
may be called the fixed frame.
It will be seen that, inasmuch as the sphere always turns on centres which are in
the plane of contact of the rollers in the fixed frame, the rollers of the fixed frame
can always freely turn on circles of larger or smaller size on the sphere independently
of the change of position of the centres. Thus, as the rollers in the fixed frame are
not required to slip in contact with the sphere when their relative velocity ratio is
changed in any required manner, their surfaces, as already pointed out, may be
made of suitable frictional material to transmit with accuracy any required motion.
One mode of obtaining the required velocity ratio is as follows. If turning
motion be imparted to one of the rollers or discs in the fixed frame then the sphere
and consequently all the other rollers or discs in that frame, as well as the two
rollers which act as centres of the movable frame, will revolve. The two other
rollers which act as the centres of the sphere alone do not turn. The rollers that
turn will do so with a velocity depending on two things.-1st, the velocity of the
driving disc or roller; 2ndly, the size of the rolling circles on the sphere against
which they are in contact which depends upon their position with respect to the
temporary axis.
By turning the first mentioned disc or roller at a known rate and altering the
position of the movable frame a variable motion may be given to any of the revolving
rollers except that one which is exactly opposite to the driving roller.
This always rotates at the same rate as the driving roller and may also be used
as a driver simultaneously with the other. This arrangement has a range of
variation which corresponds to the tangent or cotangent of the angle of inclination
which the plane of the movable frame makes with the plane of the driving discs or
rollers in the fixed frame, It may therefore be called the tangent arrangement.
Another mode is to impart known motion to one or both of the rollers which act
as centres to the movable frame (in contradistinction to those acting as centres to
the sphere). These rollers always rotate in contact with a great circle of the sphere
and, by altering the position of the frame, any required motion may be obtained
from any of the other rollers. The range of variation is in this case inore limited
and now corresponds to the sine or cosine of the angle which the moveable frame
turns through. This may be therefore called the sine arrangement.
There are two modes of determining what is the velocity ratio of two moving
bodies corresponding to the two foregoing modes of procedure. In referring in the
provisional Specification to the first of these moles it is stated that the roller (in
the fixed frame) to which motion is imparted by one moving body causes the sphere
and other rollers to turn at a corresp nding rate. The statement should be that
the said roller turning at a rate corresponding to that of the moving body turns the
sphere and other rollers. The axis of one of these latter is now a screw the roller
upon it forming a freely fitting nut. This axis is turned at a rate proportionally
with that of the second moving body. If the axis and disc or roller do not rotate
at the same speed the position of the moveable centres will, by the action of the
screw, be altered in one direction or the other until the screw and disc are moving
uniformly. A pointer attached to the moveable frame will indicate, by its position,
the velocity ratio of the two rollers and, therefore, of the two moving bodies. In
the 2nd case, by employing a similar arrangement, the two rollers in the moveable
frame which act as centres to this frame and roll on great circles of the sphere may
be turned at a rate proportional to one moving body and the screwed axis in the
above mechanism may pass through one of the rollers in the fixed frame.
To obtain the correct position of the moveable frame in order to ensure the
required velocity ratio of the rollers or dises in the first case, or to determine the
value of the velocity ratio in the 2nd case, according to the position of the frame,

page_text: various devices may be employed. Two only will be described corresponding
respectively to the tangent and sine arrangements above mentioned.
With the former, i.e. the tangent form, the driving roller in the fixed frame
is turned at a known rate. Perpendicular to the axis of this, and at a constant
distance from the centre of the sphere, is a straight guide. Sliding on this guide is
a piece, through a swivel on which passes and slides a bar or pointer rigidly
connected with the moveable frame and either perpendicular to or coinciding with
the temporary axis of the sphere, i.e. with the intersection of the two above
mentioned diametral planes. The distance along the guide at which the centre of
the sliding bar intersects it is a direct measure of the velocity at which the driven
disc or roller turns. For since the distance of the guide from the sphere is
constant, this length is a measure of the tangent of the angle of inclination
of the moveable frame.
For the sine arrangement the sliding bar or pointer passes through a sliding
block on the guide which does not swivel so that the bar and guide are always
perpendicular to each other. The extremity of the guide, i.e. where it intersects
the perpendicular from the sphere upon it in the former arrangement, is now
provided with a swivelling joint. Thus, the constant distance from the centre of
the sphere to this point is now the hypotheneuse of a right angled triangle and the
distance along the guide of the intersection of the bar one of the sides. This
distance is, as before, the measure of the velocity of the driven roller and
corresponds to the sine of the angle turned through by the moveable frame.
Although the velocity of the moving discs or rollers has been mentioned
throughout it is quite clear that the space turned through by the driven roller is a
measure.of that turned through by the driving one taken in conjunction with the
position of the moveable frame without special reference to the time in which
it is performed, the time being the same for the motion of both rollers. Also a
combination of two or more sets of frames and spheres may be employed so that
the resultant effect of any number of variable velocities or quantities may be
obtained.
And in order that my said invention may be properly understood, I now
proceed to further describe the same with reference to the accompanying sheets
of illustrative drawings and the figures and letters marked thereon.
Fig 1, sheet 1, represents a side elevation of an arrangement of the apparatus
in which my invention consists, the apparatus being shown as adapted for the
mechanical integration of areas.
Fig: 2, represents a plan of Fig: 1, with the addition of the bracket I, and the
moveable frame F. Figs. 3 and 4, sheet 2, represent different views of parts of
the sphere and roller mechanism adapted as aforesaid. Figs 5 and 6, Sheet 2,
represent diagramatic plans of the apparatus.
The moveable centres consist. of rollers C, C which, under the arrangement
illustrated, are so placed that their motion about the sphere G, which is the
rotating piece in connection with which the said centres are employed, involves a
minimum of resistance.
The centres may, however, consist of fixed points or pieces of metal or other
material. The sphere G is supported by the rollers A, A and B, B¹ of the fixed
frame F¹ and the rollers C, C and D, D¹ of the moveable frame F. The
rollers A, A and B, B¹ are respectively in contact with the sphere G at the
points a, a¹ and b, b¹ upon the great circle formed by the intersection of
the horizontal diametral plane with the sphere. The rollers C, C and D, D¹
are in contact with the sphere G at the points c, c¹ and d, d' in the great circle
formed by the intersection of a vertical diametral plane. The frames F and F¹ are
capable of relative motion in such a manner that the said diametral planes are
always perpendicular to each other.
The rollers are arranged in the same manner in each frame and rotate in planes
perpendicular to their diametral planes of contact. These diametral planes intersect

page_text: in a diameter k, k², Fig: 2, at the extremities of which two rollers C, C in the
frame F are always in contact with the sphere G, these rollers forming the centres
of rotation of the sphere.
At the same time the other two rollers D, D', which are placed equidistant from
the two first rollers C, C' and from each other, and are, therefore at the extremities
of a diameter d, d perpendicular to the aforesaid diameter, act as centres about
which the moveable frame F virtually turns round the sphere G.
The first two rollers C, C¹ always keep in the diametral plane of contact a, b, a¹, b¹
of the other or fixed frame F¹.
It will be seen that, inasmuch as the sphere G always turns on centres which are
in the plane of contact of the rollers A, A' and B, B' in the fixed frame F¹, the said
rollers can always freely turn on circles of larger or smaller size on the sphere G
independently of the change of position of the centres. Thus, as the rollers A, A¹
and B, B¹ of the fixed frame F' are not required to slip in contact with the sphere
when their relative velocity ratio is changed in any required manner, their surfaces,
as herein before mentioned, may be made of suitable frictional material to transmit
with accuracy any required motion.
A required velocity ratio may be obtained in the manner following:-If turning
motion be imparted to one of the rollers B in the fixed frame F¹ then the sphere G
and consequently all the other rollers B¹, A, A¹ in the said frame F¹, as well as the
two rollers D, D' which act as centres of the moveable frame F, will revolve.
The two other rollers C, C, which act as the centres of the sphere G do not turn.
The rollers that turn will do so with a velocity depending on two things-1st, the
velocity of the driving roller B; 2nd, the size of their rolling circles on the sphere G
which depends upon their position with respect to the temporary axis k. k².
By turning the first mentioned roller B at a known rate and altering the position
of the moveable frame F a variable motion may be given to any of the revolving
rollers except B' which is exactly opposite to the driving roller B and rotates at
the same rate.
The roller B¹ may also be used as a driver simultaneously with the roller B.
This arrangement has a range of variation which corresponds to the tangent or
cotangent of the angle of inclination (a), Fig: 5, Sheet 2, which the plane of
contact c, d, c, d, of the moveable frame makes with the plane of the driving
roller B in the fixed frame. It may therefore be called the tangent arrangement.
Another mode is to impart known motion to one or both of the rollers D, D¹
which act as centres to the moveable frame F. These rollers always rotate in
contact with a great circle of the sphere and, by altering the position of the
frame F, the required motion may be obtained from any of the other rollers. The
range of variation is in this case more limited and now corresponds to the sine or
cosine of the angle (a) Fig: 6, Sheet 2, which the moveable frame turns through.
This may be therefore called the sine arrangement.
There are two modes of determining what is the velocity ratio of two moving
bodies corresponding to the two modes of procedure above described.
In the first case the roller B (in the fixed frame F¹) which is turned by and
at a rate corresponding to that of one moving body turns the sphere G and
rollers B¹, A, A, D, D. The axis of the roller A is in this case a screw R, as
shown more particularly at Fig: 2, Sheet 1. The screw R, upon which the
roller A forms a freely fitting nut, is turned in the same direction as the said roller
and at a rate corresponding to that of the second moving body. If the axis R and
roller A do not rotate at the same speed the position of the moveable centres C, C¹
will, by the action of the screw R, be altered in one direction or the other until
the screw and roller are moving uniformly. A pointer P attached to the moveable
frame F will indicate by its position the velocity ratio of the two rollers B and A
and therefore of the two moving bodies.
In the 2nd case, by employing a similar arrangement, either of the two
rollers D D' in the movable frame F, which act as centres to this frame and roll

page_text: on great circles of the sphere, may be turned at a rate proportional to one moving
body, and the screwed axis R in the above mentioned mechanism may pass through
one of the rollers A. or A¹ in the fixed frame.
In obtaining quantitative results the correct position of the movable frame F for
ascertaining the required velocity ratio of the rollers in the first case, or to
determine the value of the velocity ratio in the 2nd case, according to the position
of the frame, various devices may be employed.
With one, which corresponds to the tangent arrangement above mentioned, the
driving roller B Fig 1, Sheet 1, in the fixed frame F¹ is turned at a known rate.
Perpendicular to the axis of this roller B and at a constant distance O. N. (Fig 5.
Sheet 2,) from the centre of the sphere G is a straight guide N. T.
Free to slide in the guide N. T is a piece m through a swivel n on which passes
and slides a bar O. M rigidly connected with the movable frame F and either
perpendicular to or coinciding with the temporary axis k. k¹ of the sphere G, i.e
with the intersection of the two hereinbefore mentioned diametral planes a, b.,
a², b¹ and c, d, c¹, d. The distance M. N, along the guide N. T. at which the
centre of the sliding bar O. M. intersects it is a direct measure of the velocity at
which the driven roller A turns. For since the distance O. N is constant, tho
length M. N. is a measure of the tangent of the angle of intersection of the movable
frame.
For the sine arrangement (see Fig. 6, Sheet 2,) the sliding bar O. M. passes
through the sliding block m² on the guide M. N. which block does not swivel, so
that the bar and guide are always perpendicular to each other.
The extremity of the guide M. N., ie where it intersects the perpendicular O. N,
is now provided with a swivelling point n¹.
Thus the constant distance O. N. from the centre or the sphere G to this point is
now the hypothenuse of a right angled triangle O. M. N. and the distance along
the guide M. N of the intersection of the bar O. M is one of the sides. The
distance is, as before, the measure of the velocity of the driven roller A and
corresponds to the sine of the angle (a) turned through by the movable frame F.
Although the velocity of the moving discs or rollers has been mentioned.
throughout it is clear that the space turned through by the driven roller is a
measure of that turned through by the driving one taken in conjunction with the
position of the movable frame without special reference to the time in which it is.
performed, the time being the same for the motion of both rollers.
Also &
combination of two or more sets of frames and spheres may be employed so that
the resultant effect of any number of variable velocities or quantities may be
obtained.
The application of the apparatus constituting this invention to the integration of
areas is, as aforesaid, illustrated at Figs 1, and 2. Sheet 1, and Figs. 3, and 4,
Sheet 2 The driving roller A is turned at a velocity corresponding to the rate of
increase of the abscissa the distance M. N. along the guide i.e the position of the
movable frame F, always corresponding to the ordinate.
Then the velocity of the driven roller B or distance turned through in a given
time corresponds to the product of the two variables, i.e. gives the area of the
figure.
The mechanism may be arranged either to move over the area or may remain
fixed whilst the area passes over the rollers in contact with them.
Work of any prime movers being a product of force exerted by space passed
through may likewise be integrated. The force may be either the fall of a spring
in a dynamometer or the pressure of a fluid in a motor of any kind.
This invention is applicable to rotary as well as reciprocating motors or
machines.
For measuring the work done by an electric current the one variable may be
the electro motive force the other the current passing. Their product is given by
the turning of the driven roller.

page_text: This invention may replace combinations of wheel work in cases where moderate
forces have to be transmitted and changes of velocity ratio are rapidly required, as,
for example, in light screw cutting lathes.
For measuring velocity. The velocity ratio of space passed over to the time
occupied in doing it is required. The driving roller in this case may be moved at
a velocity proportional to the body whose velocity is required to be known, the
axis of the driven roller by a clock. The position of the moveable frame indicates
at once the required velocity. If desired, the screw may be driven instead by the
moving body.
The horsepower or rate of working may be indicated by using one sphere and
frames to give work and a second sphere and frames to divide work by the time of
doing it as in the foregoing application.
The efficiency of any machines whatever may be similarly obtained.
By a combination of two spheres and sets of frames and rollers various problems
may be solved such as obtaining the statical moment of an area while by a
combination of three spheres and rollers the moment of inertia of an area about
a given line may be calculated.
The volume of solids of revolution or solids formed by ruled surfaces may
likewise be obtained by suitable combination of the fundamental form of mechanism
of sphere and roller frames.
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 for enabling a required variable velocity ratio between two or more
discs, rollers, or other rotating pieces to be either obtained or its magnitude
determined, of a sphere and roller mechanism in which two sets of rollers in
contact with the sphere have their axes of revolution in two diametral planes
respectively perpendicular to each other so that the sphere can only revolve about
the intersection of these diametral planes as axis substantially as described.
2. The combination of two frames each carrying a set of rollers in contact with
a rotating piece, the arrangement being such that by alteration in the position of
one set, the relative motion of rollers in the other frame can be varied according
to the mathematical principles hereinbefore set forth with special reference to
Figs 5 and 6, sheet 2 of the annexed drawings for the purposes specified.
3. The combination of parts constituting the apparatus constructed arranged
and operating substantially as described with reference to Figs 1, 2, 3 and 4 of the
drawings for the purposes set forth.
Dad AL
1007