20 
PROFESSOR T. A. HEARSON ON THE KINEMATICS OF MACHINES. 
A sliding motion will be represented by the letter I. 
This modification of the construction may be repeated where there is another 
U motion, but not where there is an O motion. The corresponding counterpart of 
an O motion would be a continuous slide in one direction, to provide for which a 
really indefinitely long link would be requisite. 
The foregoing method of showing the derivation of an I motion from a partial 
turning motion is due to Beuleaux. It is here introduced for the purpose of 
showing how the two laws previously enunciated may be applied to mechanisms 
containing I motions. 
In the application, a slide is to be regarded as a swing through a zero angle about 
an infinitely distant centre, and the adjacent links are to be imagined infinitely long, 
but having, possibly, a finite difference between them. 
If in the combination o0 3 oU an I is substituted for the U, it will become o0 3 oI, in 
which the proportions between the length of the links previously ascertained must 
still be retained, that is, the two links joining the O’s must be equal, and the other 
two links joined up by the I are to be conceived infinite and equal, which amounts 
to the construction being such that the line of slide is parallel to the line joining the 
axes of the two adjacent o motions. There being no angular velocity at the slide, 
the angular velocity of the O 3 motion must be exactly twice that of the two 
o motions. 
This property, together with that of symmetry of motion, has caused this combi¬ 
nation to be adopted in the design of a high-speed engine. 
If a slide is substituted for a swing in the combination OoUU, it will become 
o y 
OoTTI, many important examples of which are in every day use, as further described. 
P. 26. 
