Page:The Kinematics of Machinery.djvu/363

 AUGMENTATION OF CHAINS. 341

compound mechanisms it can often be very advantageously employed, and the exact analysis of these combinations forms a very interesting and instructive problem in applied Kinematics. 49

77- Augmentation of Kinematic Chains.

The augmentation of a chain stands logically as the contra-positive of its reduction. A chain which has been already reduced can obviously be restored to its original completeness by such a process. But there is no reason why the augmentation should stop here ; the pairing between any two pieces may be replaced by chaining, i.e. by linkage, if the link introduced between them be so arranged as not to alter their relative motions. If the chain already possess the largest number of links which it can have as a simple closed chain, any augmentation must be so arranged as to make it a compound closed chain ( 3, p. 49). In general therefore the process leads us to such chains, which do not belong to the part of our subject at present under consideration. We may merely mention a few illustrations of it. The (so-called) parallel motions are augmentations of this kind: the parallel motions of Watt or Evans, for instance, replace a prism pair by a kinematic chain having only turning pairs, which therefore essentially is a crank mechanism. A common train of wheel- work again, which is used really as a substitute for a pair of wheels of inconveniently large diametral ratio, may be considered an augmentation in the same way. It will be seen from these examples alone that a very extended use is made in practice of this method of chain augmentation. We shall content ourselves here with having thus stated the general nature of the principle, and shall not go further into the matter. Its further considera- tion forms indeed a part rather of applied than of theoretical Kinematics.