PROFESSOR T. A. HEARSON ON THE KINEMATICS OF MACHINES. 
33 
Cylindrical Mechanism s. 
Whilst the plane mechanism III cannot be adapted to the surface of a sphere, 
it can be fitted to the surface of a cylinder, and it is the only one of the OUI 
mechanisms which can. 
If such a triangle of slides be imagined to be wrapped around the surface of a 
cylinder, one at least of the slides will have to become helical. Two or even three 
may be. 
In this way we are led to the very important Third Division of machines contain¬ 
ing screw motions. 
The projected view of a helix has a shape, much like the letter V, so this letter 
will suggestively stand for helical motion. 
In this division there are the following combinations :— 
UVI with three inversions. The common screw press is one example. 
VVI with two inversions. The differential screw press and micrometer are 
examples. 
YVU with two inversions, and 
YYY one inversion only. 
In total, four combinations, containing eight inversions. 
But not only is the plane mechanism III capable of being adapted to a cylinder, 
but also IWI. If for one of the slides of the former mechanism a curved slotway of 
uniform width fitted by a cylindrical pin were substituted, a mechanism represented 
by the latter formula would be obtained in which the relative velocities of sliding 
would not be constant, but vary from point to point. If, further, the resulting 
mechanism be conceived to be wrapped around a cylinder, we should have one helix 
of varying pitch. In order that the pin may fit such a helical groove, it will be 
necessary to restrict the contact between the two to that of one or a pair of points 
only. Such a mechanism is known as a cylindrical cam, and there are many 
applications of it in practice. 
Adopting the letter H for the motion with the varying-pitch helix, the following 
four combinations are possible, and they have eleven different inversions, viz. :— 
UHI with three inversions. 
„ two 
No other combinations belonging to this division or sub-division appear to be 
possible. 
MDCCCXCVI.—A. F 
VHI 
YHU 
VHY 
