| N1 —— N2 | = | D2 ——. D1 |
If there be considerable resistance to the motion of the follower slipping may take place, and it may stop. To prevent this the rollers may be provided with teeth; then they become spur wheels; and if the teeth be so shaped that the ratio of the speeds of the toothed rollers at any instant is the same as that of the smooth rollers, the surfaces of the latter are called the pitch surfaces of the former.
Pitch Circle.—A section of the pitch surface of a toothed wheel by a plane perpendicular to its axis is a circle, and is called a pitch circle. We may also say that the pitch circle is the edge of the pitch surface. The pitch circle is generally traced on the side of a toothed wheel, and is rather nearer the points of the teeth than the roots.
Pitch of Teeth.—The distance from the centre of one tooth to the centre of the next, or from the front of one to the front of the next, measured at the pitch circle, is called the pitch of the teeth. If D be the diameter of the pitch circle of a wheel, n the number of teeth, and p the pitch of the teeth, then D × 3·1416 = n × p.
Fig. 34.
By the diameter of a wheel is meant the diameter of its pitch circle.
Form and Proportions of Teeth.—The ordinary form of wheel teeth is shown in fig. 34. The curves of the teeth should be cycloidal curves, although they are generally drawn in as arcs of circles. It does not fall within the scope of this work to discuss the correct forms of wheel teeth. The student will find the theory of the teeth of wheels clearly and fully explained in Goodeve's 'Elements of Mechanism,' and in Unwin's 'Machine Design.'
The following proportions for the teeth of ordinary toothed wheels may be taken as representing average practice:—