274 SECTION MECHANICS. 



same peculiarity. It is none the less important that it is almost 

 absurdly obvious. The motions of every link relatively to every 

 other, in other words the relative motions of the links, are absolutely 

 determined ; the absolute motion of the whole chain, or, what is the 

 same thing for our purpose, the motion of the links relatively to this 

 table, is left entirely indefinite. 



The conversion of the relative motion into absolute motion (in the 

 restricted sense in which we have used this expression) is a very simple 

 matter. In the case of the pair of elements, all that is required is that 

 one element should bejfe;/, that is prevented from moving relatively 

 to any portion of space which is, for our purposes, stationary it may 

 be to a room (as here), or to a railway carriage, or a ship, &c. The 

 same method applied to the kinematic chain enables us to convert the 

 relative motions of the links into absolute motions. We must, that is 

 to say, fix or make stationary one link of the chain. 



A combination of kinematic links, therefore, whose absolute motions 

 are unconstrained, is a kinematic chain. The same combination, 

 when one of its links is fixed, forms what is universally known as 

 a mechanism. By fixing, for instance, the link a h (Fig. 3), we obtain 

 a mechanism similar to the beam and crank of an ordinary beam 

 engine, b c revolves, while/ swings to and fro. But the chain has 

 four links, and it is obvious that I may fix any one of them. The 

 combination, that is the kinematic chain, remains the same, but the 

 nature of the mechanism may be entirely altered. Suppose, for 

 instance, the link b c be fixed, we obtain a mechanism which you see 

 at once differs entirely from the last, and which you will recognise as 

 the common drag link coupling, a h and d e both revolving as cranks 

 about the fixed centres b and c. 



A mechanism is, therefore, a kinematic chain of which one link is 

 fixed. Two links cannot be fixed simultaneously without making the 

 whole chain immovable. Any one link, however, can be fixed, and 

 thus from any chain we can obtain as many mechanisms as it has 

 links. I shall endeavour to show you, by a few illustrations, what a 

 ivonderful insight this gives us into the nature of some familiar 

 mechanisms. I will only mention in passing what may, perhaps, be 

 new to some, that this chain (Fig. 3), with which we are so very 

 familiar, is not moveable because the axes of all its pairs are parallel, 



