Page:The Kinematics of Machinery.djvu/602

 I can here only mention further, that if the prism pairs in the chain (C″5Cz) be made instead of normal to the axes of the cylinder pairs, a number of special cases occur: these must be here left altogether unexamined.

§ 162. Closing Remarks.

The sketch of the synthesis of machines which we have now ended has given us several results differing greatly from those which have hitherto been deduced from a general and apparently scientific treatment of the subject. The most important discovery which we have made is undoubtedly that the region within which kinematic combinations are formed is much more narrowly limited than has usually been supposed. This is apart, I think, from the inexactness of the treatment with which so many former writers have been satisfied, for even the more accurate ideas as to combinations of elements with which we commenced our study of the problem did not in themselves indicate that the synthesis could be successfully used over so large a field as that in which we have found it available.

It is very noteworthy also, in regard especially both to practice and to instruction, that all the principal problems of machinery are connected with a comparatively very small number of kinematic chains. These are:—


 * the screw-chain,
 * the wheel-chain,
 * the crank-rchain,
 * the cam-chain,
 * the ratchet-chain,
 * the pulley-chain,—

in all of which flectional elements may take the place of rigid ones. The problems not covered by these chains are all more or less inferior in importance.

In § 92 I directed attention to the extraordinary unanimity with which the inventors of "rotary" engines and pumps have chosen crank-trains as the foundation for their chamber-gear. This now