THE KINEMATICS OF MACHINERY. 85 



(ii.) That the motion of any link relative to any other 

 than its adjacent links depends on all the elements of the 

 chain. 



(iii.) That no one link of a mechanism can be moved with- 

 out moving all the other links except the fixed one, and 



(iv.) That there can be only one fixed link in a mech- 

 anism. 



The two last propositions require a few words of explana- 

 tion. Suppose that in any combination of, say, four links, 

 two can be moved without moving the other two, the com- 

 bination is actually one of three links only, for clearly the 

 two immovable links may be made into one, and are two 

 only in name. This is very often the case in machinery, 

 where special mechanisms are frequently used for the express 

 purpose of connecting rigidly two or more links, and making 

 them act as one, at certain intervals. 



If, however, in the combination supposed, one link be fixed, 

 while two can be moved and the fourth can either move or be 

 stationary, the combination no longer comes under our defini- 

 tion of constrainment, for the motions are at a certain point 

 indeterminate, at the point, namely, when it is possible for 

 the fourth link either to move or to stand. Chains often 

 occur in which this would be the case were it not that mecha- 

 nicians take means, either by adding other chains or in other 

 ways, to constrain the motion which would otherwise be 

 useless to them. 



We have now obtained some idea of the way in which 

 mechanisms are formed, of the elements of which they consist. 

 Before applying the knowledge we have thus acquired I must 

 direct your attention to some geometric propositions which 

 will greatly facilitate the theoretic dealing with these 

 mechanisms. 



In order that I may not enter into too wide a subject, I 

 shall confine myself here to the consideration only of " con- 

 plane " motions, or motions in which all points of the moving 

 body move in the same plane or in parallel planes. The 

 limitation is a large one, but the cases included under 

 conplane motion cover the greater part of those which occur 

 in practice. The method I have to describe is equally 

 applicable to general motion in space as to simple constrained 

 conplane motions of which I shall speak. 



Let me remind you that the motion of any figure moving 



