Fig. 75.
If the teeth of the wheel are straight and are set at an angle equal to the angle of the worm thread to its axis, as in [Fig. 75], p p representing the pitch line of the worm, c d the line of centres, and d the worm axis, the contact of tooth upon tooth will be at the centre only of the sides of the wheel teeth. It is generally preferred, however, to have the wheel teeth curved to envelop a part of the circumference of the worm, and thus increase the line of contact of tooth upon tooth, and thereby provide more ample wearing surface.
Fig. 76.
In this case the form of the teeth upon the worm wheel varies at every point in its length as the line of centres is departed from. Thus in [Fig. 76] is shown an end view of a worm and a worm gear in section, c d being the line of centres, and it will be readily perceived that the shape of the teeth if taken on the line e f, will differ from that on the line of centres c d; hence the form of the wheel teeth must, if contact is to occur along the full length of the tooth, be conformed to fit to the worm, which may be done by taking a series of section of the worm thread at varying distances from, and parallel to, the line of centres and joining the wheel teeth to the shape so obtained. But if the teeth of the wheel are to be cut to shape, then obviously a worm may be provided with teeth (by serrating it along its length) and mounted in position upon the wheel so as to cut the teeth of the wheel to shape as the worm rotates. The pitch line of the wheel teeth, whether they be straight and are disposed at an angle as in [Fig. 75], or curved as in [Fig. 76], is at a right angle to the line of centres c d, or in other words in the plane of g h, in [Fig. 76]. This is evident because the pitch line must be parallel to the wheel axis, being at an equal radius from that axis, and therefore having an equal velocity of rotation at every point in the length of the pitch line of the wheel tooth.
