Fig. 77.
If we multiply the number of teeth by their pitch to obtain the circumference of the pitch circle we shall obtain the circumference due to the radius of g h, from the wheel axis, and so long as g h is parallel to the wheel axis we shall by this means obtain the same diameter of pitch circle, so long as we measure it on a line parallel to the line of centres c d. The pitch of the worm is the same at whatever point in the tooth depth it may be measured, because the teeth curves are parallel one to the other, thus in [Fig. 77] the pitch measures are equal at m, n, or o.
Fig. 78.
But the action of the worm and wheel will nevertheless not be correct unless the pitch line from which the curves were rolled coincides with the pitch line of the wheel on the line of centres, for although, if the pitch lines do not so coincide, the worm will at each revolution move the pitch line of the wheel through a distance equal to the pitch of the worm, yet the motion of the wheel will not be uniform because, supposing the two pitch lines not to meet, the faces of the pinion teeth will act against those of the wheel, as shown in [Fig. 78], instead of against their flanks, and as the faces are not formed to work correctly together the motion will be irregular.
The diameter of the worm is usually made equal to four times the pitch of the teeth, and if the teeth are curved as in [figure 76] they are made to envelop not more than 30° of the worm.
The number of teeth in the wheel should not be less than thirty, a double worm being employed when a quicker ratio of wheel to worm motion is required.
