84 LECTURES TO SCIENCE TEACHERS. 



the link connection by a line, we may indicate some of the 

 chains obtainable from 4 pairs and 4 links, thus : 



a bb cc dd a 



(we suppose the " chain " to return on itself and the two ele- 

 ments a to be paired, the whole forming a closed chain) ; or, 



a cc bb dd a 



or 



a dd cc bb a &c. 



FIG. 3. 



For the sake of illustration we give in Fig. 3 a sketch 

 of a familiar chain containing four links, each connected to 

 the adjacent link by a cylinder-pair of elements. The axes 

 of the four pairs of elements are parallel. 



We have then, in the kinematic chain a combination so 

 constructed that all its parts have determinate motions, 

 motions absolutely fixed by the form of the elements carried 

 by its links, and independent (considered as changes of posi- 

 tion) of the application of external force. To convert the 

 chain into a mechanism we have only to do what we have 

 already done in connection with pairs of elements, fix one 

 element, or, as each element is rigidly connected with a link, 

 we may say preferably fix one link. Any link may be fixed, 

 the chain therefore gives us as many mechanisms as it has 

 links. In general these are different, in special cases only 

 two or more of them are the same. We shall be able to enter 

 into this part of our subject at some length in the next lecture ; 

 at present it will suffice to note two or three of the leading 

 characteristics of chains and mechanisms which we can now 

 easily recognise. These are 



(i.) That the motion of any link relative to either adjacent 

 link is determined by the pair of elements connecting them. 





