Page:The Kinematics of Machinery.djvu/66

In the pair shown in Fig. 6, which consists of a solid prism enclosed by a corresponding hollow one, all points of the latter describe straight lines of equal length if it be set in motion after the former has been fixed.

Fig. 7.

A large number of motions can be obtained in this way simply by pairs of elements, as we shall have occasion further on to see more in detail, while the complete development of their properties affords the means of multiplying indefinitely the motions obtainable by single pairs. This can be done by the combination of pairs.

Fig. 8.

Let it be desired to combine two pairs of elements, $ab$ and $cd$;—this must take place so that each of the elements of one pair be combined with, that is made part of the same solid body as, one of the elements of the other pair. This, moreover, may occur so that the mutual relation of the parts is not altered, and no new motion obtained. If the element $b$ be joined to $c$, then $d$ must be combined with $a$; or if $b$ be combined with $d$, then $a$ must be joined to $c$. We may illustrate this by an example, Fig. 7. Suppose that $ab$ and $cd$ be two similar pairs, $b$ and $c$ being cylinders, $a$ and $d$ prismatic slots in bars, having such a form as to prevent either sideway or endlong motion of the cylinders. Let $b$ and $c$ be so joined that