530 KINEMATICS OF MACHINERY.
( 56) that the number of elements is not very large, for we have been able to express them all by a very moderate number of symbols. It follows necessarily that the pairs built up from these elements can only vary within tolerably narrow limits. This is really the case ; we see at once therefore that a field for the application of kinematic synthesis is becoming visible.
The object of general indirect synthesis is to do for the kinematic chain what the special synthesis does for the pair of elements. The great number of possible cases at once presents itself as a difficulty. On examination, however, it will be found that these fall together very much. The number of simple chains especially that is, of chains in which no link contains more than two elements is by no means as large as might be at first sight imagined. The determination of these possible simple kinematic chains alone, however, forms no inconsiderable part of the whole problem.
There is, of course, no limit to the number of com pound chains which can be formed, so that in this direction the solution of the problem can never be complete, and these compound chains demand investigation on just the same terms as the simple ones. In actual machinery, however, the compounding of chains is not carried very far. In those cases which appear most complicated it is almost always possible to subdivide the whole according to the purpose of each of its groups of parts, and to treat it as a series of separate mechanisms, no one of which is in itself very com- plex. The method of descriptive analysis ( 135) has given us very extensive and satisfactory illustration of this, and we shall further on find a more exact method of distinguishing between different cases of compound chains. There are certainly, however, many compound chains which cannot be subdivided in this way. Some of the more important of these we can already treat fully synthetically without extending their investigation to any excessive length ; others will no doubt yield in time to synthetic methods.
We see, therefore, that we may apply the method of indirect synthesis to our subject with every prospect of obtaining by its means results which are really of practical value.
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