34 
PROFESSOR T. A. HEARS ON ON THE KINEMATICS OF MACHINES. 
Skew Mechanisms. 
It is proposed to group all the remaining simple mechanisms in a fourth division. 
They may be described generally as consisting of those in which the axes of the 
elementary motions neither meet nor are parallel. 
These may be referred to under the name of skew mechanisms. 
The general case may be described as consisting of a link T secured to a shaft, 
which turns or swings in bearings provided in a piece V, which also provides bearings 
for another shaft which is neither parallel to nor meets the former shaft T. This 
second shaft has a link X secured to it so that it also turns or swings relatively to V. 
The two links T and X, which are either cranks or levers, are joined together by a 
link Z, which has ball and socket connections with T and X. 
With such a construction the movement will be of a definite character, and the 
mechanism will be capable of serving the purpose of a machine. By imagining either 
or both links T and X to be infinitely long, a slide or slides may be substituted for 
one or both of the turns or swings. 
Thus a variety of combinations are possible, and each one will be capable of a 
certain number of inversions. 
In the formulae for these it is proposed to use the Greek letter © for the movement 
at the ball and socket connection. 
A certain limited number of OUl© combinations will be possible of which an 
exhaustive list could be prepared. 
Besides these another set of skew mechanisms will result from suppressing one of 
the links and amalgamating the two adjacent simple motions. The best known 
examples of such a combination is seen in the use of a pair of skew-bevil-wheels and 
in the worm-and-worm-wheel. The relative motion between two such pieces may be 
represented by the Greek letter O. 
Summary of Simple Mechanisms. 
The method of classification, according to the proposed scheme, may be summarized 
as follows :— 
All simple machine movements may be ranged in four divisions, viz. : 
1. Consisting of plane mechanisms in which the pieces move in or parallel to one 
plane. 
2. Spherical mechanisms in which the pieces move in or parallel to the surface of a 
sphere. 
3. Cylindrical mechanisms in which the pieces move in or parallel to the surface of 
a cylinder ; and 
4. Skew mechanisms, being those in which the axes of the turning or swinging 
motions neither meet nor are parallel. 
