36 
PROFESSOR T. A. HEARSON ON THE KINEMATICS OF MACHINES. 
The next step in the discrimination of one machine movement from another will 
consist in distinguishing the various different movements derived from any one 
combination by inversion. 
Compound Mechanisms. 
In most of the important machines it will be found that there are more than four, 
and often many more than four, separately moving pieces and yet the motions are of a 
perfectly determinate character. It is left to explain how this is so, and how the 
previous considerations apply to such machines. 
In practically every one of these machines it will be found, on examination, that 
there is a mechanism consisting of not more than four pieces associated together in one 
continuous chain. The pieces or links of this chain, which for reference may be called 
A, will therefore have a perfectly definite motion, either relatively to the user of the 
machine, if one of the links is the frame, or only relatively to one another if neither of 
those links is the frame. 
The compound machine will lie formed by one or more of the links of A being 
combined with other pieces to form a second mechanism B. 
Suppose one link only of A to be joined up in chain with three fresh pieces to form 
the second continuous or closed chain B, then the movement of B will be independent 
of A, for we may imagine the link which is common to the two to be the frame link, 
in which case A may be in movement whilst B is at rest, or vice versa , or both may be 
in motion at the same time. 
But more often it will be found that two of the links of A are adopted to compose 
with two new links the second mechanism B. In this case, a movement of A cannot 
take place without causing a definite movement in the two new links which, together 
with two of A, form the second mechanism B. Of the six links, which in this way 
have definite relative motions, any two may be adopted to form, in conjunction 
with two additional links, a third mechanism C producing a machine consisting of 
eight pieces, having a perfectly definite motion relatively to one another, and so on. 
Compound mechanisms may be conceived and constructed in which there is a definite 
relative motion, but in which there is not a four-linked continuous chain of pieces. 
The most simple construction of this character may be described as consisting of a 
continuous chain of six links, of which two pairs of links, which are opposite to one 
another, are linked together by the addition of two more links. In this case the 
shortest continuous chain will contain live links. Of the eight links which make up 
the complete mechanism, four will form a part of three five-linked chains, and four a 
part of two. 
The simultaneous control due to the two or three partial restraints are sufficient to 
determine a definite motion. 
In this mechanism there will be U motions at all the ten joints, and there will 
be four bars, each containing three joints. Each of these bars will be continuous 
