263.] PLANE MOTION. ! 4I 



machines than lower pairs. The only very common example of 

 higher pairing is found in toothed wheel gearing. 



262. For the purposes of kinematics a machine may be 

 regarded as consisting of a number of bodies (links} connected 

 by pairs in such a way that when one of the links is fixed all 

 other links are constrained in their motion. In most cases 

 this constraint is such as to leave but one degree of freedom 

 to every link. 



A system of links of this kind forming, so to speak, a skeleton 

 of the machine is called a kinematic chain (Reuleaux). When 

 one link of such a chain is fixed, the 

 chain becomes a mechanism. As a 

 typical example we may take the 

 " slider crank " in Fig. 57. 



If the pairs are all turning pairs 

 with parallel axes, the chain is called a 

 linkage (Sylvester). A typical example 

 is the four bar linkage in Fig. 58. A 

 linkage with one link fixed has been called a linkwork (Sylves- 

 ter). The four bar linkwork in Fig. 58 is also called a "lever 

 crank " (Kennedy). 



263. The Four Bar Linkage 1234 (Fig. 59). Whatever may be 

 its motion, each link considered separately moves as an invariable 

 plane figure and has therefore at any moment an instantaneous 

 centre C and an angular velocity a> about this centre. 



The centre \ 2 of I 2 and the centre C 2S of 2 3 must always lie 

 on a line passing through 2 since the velocity of 2 is perpen- 

 dicular to both 6\ 2 2 and ^ 23 2. 



Similarly, 3 must lie on the line joining the centres C 23 and 

 C M ; and so on. 



The quadrilateral 1234 is therefore, and always remains, 

 inscribed in the quadrangle C IZ C ZB C M C^. This can ^ e shown 

 to hold even for the complete quadrilateral and quadrangle. 

 The complete quadrilateral, or four-side, 1234 has six vertices, 

 viz. the six intersections i, 2, 3, 4, 5, 6 of its four sides ; the 



