Page:The Kinematics of Machinery.djvu/571

 CYLINDER CHAINS. 549

� Cylinder-Chains.

We have already (Chap. VIII.) studied the chains ( 6 r/ 4 ') and (C^) t and found that they divided themselves into twelve classes con- taining fifty- four mechanisms. Our investigation resembled so very much a synthetic treatment of these chains that it is not necessary here to repeat the investigation. Let us look what other simple chains containing none but cylinder pairs can be formed.

If we attempt to form a chain from three cylinder pairs we see at once that its closure is fixed (Fig. 387), we need not, therefore, examine it further.

���FIG. 387. FIG. 388.

Five parallel or conic cylinder pairs give us a simple chain which is unconstrained, so that this combination also is of no importance to us. If we put a normal or normally crossed pair in place of one of the parallel pairs we obtain a chain which is con- strained, and which contains five cylinder pairs, but here no motion can take place in the normal pair. It might thus be altogether omitted without affecting the motion of the chain, which is there- fore really one of four links only. If the pair instead of being normal be oblique or obliquely crossed, as in Fig. 388, the chain becomes fixed, no motion whatever can take place in it. We have not, however, reached the limits of the cylinder chain, the two last mentioned may be considered to be only special cases of one con- taining a larger number of links. Working upwards to this from Fig. 388 we obtain first, by the addition of another cross-joint, and by destroying the parallelism of 1 and 6, the six-linked chain of Fig. 389, which again, like Fig. 388 is immoveable. If, however, we divide the link joining the cross-blocks into two parts, as in Fig. 390 for example, where a cylinder pair whose axis passes

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