99 , 
Li Li 
PROFESSOR T. A. HEARSON ON THE KINEMATICS OF MACHINES. 
can be formed, causes these motions to be so very largely employed in the composition 
of the machines found in ordinary use. 
If the foregoing analysis be compared with that instituted by Reuleaux, to which 
it bears a close resemblance, it will be seen that Reuleaux conceives that the 
elementary essential components of machines are the pairs of consecutive links which 
are in mutual contact, whereas it is here proposed that the relative motions of con¬ 
secutive links should be regarded as the essential elements or components of a 
machine movement. 
Whilst the pairs of surfaces of contact of consecutive links should be formed to 
suit the kind of relative motion which those pieces are required to undergo, yet the 
forms of those surfaces do not themselves entirely govern the character of the motion. 
Reuleaux assumes that the turning and sliding motions are entirely governed by 
the forms of the surfaces of mutual contact of the consecutive links, but shows that, 
to insure a more complex relative motion, a restraint is often imposed by means which 
are external to the two links which so move. Those additional means of constraint 
have to be included with that due to the forms of the surfaces of mutual contact, in 
the full conception of a complete pair. The apprehension of what exactly constitutes 
a pair is often extremely difficult. 
Reuleaux, acting on this assumption, does not directly discriminate between a 
turning and a swinging pair, for there is no difference between the forms of the pairs 
of surfaces which are suitable for the O and U motions. Yet the difference in the 
two motions is most apparent, and very important, both kinematically and also from the 
practical engineer’s point of view. So also, whilst the difference between the motions 
represented by a large O and a small o is easy to understand, and is of much 
practical importance, yet the necessary difference in the construction of the corre¬ 
sponding pairs is very intangible, and may even be non-existent. 
Although Reuleaux supposes a mechanism to be made up of a number of pairs, 
yet, in some cases, he has to admit that the entire mechanism is needful to complete 
only one of the pairs. This he refers to as “ chain closure.” It will be seen that, if 
what Reuleaux calls a turning pair is differentiated into the pairs requisite for the 
three motions denoted by OoU, then, whenever either of those motions occurs, the 
whole mechanism will be needful for the completion of one pair contained in it. 
Thus, whilst saying that the whole is made up of a number of parts, yet each part 
complete will include the whole, and so the analysis fails. 
In offering the proposed modification of the analysis of machines, the author desires 
to pay to Reuleaux a tribute of admiration for his work, and to gratefully acknow¬ 
ledge it as the source of his inspiration. 
Although exception is taken to some of the premises of Reuleaux, yet the greater 
portion of his work will remain of undiminished value. 
In designing or constructing a machine so that it may embody any one of the 
previously-mentioned combination of motions, the provision of suitable forms for the 
