IMPROVEMENTS IN THE MEANS OF REVERSING AND MULTIPLYING ANGULAR MOTION, EFFECTING RECTILINEAL AND PARALLEL MOTIONS, AND DIVIDING ANGLES
Year: 1874

page_text: PROVISIONAL SPECIFICATION left by Alfred Bray Kempo at the
Office of the Commissioners of Patents, with his Petition, on the.
12th November 1874.
I, ALFRED BRAY KEMPE, of No. 7, Crown Office Row, Temple, in the
City of London, do hereby declaro the nature of the said Invention for
"IMPROVEMENTS IN THE MEANS OF REVERSING AND MULTIPLYING ANGULAR MOTION,
EFFECTING RECTILINEAL AND PARALLEL MOTIONS, AND DIVIDING ANGLES," to be as
follows:-
This Invention relates to means of reversing and multiplying angular
motion, effecting rectilineal and parallel motions, and dividing angles.
by the use of certain systems of jointed rods which I will describe,,
referring to the accompanying Sheets of diagrams, and to the figures.
and letters marked thereon.
The fundamental portion of the system consists of two pairs of
primary rods, the two constituting each pair being equal to one another,
but those of the one pair being greater or less than those of the other
pair, jointed together in either of two ways, namely, either with the
equal rods of cach pair adjacent to one another so as to constitute a
་

page_text: additional or secondary rods, and these secondary rods being jointed to
two of the primary rods have the effect of controlling the relative move-
ments of the several parts of the system in the manner which I will now
explain.
According to the arrangement shewn diagrammatically in Fig. 1 BC
and DC are equal rods jointed together at C, and BA and DA are also
equal rods jointed together at A, and jointed at B and D to BC and DC
respectively; D F is made of such length as to bear the same proportion
to DA as D A bears to D C, and at F is jointed a rod FE equal to FD,
E being connected to A by a rod EA equal to DA. The smaller
figure A EFD is therefore similar to the larger figure CDA B, and it
may be demonstrated that a line A G parallel to DC will always bisect
the angle BA E. If now the point G be taken at a distance from A
equal to DC, and be connected to C by a rod GC equal to A D, as
shewn in Fig. 2; and if the system of rods be moved about two fixed
pivots at A and G respectively, then the two rods A B and A E will be
constrained to move in opposite directions, but with equal angular
motion on each side of the line A G, joining the pivots A and G. The
thin lines marked by small letters, corresponding to the capital letters
marking the thick lines of the diagram indicate a changed position of
the parts of the system. Further, on moving the system round pivots
fixed at E and G, as shown in Fig. 3, G being determined by making EG
equal to FC, and the radius GC equal to E F, the point B will be
constrained to move in the straight line E B perpendicular to EG; also,
if to AB be attached a rod of equal length AH, making always a
constant angle with AB, the point H will move in a straight line
through E. A like result is obtained by the arrangement shown in
Fig. 4, where B and G are the fixed pivots round which the system
moves, BG and G D being each equal to BC or DC. In this case the
point E is constrained to move in the line B E perpendicular to B G. If
the system of jointed rods be duplicated, as shewn in Fig. 5, and the
side K L of the added figure remain at rest while the rest of the system
is moved, then the opposite side CD of the primary figure will be con-
strained to move in a path always parallel to KL, every point of it

page_text: moving in a straight line, as Cc, Dd, or Ff, perpendicular to KL
or DC; and again, by duplicating the system, as shewn in Fig. 6, the
side CD being fixed, then the side KL will be constrained to move
always in the same straight line, which is the prolongation of CD.
According to the arrangement shewn in Fig. 7 A B and CD are the
two shorter rods equal to one another, and AC and BD are the two
longer rods equal to one another and crossing each other. CD is pro-
longed to any point F, and BD is prolonged to E, so that DE bears the
same proportion to D F as A B bears to D B, and E and F are connected
by the rods F G equal to DE, and GE equal to D F. The angle GED
will then always be equal to the angle ABD, and if the rod BE be
fixed, and the system moved about it, the radius EG will move with the
same angular velocity as BA, but in the opposite direction. This
arrangement of the system may be modified, as shewn in Figs. 8 and 9,
by taking D E within the line BD instead of in its extension, and DF
within DC or its prolongation, the radius E G being in this case also
constrained to move with the same angular velocity as BA, but in the
opposite direction. With the same construction as in Fig. 9, where the
points C and F coincide in C, the side CD being fixed, as shewn in
Fig. 10, the rods CA and CG move with equal angular velocity in
opposite directions round the pivot Ċ.
In the arrangement shown in Fig. 11 two equal rods BK and E L are
made to move with equal angular velocity in opposite directions round
fixed pivots B and E by such a system of rods as is shewn in Figs. 7, 8,
9, or 10 (the system being omitted in the diagram, Fig. 11, as well as
in Figs. 12 and 13 to avoid confusion of lines). Two equal rods KM
and LM being jointed together at M and jointed respectively to B K
and EL the point M will be constrained to move in a straight line
perpendicular to BE.
In the arrangement shewn in Fig. 12 BK, EL, and EP are three
equal rods, of which BK and EL are constrained, as before described,
to make equal angles in opposite directions with BE, the system being
pivotted at K and P, so that KP is equal to B E, then the point L will
be constrained to move in the straight line joining the pivots K and P,
according to the modification of this arrangement shewn in Fig. 13,
BK and EL being the two rods which are constrained to make equal
angles towards opposite directions with B E, any points R and S may be

page_text: taken in B E or in its prolongation, as shewn in the diagram, and rods
RQ and ST equal and parallel respectively to BK and EL may be
jointed, the one RQ to a fixed pivot Q at the same distance from K as R
is from B, and the other to a rod LT equal to ES; then the rod LT will
always move parallel to KQ, every point in it travelling in a straight
path perpendicular to K Q.
By repeating the system of linkage in the manner shewn in Fig. 14
I am enabled to produce mechanically the double, the triple, or any
desired multiple of an angle, or to make a radius revolve round a pivot
with twice, thrice, or any desired number of times the angular velocity
with which another radius revolves round it. Referring to Fig. 14 it
will be seen that ABCD being the primary linkage of four rods, and
CGED being the secondary linkage, and CJ HG a tertiary linkage,
the secondary and tertiary linkages forming figures similar and pro-
portional to that formed by the primary linkage; then the three angles
at C, namely, ACD, DCG, and GCJ will be always equal to onc
another, and thus if A C be fixed, while the radius CD revolves round C,
OG revolves with double the angular velocity, and CJ revolves with
triple the angular velocity of CD; and in like manner by repetition of
similar and proportional linkages a radius of the final linkage can be
made to revolve round C with an angular velocity, which may be any
desired multiple of the velocity with which the radius CD of the primary
linkage revolves round C. Conversely, any angle, such as JOA, may
thus be mechanically divided into any desired number of equal parts,
such as DCA, which in the case of Fig. 14 is one-third.
It is to be understood that the points and lines in the diagrams are
intended to represent respectively joints and rods, which may be made of
any suitable form, material, and strength, according to the mechanical
purposes to which the several systems of rods may be applied.