An annular gear is a ring with teeth on the inside of it. Fig. 115 shows such a gear, with center at A, meshing with its pinion. The method of drawing such a pair of gears is similar to that just described for two spur gears. Here the circle C, by rolling on the inside of the pitch circle of A, generates the faces of the teeth on A; and the circle D, by rolling on the outside of the pitch circle of A, generates the flanks of the teeth on A. The shape of the teeth of the pinion in the figure is found with the same describing circles placed at C' and D' to avoid confusing the lines.
Fig. 116. Construction for Epicycloidal Rack and Pinion.
In designing an annular gear and pinion, the diameter of the gear must never be so small that the distance from center A to center B shall be less than the sum of the radii of the two describing circles. If this should be the case, the teeth would interfere with each other.