Page:The Kinematics of Machinery.djvu/269

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52. Necessity for a Kinematic Notation.

THE investigations concluded in the last article have conducted us again through the lower and higher pairs of elements to the kinematic chain, the form which, as we have already seen ( 3), represents the general solution of the machine problem. What we found before to follow directly from simple fundamental propositions, we have now been led to a second time, indirectly, in the course of natural development, and we have seen further the employment of the kinematic chain extending rapidly in all directions. The glance which we have taken at the history of machine development has shown us the course of the mental processes which have produced the chain, and by a continuation of which we may suppose it may be still further improved and applied. We must now turn to the direct consideration of the thing itself.

Such an immense variety of cases existing and possible here present themselves, that it becomes increasingly difficult to comprehend them all. This difficulty presents itself specially in the indication by names of their separate characteristics, and in distinguishing between cases which ought to be separated ; and it