Page:The Kinematics of Machinery.djvu/355

 REDUCTION OF CHAINS. 333

R Skew double slider-crank chain (G^G^ Fig. 265, a and c are acute, b and d right-angled. This chain corresponds both to the cylindric skew double slider chain and to the cylindric crossed slide chains F and G (p. 322). It gives us three mechanisms (22 to 24), of which very occasionally we find an application existing.

In all, therefore, this conic crank chain gives us 24 mechanisms, dividing themselves into five different classes. The majority of these have been hitherto unknown ; whether they are " practical " or " unpractical " is not a question which concerns us here. Our unerring analysis will allow us further on to obtain very important results from them. Summing up the results of the last ten sections we find that the number of mechanisms formed or essentially derived from the quadric crank chain has been 54, and that they have occurred in 12 distinct classes.

76. Reduction of a Kinematic Chain.

If we wish to obtain the motion of any particular link in a complete mechanism, without requiring at the same time to use the motions of any other of its links, it is often possible to remove one of these, its place being supplied by a suitable pairing between the two links which it connected. The number of links in the chain can thus be diminished without affecting the particular motion which is required, and it is evident that this may often be very advantageous. "We shall examine some examples of it.

Suppose that it be wished to obtain a reciprocating sliding motion by means of the turning slider-crank (C^P^ Fig. 266, and that none of the other motions in the chain be required, then the coupler I may be removed if we pair the crank a to the block c direct. This can be done, for example, by attaching to a a pin of suitable diameter, and connecting with the block an envelope (3, Fig. 4) for it, which will in this case take the form of a curved slot touched by the pin upon both sides, as in Fig. 267. The pin and its envelope form together a higher pair of elements. The simplest arrangement will be obtained by using the former crank pin, which will pair with a slot described from the centre of the