Internal gears must frequently be used when there is not room for spur gears or when the nature of the work or the design of the machine of which they are a part renders this form necessary or advisable. Thus far we have considered gears represented by cylinders whose outer surfaces rolled together. In the case of the internal gear the outer surface of a smaller cylinder is supposed to roll on the internal surface of a larger cylinder. Therefore, the larger gear will have teeth projecting inwardly or toward its axis. Theoretically the proper curve for the teeth of an internal gear will be the internal epicycloid, as this is the curve traced by a point on the surface of one cylinder rolling inside of another cylinder. The method of laying out the teeth is shown in Fig. 267. The pitch circle A, addendum circle D, and dedendum circle E are drawn as in the previous examples, the vertical line BC indicating the center of the work. The pitch is spaced off on the pitch circle A, each way from the line BC, and the thickness of the teeth and width of the spaces indicated. At the point of intersection of the vertical line BC with the pitch circle A, is drawn an inclined line FF at an angle of 78 degrees to the vertical line BC. Through the point of intersection a of this line with the center line 4 of the adjacent tooth, the base circle H is drawn, giving the location of the centers for the faces of the teeth, which are described by the arc of the radius ah.

Fig. 269. Accurate Method of Laying Out Teeth of Rack

Fig. 268. First Method of Laying Out Teeth of Rack

In a similar manner the line GG is drawn at an angle of 87 degrees with the vertical line BC; and through the point of intersection c with the radial line 4, the base circle J is drawn, which gives the location of the centers for the flanks of the teeth, which are described by the arc of the radius cd. The arc joining the flank curve with the dedendum circle is the same as in previous examples.