Page:The Kinematics of Machinery.djvu/97

 Secondary centroids are of service to us also in many cases where it is possible, and even easy, to draw the primary curves, but where they would be inconveniently large; as for instance in the case of a pair of bodies which revolve in the same direction with a uniform angular velocity-ratio not equal to unity. Such bodies would have as centroids a pair of circles of which one would touch the other internally. Their secondary centroids would be circles whose diameters bear the same ratio to each other as those of the original curves,* by which means the position of the tangent

. 28.

He can be determined, as in Fig. 27. These centroids are also suitable for cases in which rotation with constant -velocity -ratio takes place in opposite directions, as in Fig. 28. In the various methods for drawing the forms of the teeth of spur-wheels, 10 these secondary centroids often play an important and acknowledged part. They have thus already made their way into practice, and enable us to reduce a much used practical method to general phoronomic principles.

The secondary circles being drawn, the point in which their tangent cuts the line of centres is always the point of contact of the primary centroids; and from this, conversely, the secondary circles can be drawn as circles touching anyline ik passing through it. It must be remembered that the point of contact of t'he centroids is always the instantaneous centre for the motion actually occurring.