Page:The Kinematics of Machinery.djvu/95

 wheel fixed to the axis of one of the arms, as d - with another equal and similar wheel upon

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- e, and gearing third axis k.

This axis then turns with precisely the same velocity as d e

but in the opposite direction. If now the centroids be found for the motion of an arm i Jc upon the axis Jc relatively to the first

arm a A, these can evidently, so far as the velocity -ratio

between a h and d e goes, take the place of the less

easily comprehended centroids of Fig. 22. We transform, as it were, the first two centroids into two new ones. Fig. 25 shows these transformed or reduced centroids for this special case. If these be considered as the pitch lines of non-circular spur-

. 26.

wheels, we have at once an easily understood representation of the

communication of rotation between a h and d e. We shall

return later on to the methods of drawing such reduced curves. It is sufficient just now to point out that here the sum of the instantaneous radii is constant (being = a k), while with the original centroids Fig. 22 their difference was constant (being Oa-Od = ad). The infinitely distant points have disappeared, as will be seen, and the whole representation is very simple and can very frequently be employed.

The infinitely distant parts of centroids may under some cir- cumstances be even more troublesome than in the case we have