

KINEMATIC MODELS. 



these paths are very beautiful curves, as you will see if you can follow 

 the motion of the pointer in the model (see Fig. 2). These paths are, 

 in this case, combinations of epi-and-hypotrochoidal arcs. I cannot 

 here go more fully into their nature, I merely show them to illustrate 

 the fact that enclosure is not an essential characteristic of pairs of 

 elements having constrained motion. 



If two elements be joined together rigidly by a body of any form 

 whatever, we have what is called a kinematic link. If I take, for 

 instance, this nut, and fasten it to this open cylinder, I have such a 

 link. This solid cylinder, connected to the screw, gives another link, 

 and so on. By pairing together a number of links we get a combination 



Figure 3. 



which Reuleaux has called very happily a kinematic chain. In the 

 particular chain which I have here (Fig. 3) there are four links, each 

 being a bar rigidly connecting two elements, and these elements 

 belong in each case to a turning (closed) pair of elements. Before me 

 on the table are a number of other chains similarly constituted, and 

 containing both turning and sliding pairs of elements. 



I must now direct your attention to a matter which is of the greatest 

 simplicity, but of equally great importance. If I take any pair of 

 elements in my hands, and move it, you see at once that although the 

 motions of each element, relatively to the other, are perfectly determi- 

 nate, the absolute motions are perfectly indeterminate. The elements 

 may move anywhere in space. In the kinematic chain there is just the 



