38 
PROFESSOR T. A. HEARSON ON THE KINEMATICS OF MACHINES. 
at two or more joints, those of B will preclude it, in which case the motions will he 
restricted to U motions 
In Conjunction II., two adjacent links of A are adopted, but only one in its full 
length. Thus the two new links which are added to form B are connected to the two 
chosen ones of A at, say, the joints s and iv 2 . In this case the third mechanism 
B' will consist of five links coupled at the joints w 2 , w x , y x , s, y 2 . Supposing, as 
before, U motions only, the formula for such a conjunction may be written thus, 
The link shown by the thick line is as explained (p. 24), intended to represent the 
frame link. The preceding formula will represent a portion of the mechanism of a 
beam engine consisting of the frame of the engine, the half beam, and the parallelo¬ 
gram and radius rod of Watt’s parallel motion. 
Another example of Conjunction II. may be quoted for the purpose of showing how 
the formula may be written when there is an I motion in the mechanism. The 
portion of a locomotive engine consisting of frame, piston, connecting-rod, crank, 
outside coupling-rod, and the crank of a second driving wheel, will have a movement 
which may be written thus, 
O—o-r-I—U—o—O. 
The letter I does not lend itself to showing whether the two adjacent links form 
one rigid piece or not; but if it be remembered that a slide is to be regarded as a 
swing about an infinitely distant joint, it will be seen that two lines meeting at an I 
cannot represent one link continuous through the joint, but must always be under¬ 
stood to indicate two separate links. Thus, no difficulty will occur in the use of the 
letter I. 
In the next, Conjunction III., neither of the two adjacent links of A, which are 
adopted, are used with their original length in mechanism B, so that each of these 
two links possess three joints. Thus, the mechanism B' will consist of six links con¬ 
nected at the joints w 2 , w x , y x , s 1 , s 2 , y 2 . Supposing U motions only, the formula for 
this conjunction may be written thus, 
\ 
or so A, 
when one of the three-joint links is the frame link. 
Of this, two examples may be quoted with which the reader will be sufficiently 
familiar to dispense with illustrations. One is the mechanism of Richard’s indicator 
for taking diagrams of steam pressure in engines, the formula for which may be 
