1895.] The Kinematics of Machines. 173 



4. The remainder, to which the name conoidal mechanisms is given, 

 in which the axes of the swinging and turning motions neither meet 

 nor are parallel. 



The mechanisms in each of these divisions are classed in two sub- 

 divisions. 



Sub-division S, with surface contact of consecutive lints. 

 Sub-division P, with point contact of consecutive links. 



The mechanisms of sub-division S of divisions 1 and 2, 1, and 2, 

 will consist of those in which U I motions only are used. 



Those of 3, will include the helical or V motion, and 



Those of 4, will include the motion @ requiring the use of a ball- 

 and-socket joint. 



To the pairs of links which have the -relative motions O, U, I, V, 

 Reuleaux has given the name lower pairs. Reuleaux claimed two' 

 characteristics for lower pairs, viz. : 



1. Definiteness of motion derived from the surfaces of mutual con- 

 tact themselves. 



2. Tbe possibility of distributing the -contact over an area which 

 may be extended as much as desired. 



If it is desired to differentiate between the and U motions, 

 Reuleaux's turning pair cannot possess the first characteristic. 



The second characteristic is of considerable value in relation to the 

 liability to abrasion and wear, but the advantage of greater immunity 

 against wear has to be purchased at the cost of a more complicated 

 construction and a more restricted character of movement. 



As examples 



The mechanism consisting of a pair of spur wheels turning in 

 bearings which are at a fixed distance apart will belong to \ p . 



A pair of bevel wheels will belong to 2 P . 



The so-called cylindrical cam motion will belong to 3 f , and the 

 worm-and-worm wheel mechanism to 4 P . 



The mechanisms in each of the eight sub-divisions are still further 

 sub-divided into combinations. The combinations of 1,, 2,, and 3,, 

 are exhaustively enumerated, and it is suggested that an extension of 

 the methods of applying the geometrical laws would lead to the 

 preparation of an exhaustive list of the possible combinations in the 

 other sub-divisions. The combinations are still further sub-divided 

 into inversions according to Reuleaux's principle of the inversion of 

 a machine. 



Further than this there will be varieties of any inversion differing 

 in the details of the construction and uses of the machine move- 

 ment. 



Lastly, the author proceeds to show how the foregoing considera- 

 tions assist in the analysis of compound mechanisms. It is assumed 



