When a shaft is driven by means of gearing the driving torque is measured by the product of the resultant pressure P acting between the wheel teeth and the radius of the pitch circle of the wheel fixed to the shaft.
The radius of the pitch-circle of a wheel is called the geometrical radius; a circle touching the ends of the teeth is called the addendum circle, and its radius the real radius; the difference between these radii, being the projection of the teeth beyond the pitch-surface, is called the addendum.
It also determines the forms of the teeth of straight racks, if one of the centres be removed, and a straight line EIE, parallel to the direction of motion of the rack, and perpendicular to CilCi, be substituted for a pitch-circle.
Consequently, one of the forms suitable for the teeth of wheels is the involute of a circle; and the obliquity of the action of such teeth is the angle whose cosine is the ratio of the radius of their base-circle to that of the pitch-circle of the wheel.
If the same rolling curve R, with the same tracing-point T, be rolled on the outside of any other pitch-circle, it will have the fare of a tooth suitable to work with the flank AT.
