When the machine is in operation, a heavy weight, seen in [Fig. 98] ([Plate I.]), acts to move c about the pivot d, being attached to the carrier by a cord guided by suitably arranged pulleys; this keeps the cutter m up to its work, while the spindle l is independently driven, and the duty left for the worm g to perform is merely that of controlling the motions of the cutter by the means above described, and regulating their speed.

The centre line of the cutter is thus automatically compelled to travel in the path r s, [Fig. 105], composed of an epicycloid and a hypocycloid if a a be the segment of a circle as here shown; or of two cycloids, if a a be a straight bar. The radius of the cutter being constant, the edge of the template t is cut to an outline also composed of two curves; since the radius m is small, this outline closely resembles r s, but particular attention is called to the fact that it is not identical with it, nor yet composed of truly epicycloidal curves of any generation whatever: the result of which will be subsequently explained.

Number and Sizes of Templates.

With a given pitch every additional tooth increases the diameter of the wheel, and changes the form of the epicycloid; so that it would appear necessary to have as many different cutters, as there are wheels to be made, of any one pitch.

But the proportional increment, and the actual change of form, due to the addition of one tooth, becomes less as the wheel becomes larger; and the alteration in the outline soon becomes imperceptible. Going still farther, we can presently add more teeth without producing a sensible variation in the contour. That is to say, several wheels can be cut with the same cutter, without introducing a perceptible error. It is obvious that this variation in the form is least near the pitch circle, which is the only part of the epicycloid made use of; and Prof. Willis many years ago deduced theoretically, what has since been abundantly proved by practice, that instead of an infinite number of cutters, 24 are sufficient of one pitch, for making all wheels, from one with 12 teeth up to a rack.

Accordingly, in using the epicycloidal milling engine, for forming the template, segments of pitch circles are provided of the following diameters (in inches):

12,16,20,27,43,100,
13,17,21,30,50,150,
14,18,23,34,60,300.
15,19,25,38,75,

Fig. 106.