1895.] The Kinematics of Machines. 109 



to permit of complete turning. This is founded on the fact that 

 one side of a triangle cannot be greater than the sum of the other 

 two. From these two laws together it is shown that it is impossible 

 to have two O's alternating with two U's. 



Next it is pointed out how the U motion may be provided for by 

 constructing a circular slotway in one piece, and shaping the other 

 piece to fit the slotway, so that by imagining the radius of curvature 

 of the slotway to be indefinitely increased a relative movement of 

 reciprocating sliding motion, represented by the symbolical letter I, 

 will be substituted for the swinging motion U. A slide being con- 

 ceived to be a swing through a zero angle about an infinitely distant 

 centre, the previously mentioned laws will apply to associations con- 

 taining I motions, and it will follow that a combination of three 

 slides and one swing is precluded by the first law. 



If four slides are associated, in which all four of the links of 

 the original mechanism are to be conceived to be infinitely long, 

 an indeterminate motion will result comparable to the motion which 

 would be possible if five bars were joined by pairs in a closed circuit. 



One of the slides may be suppressed, and a definite motion will 

 result from three slides. 



If the foregoing analysis be compared with that due to 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 consecutive links 

 should be regarded as the essential elements or components of a 

 machine movement. Whilst the pairs of surfaces of contact of con- 

 secutive pieces 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 what he calls a turning motion and the I 

 motion are entirely governed by the forms of the surfaces of mutual 

 contact, but shows that to ensure a more complex motion a restraint 

 is required to be imposed by means external to the two links. Those 

 additional means of constraint have to be included with that due to 

 the forms of the surfaces of mutual contact in the conception of a 

 complete pair, and often the whole mechanism is required to complete 

 one pair contained in it. 



Reuleaux does not attempt to discriminate between a turning and 

 a swinging pair ; the same pair of surfaces of mutual contact is 

 suitable for both ; the difference consists of a difference only in the 

 rest of the mechanism, yet the difference in the two motions is most 

 apparent, and is very important, both kinematically and also from, 

 the practical engineer's point of view. 



