THE KINEMATICS OF MACHINERY. 95 



THE KINEMATICS OF MACHINERY. 



LECTUKE II. 



WE shall in the present Lecture examine in some detail a few 

 of the results which can be obtained by treating mechanisms 

 upon the plan which Rouleaux has proposed, and which is 

 illustrated by his models ; that is to say, by the analytical 

 treatment of which we have already seen the general nature. 



We have seen how kinematic chains are built up from pairs 

 of elements and links. The pairing and the linkage renders 

 the relative motions in the chain absolutely determinate, and 

 the determinate relative motion exists equally whether or not 

 any link of the chain be fixed relatively to the earth or to any 

 portion of space that we choose to treat as stationary. 



We have now to consider in more detail the effect of fixing 

 one link of the chain. In practice, of course, one link is 

 always fixed, or in other words, its motion relatively to the 

 earth, to a locomotive or whatever it may be, is made zero. A 

 chain with one link fixed is simply what we know as a me- 

 chanism. 



In examining pairs of elements we saw that we could fix 

 either element of the pair with lower pairs, the relative motions 

 remaining unaltered ; with the higher pairs the inversion gives 

 us a totally different motion. We have seen also that we can 

 fix any one link of a kinematic chain just as we can fix either 

 element of a pair. We therefore can get as many mechanisms 

 from any chain as it has links. From any such chain as Fig. 

 3, for instance, which has four links, we can get four mecha- 

 nisms. The fact that a kinematic chain gives us as many 

 mechanisms as it has links appears, looked at from this 

 point of view, a mere matter of course. It has, however, 

 never been hitherto distinctly recognized, so far as I know, 

 and it can hardly be realized too distinctly, the consequences 

 which result from it being most important, as we shall see. All 

 that I shall attempt to do in this lecture will be to look at 

 some of the mechanisms obtained from the particular chain 

 just mentioned, and various modifications of it. 



