16 
PROFESSOR T. A. HEARSON OH THE KINEMATICS OF MACHINES. 
If, in the case in which the pieces move in or parallel to one plane, the links are 
connected together in one continuous chain, the last being joined to the first, the 
number of links and motions will often be required to be not less than four to permit 
of any movement, and, if the number so joined exceeds four, the movement will 
be indeterminate and the linkage will not be suitable to serve the purpose of a machine 
in which a definite movement is required. 
The general case of a simple plane mechanism is represented in fig. 1 , in which 
four links are united together in one continuous chain by four pins, the axes of 
which are parallel to one another. If three links only were joined together in 
this way, they would form a rigid triangle, whereas, if five were so joined the relative 
movement would be indeterminate. 
It will be seen further on that, by imagining the lengths of the links to be suitably 
changed up to the limits of zero and infinity, this mechanism may be made to move 
in all the ways which are possible for a simple machine, the parts of which move in or 
parallel to one plane, also by supposing other changes to occur the same mechanism 
will be seen to be representative of other classes of mechanisms in which the parts do 
not move in or parallel to one plane. P. 31. 
It will be shown later, p. 36, that machines which consist of more than four links 
are compound mechanisms, which may be analysed into two or more simple ones, in 
which one or more links are common to two or more of the simple mechanisms which 
together compose the compound machine. 
Simple Plane Mechanisms. 
If, in the mechanism of fig. 1, the links are all of finite length, each link will be 
capable of moving relatively to an adjacent one, either by turning completely and 
continuously around, which will be referred to as a turning motion and represented by 
he letter O, or by swinging through a part of a revolution and reciprocating to and 
