Page:The Kinematics of Machinery.djvu/581

 HIGHER PAIES IN CRANK CHAINS. 559

We see that chains derived from ($+) take in themselves many forms which are of practical value ; they can and do also receive very numerous useful applications in compound chains.

155. Substitution of Higher Pairs for Pairs of Revolutes.

We have seen that we can regard the chains ((7 7 ), (C Q ), ((7 5 ) and (<7 4 ) with all their special cases as derived from the chain, ($ 7 ), as the highest form of the chains formed from closed pairs. This, however, we are not obliged to do. For the element C may be considered as a special case not only of S but of other higher forms, namely the general cylinders and cones C and K, with which (as we saw in 21, etc.), we can form higher pairs of elements. Considering, then, the circular cylinder C as a particular case of the general cylinder (7, we can substitute the pair ((5,), formed from the latter, for the pair (C) where it occurs, and thus obtain entirely new motions in the cylinder chains. In this way an immense series of chains can be formed, and an almost inexhaustible series of constrained motions obtained.

The substitution of (#,) for ((7) in the general chain ((7 7 ) is not, however, possible in every case. It cannot, for instance, be carried out in the chain (<7^-) or (generally) in those cases where oblique cylinder-pairs are applied, for here the universal condition of the closed pairs, the coincidence of the axes of the two elements, becomes essential, and this is not fulfilled by the elements of the higher pair. In these cases, however, we can still use the higher pairing if we substitute (K^) for (<7.), the higher cone for the higher cylinder. The instantaneous axis of the pair then always passes through the same point.

It must not be supposed that this use of (&,) or (K,) instead of (C) is mere speculation. We find many instances of it in practice, especially in chains of the class (C" 4 '). As an example very often met with I may give Horn blower's curve-triangle train (Fig. 407), beside which is placed (in Fig. 408) the slider crank-train from which it is derived. The latter is a reduced turning double slider-crank


 * Civil Ingenieur, 1863, p. 215, 1864, p. 21.

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