Page:The Kinematics of Machinery.djvu/362

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KINEMATICS OF MACHINERY.

omitting the frame. The complete chain has the formula (C+C') in its reduced form it will therefore be written ( G\ C" 2 ') c.

It must not be supposed that the reduced chains have actually been derived in this way from the complete ones. We have on the contrary (Chapter VI.) seen cause to suppose that the process

FIG 274.

of development has moved in the opposite direction. This how- ever need not prevent us from treating the matter deductively when such a treatment greatly facilitates its comprehension, and enables us to avoid endless repetitions. If we had to consider each reduced chain as a separate form of kinematic linkage we should obtain, through the very various forms which the higher

pairing can take, an enormous number of additional combinations, without at the same time having added a single new motion to those already existing in the complete chains. The admittance therefore, of the principle of chain-reduction into our work helps us very greatly in simplifying its arrangement. In the case of