THE KINEMATICS OF MACHINERY. 103 



We Lave seen in connection with Fig. 1 4 that we can to a 

 certain extent alter the size and extent of a pair of elements 

 without altering its nature or changing the motion of the 

 chain to which it belongs. This alteration in the size of 

 elements, or what may be called the " expansion " of elements, 

 is a process continually carried out by engineers for practical 

 constructive reasons.; and often gives to identical mechanisms 

 extremely different forms. It is impossible here to go into 

 this in detail, a somewhat extreme case of it is shown, for 

 the sake of illustration, in Fig. 18. Here we have the 

 mechanism shown already in Fig. 8, ((7 3 ' J P- L ) <i . The pin 

 of the pair 2 is so enlarged as to include altogether the pair 

 3, the connecting-rod 6 being simply a circular disc, with 

 an eccentric cylindric hole in it. The pin 1 again (the 

 " crank-shaft "), is made large enough to include the whole 

 of 2. We have therefore 3 within 2, and 2 within 1. 

 We have one very common illustration of the extent 

 to which this expansion of pairs is carried practically 



in the link motion. The curved link and block are in their 

 kinematic relations simply a very much expanded pair of 

 cylindric elements reduced in extent by use of a process 

 similar to that by which we got Fig. 14 from Fig. 10. 



We have seen what results have been obtained by making 

 two links of the chain (C^ infinitely long. The same 

 process can be carried still further. In the familiar chain 

 shown in Fig. 7, for instance, three links, d, c and b, 

 are made infinite. We have therefore another prism pair in it, 

 and its formula becomes (C\ 2 P 2 ). It gives us the two 

 mechanisms already mentioned and a third one, all of which 

 are practically applied. 



