First by rolling the true curves with segments as already described, and the setting the compass points (by trial) to that radius which gives an arc nearest approaching the true curves. In this operation it is not found that the location for the centre from which the curve must be struck always falls on the pitch circle, and since that location will for every tooth curve lie at the same radius from the wheel centre it is obvious that after the proper location for one of the curves, as for the first tooth face or tooth flank as the case may be, is found, a circle may be struck denoting the radius of the location for all the teeth. In [Fig. 129], for example, p p represents the pitch circle, a b the radius that will produce an arc nearest approaching the true curve produced by rolling segments, and a the location of the centre from which the face arc b should be struck. The point a being found by trial with the compasses applied to the curve b, the circle a c may be struck, and the location for the centres from which the face arcs of each tooth must be struck will also fall on this circle, and all that is necessary is to rest one point of the compasses on the side of the tooth as, say at e, and mark on the second circle a c the point c, which is the location wherefrom to mark the face arc d.
Fig. 130.
If the teeth flanks are not radial, the locations of the centre wherefrom to strike the flank curves are found in like manner by trial of the compasses with the true curves, and a third circle, as i in [Fig. 130], is struck to intersect the first point found, as at g in the figure. Thus there will be upon the wheel face three circles, p p the pitch circle, j j wherefrom to mark the face curves, and i wherefrom to mark the flank curves.
Fig. 131.
When this method is pursued a little time may be saved, when dividing off the wheel, by dividing it into as many divisions as there are teeth in the wheel, and then find the locations for the curves as in [Fig. 131], in which 1, 2, 3 are points of divisions on the pitch circle p p, while a, b, struck from point 2, are centres wherefrom to strike the arcs e, f; c, d, struck also from point 2 are centres wherefrom to strike the flank curves g, h.
It will be noted that all the points serving as centres for the face curves, in [Fig. 130], fall within a space; hence if the teeth were rudely cast in the wheel, and were to be subsequently cut or trimmed to the lines, some provision would have to be made to receive the compass points.