172 Prof. T. A. Hearson. [May 30, 



Reuleaux was the first to show that if the links of the previously 

 mentioned kinematic chains be bent to the form of great circles of a 

 sphere the axes of the connecting pins will be radial, and the pre- 

 viously mentioned machine movements will be possible under the 

 modified circumstances. 



In spherical motion the counterpart of what is a slide in plane 

 motion could be obtained by a swinging motion about a pole of 

 which the bent link is the equator. The motion is to be conceived 

 as due to the use of two bent links, the length of one of which is a 

 quadrant of a great circle of the sphere. 



In these so-called spherical mechanisms, Law I has to be modified 

 as follows : 



The sum of the .four angles of the spherical quadrilateral varies, 

 having a value of STT for a maximum and 2?r for a minimum. 



This and Law II, which is the same as before, will preclude the 

 same combinations in spherical mechanisms which were precluded in 

 plane mechanisms. 



Law I explains at once why in Hooke's joint, which is the spherical 

 counterpart of Oldham's coupling, the angular velocity-ratio of the 

 connected shafts is not constant, whereas in Oldham's coupling it is. 



The author points oat that the kinematic chain containing three 

 slides cannot be adapted to give a movement on a sphere. The 

 virtual construction would consist of a spherical triangle between 

 the links of which no relative motion is possible, and there is not 

 room on the sphere for a movement at each joint of a bent quadri- 

 lateral, the length of each side of which is equal to a quadrant. But 

 a three-slide mechanism can be adapted to give motion on the surface 

 of a cylinder, and it is the only one of the fourteen kinematic chains 

 which can be so adapted, and examples of it are found in the various 

 helical motions so largely used. (The letter V is used to represent 

 helical motions.) This method of showing the relation between 

 screw motions and plane motions is a novel feature of the paper. 



The remaining mechanisms consist of those in which the axes of 

 the turning and swinging motions neither meet nor are parallel. 

 They include the motion which occurs at a ball-and-socket joint 

 represented by @. The method of classification according to the 

 proposed scheme is summarised as follows : 



All simple machine movements may be ranged in four divisions, 

 viz. : 



1. Consisting of plane mechanisms, in which the pieces move in or 

 parallel to the surface of a plane. 



2. Spherical mechanisms, in which the pieces move in or parallel 

 to the surface of a sphere. 



3. Cylindrical mechanisms, in which the pieces move in or parallel 

 to the surface of a cylinder. 



