Page:The Kinematics of Machinery.djvu/67

 their axes are parallel, and let the two slotted bars be also placed parallel to each other and joined. Then evidently, if $$a d$$ be fixed, every point in $$b c$$ must move parallel to the centre line of the slots, as shown by the arrow. All such points therefore describe equal straight lines. Thus the motion takes place exactly as it would if $$b c$$ were a solid prism enclosed by a hollow one, like the pair $$a b$$ in Fig. 8. Thus by combining two pairs we have obtained nothing but what we could have got by means of a single one. So far the experiment has led to no result.

. 9.

But if we do not place $$a$$ and $$d$$ parallel to each other, but set them obliquely as shown in Fig. 9, the case is entirely altered. The centres of $$b$$ and $$c$$ no longer move in similar directions in the slots, and consequently the various points in $$b c$$ no longer have similar paths,—the point $$p$$, for example, describes a curve. The motion is thus quite different from what it was before.

Nevertheless in these two different cases, Figs. 7 and 9, the same relation obtains; in both, $$b c$$ and $$a d$$ form rigid bodies, or what may be considered as such,—that is to say, we have in the end one pair of elements only, by combining two pairs of bodies. With different methods of combination different results are obtained, but in every case there results only one pair.

Accordingly the reciprocal combination of the elements of two pairs gives us again a. Thus we obtain already an important result, and one having many consequences.