Fig. 60.
In [Fig. 60] let a a represent the axis of one shaft, and b the axis of the other, the axes of the two meeting at w. Mark e, representing the diameter of one wheel, and f that of the other (both lines representing the pitch circles of the respective wheels). Draw the line g g passing through the point w, and the point t, where the pitch circles e, f meet, and g g will be the line of contact between the cones. From w as a centre, draw on each side of g g dotted lines as p, representing the height of the teeth above and below the pitch line g g. At a right angle to g g mark the line j k, and from the junction of this line with axis b (as at q) as a centre, mark the arc a, which will represent the pitch circle for the large diameter of pinion d; mark also the arc b for the addendum and c for the roots of the teeth, so that from b to c will represent the height of the tooth at that end.
Similarly from p, as a centre, mark (for the large diameter of wheel c,) the pitch circle g, root circle h, and addendum i. On these arcs mark the curves in the same manner as for spur-wheels. To obtain these arcs for the small diameters of the wheels, draw m m parallel to j k. Set the compasses to the radius r l, and from p, as a centre, draw the pitch circle k. To obtain the depth for the tooth, draw the dotted line p, meeting the circle h, and the point w. A similar line from circle i to w will show the height of the addendum, or extreme diameter; and mark the tooth curves on k, l, m, in the same manner as for a spur-wheel.
Similarly for the pitch circle of the small end of the pinion teeth, set the compasses to the radius s l, and from q as a centre, mark the pitch circle d, outside of d mark e for the height of the addendum and inside of d mark f for the roots of the teeth at that end. The distance between the dotted lines (as p) represents the full height of the teeth, hence h meets line p, being the root of tooth for the large wheel, and to give clearance, the point of the pinion teeth is marked below, thus arc b does not meet h or p. Having obtained these arcs the curves are rolled as for a spur-wheel.
A tooth thus marked out is shown at x, and from its curves between b c, a template for the large diameter of the pinion tooth may be made, while from the tooth curves between the arcs e f, a template for the smallest tooth diameter of the pinion can be made.
Similarly for the wheel c the outer end curves are marked on the lines g, h, i, and those for the inner end on the lines k, l, m.
Fig. 61.