KINEMATICS OF MACHINERY. 91 



connected a that point by a cylindric pair of elements. 

 There are many problems of which the solution is greatly 

 simplified by the recollection of this fact. The point in each 

 figure which coincides with the instantaneous centre, has, 

 therefore, no motion relatively to the other figure. We have 

 already seen this in the special case where the one figure is 

 stationary, for then the point in which the moving centroid 

 touches the fixed one is, by hypothesis, also stationary for 

 the instant ; in other words, it has no motion relatively to the 

 fixed centroid. We now see the general condition of which 

 this is a special case. 



Fig. 6 shows the centroids for the higher pair of elements 

 of Fig. 1. The curve-triangle U TQis the centroid of the 



Fio. 7. 



triangle ABC, and the shaded duangle P V Q W is the 

 centroid of the duangle R P S Q. 1 As the duangle moves 

 in the triangle (the elements sliding upon each other), its 

 centroid rolls within the centroid of the triangle. Both 

 centroids are in this case formed of arcs of circles, and all 

 the point-paths (being determined by the rolling of one 

 circular arc upon another) are combinations of trochoidal 

 arcs. 



The centroids of kinematic chains are generally of greater 

 complexity that those of the pairs of elements just mentioned, 



1 These centroids are shown on a larger scale, apart from the elements 

 to which they belong, in Fig. 2. 



