Fig. 234.
Fig. 235.
It is obvious that the points of the teeth and the bottoms of the spaces, as well as the pitch circle, are concentric to the axis of the wheel bore. And to pencil in the teeth these circles must be fully drawn, as in Figure 234, in which P P is the pitch circle. This circle is divided into as many equal divisions as the wheel is to have teeth, these divisions being denoted by the radial lines, A, B, C, etc. Where these divisions intersect the pitch circle are the centres from which all the teeth curves may be drawn. The compasses are set to a radius equal to the pitch, less one-half the thickness of the tooth, and from a centre, as R, two face curves, as F G, may be marked; from the next centre, as at S, the curves D E may be marked, and so on for all the faces; that is, the tooth curves lying between the outer circle X and the pitch circle P. For the flank curves, that is, the curve from P to Y, the compasses are set to a radius equal to the pitch; and from the sides of the teeth the flank curves are drawn. Thus from J, as a centre flank, K is drawn; from V, as a centre flank, H is drawn, and so on.
The proportions of the teeth for cast gears generally accepted in this country are those given by Professor Willis, as average practice, and are as follows:
| Depth to pitch line, | 3/10 | of the | pitch. |
| Working depth, | 6/10 | " | " |
| Whole depth, | 7/10 | " | " |
| Thickness of tooth, | 5/11 | " | " |
| Breadth of space, | 6/11 | " | " |
Instead, however, of calculating the dimensions these proportions give for any particular pitch, a diagram or scale may be made from which they may be taken for any pitch by a direct application of the compasses. A scale of this kind is given in Figure 235, in which the line A B is divided into inches and parts to represent the pitches; its total length representing the coarsest pitch within the capacity of the scale; and, the line B C (at a right-angle to A B) the whole depth of the tooth for the coarsest pitch, being 7/10 of the length of A B.