PROFESSOR T. A. HE ARSON ON THE KINEMATICS OF MACHINES. 
35 
The mechanisms in each of these divisions may be classed in two sub-divisions : 
S being the sub-division in which each pair of consecutive links is in contact one 
with the other over a surface. 
P being those in which one or more pairs of consecutive links are in contact with 
one another at a point or along a line of points only. 
The mechanisms of Sub-division S of Divisions 1 and 2 will consist of those in 
which the OUT motions only are used. 
Those of Division 3 will include the V or helical motion ; and 
Those of Division 4 will include the motion ©, requiring the use of a ball-and-socket 
joint. 
To the pairs of links which have the relative motions denoted by OUIY, Reuleaux 
has given the name “Lower Pairs.” 
Reuleaux claimed two characteristics for lower pairs, viz. : 
1. Definiteness of motion derived from the forms of the surfaces of mutual contact 
and depending on nought else. 
2. The possibility of distributing the contact of consecutive links over an area which 
may be extended as much as desired, the contact not being confined to a point or a 
line of points as in “ Higher Pairs.” 
It has been shown that if the motions represented by Oo and U are required to be 
differentiated from one another, Reuleaux’s so-called turning pair cannot possess 
the first characteristic. (There is scarcely a mechanism in which the nature of the 
motion between two consecutive links'does not depend on the other links.) 
The second characteristic is of considerable value in relation to the liability to 
abrasion and wear ; but the advantage of greater immunity against wear has to be 
purchased at the cost of a more complicated construction, and a more restricted 
character of movement. 
As the first characteristic cannot be secured, the author proposes to adopt the 
second only for the criterion as to whether a mechanism should be regarded as 
belonging to Sub-division S or P. 
Therefore, in Division 4, the motion 0 requiring the ball-and-socket joint should be 
included in the motions of Sub-division S. Reuleaux considered the ball-and-socket 
joint a “ higher pair.” 
If die motion of any two consecutive pieces of a mechanism differs from the motions 
OUIY and 0, the mechanism will belong to Sub-division P. 
Next, the mechanisms included in either of the eight sub-divisions may be 
separated into sections as numerous as the combinations of the various elementary 
motions, which will satisfy the governing geometrical laws. 
For example, in Sub-division 1$, it has been shown that there are fourteen, and 
only fourteen, possible combinations. (These have been placed in four groups, chiefly 
to aid the memory in enumerating them.) In the Sub-divisions 2s there are only six 
distinct combinations, and in 3s there are four. It is probable that in the other sub¬ 
divisions the number of possible combinations will be finite. 
F 2 
