Fig. 88.
Fig. 89.
Involute teeth.—These are teeth having their whole operative surfaces formed of one continuous involute curve. The diameter of the generating circle being supposed as infinite, then a portion of its circumference may be represented by a straight line, such as a in [Fig. 88], and if this straight line be made to roll upon the circumference of a circle, as shown, then the curve traced will be involute p. In practice, a piece of flat spring steel, such as a piece of clock spring, is used for tracing involutes. It may be of any length, but at one end it should be filed so as to leave a scribing point that will come close to the base circle or line, and have a short handle, as shown in [Fig. 89], in which s represents the piece of spring, having the point p′, and the handle h. The operation is, to make a template for the base circle, rest this template on drawing paper and mark a circle round its edge to represent on the paper the pitch circle, and to then bend the spring around the circle b, holding the point p′ in contact with the drawing paper, securing the other end of the piece of steel, so that it cannot slip upon b, and allowing the steel to unwind from the cylinder or circle b. The point p′ will mark the involute curve p. Another way to mark an involute is to use a piece of twine in place of the spring and a pencil instead of the tracing point; but this is not so accurate, unless, indeed, a piece of wood be laid on the drawing-board and the pencil held firmly against it, so as to steady the pencil point and prevent the variation in the curve that would arise from variation in the vertical position of the pencil.
The flanks being composed of the same curve as the faces of the teeth, it is obvious that the circle from which the tracing point starts, or around which the straight line rolls, must be of less diameter than the pitch circle, or the teeth would have no flanks.
A circle of less diameter than the pitch circle of the wheel is, therefore, introduced, wherefrom to produce the involute curves forming the full side of the tooth.