III. PRINCIPLES OF MECHANISM. 119 



m. PRINCIPLES OF MECHANISM. 



529a. Models (13) of the various Linkworks for effecting 

 the exact rectilinear motion of a point, commonly known as 

 " parallel motions." A. B. Kempe, B.A. 



Described by the contributor in a paper published in the " Proceedings of 

 the Royal Society," No. 163, 1875, and entitied, " On a General Method of 

 " producing exact Rectilinear Motion by Linkwork," which points out the 

 common principle on which the linkworks depend. The linkwork No. [8} 

 was discovered by M. Peaucellier in 1864, and No. [13] by Mr. Hart in 1874 ; 

 the rest were discovered subsequently by the contributor. 



The lengths of the links will be found marked on them, and the points 

 which have rectilinear motion are denoted by stars. 



529b. The Sylvester-Kempe Parallel-Motion. Model of 

 a linkwork for effecting the exact rectilinear motion of a point. 



A. B. Kempe, B.A. 



Discovered simultaneously by Professor Sylvester and the contributor in 

 1875. The main portion of the apparatus consists of a linkwork of four bent 

 rods called a " Quadruplane," which is such that four points, one on each rod, 

 always He at the angles of a parallelogram of constant area and angles. Two 

 of the points consequently are situate at such distances from a third that the 

 one distance is the inverse of the other. One of the points being fixed, 

 another is made by means of a link to move in a circle passing through the 

 fixed point, the other then describes a straight line. If the bent rods are 

 made straight, the four points lie in a straight line, and the parallel motion 

 becomes that of Mr. Hart, No. [13]. e 



529c. Model of a Linkwork, by which two rods may be 

 made to rotate about different parallel axles with equal velocities 

 in contrary directions. A. B. Kempe, B.A. 



This and the four following linkworks are described by the contributor in 

 the "Messenger of Mathematics," No. 44, 1874. 



52 9d. Model of a Linkwork, by which two rods may be made 

 to rotate about the same axle with equal velocities in contrary 

 directions. A. B. Kempe, B.A. 



529e. Model of a Linkwork, by which rods may be made to 

 rotate about the same axis with velocities proportional to 1, 2, 

 3, &c. The linkwork can also be used to divide angles into a 

 number of equal parts. A. B. Kempe, B.A. 



529 f. Model of a Linkwork, by which two rods, otherwise 

 free, may be made to remain always in the same straight line with 

 each other. A* B. Kempe, B.A. 



52 9g. Model of a Parallel Ruler. A. B. Kempe, B.A. 

 529h. Model of a Parallel Ruler. A. B. Kempe, B.A. 



