The Involute Curve
The virtual curve made the movement of a point of contact away from that point while the gears are in motion is a called an Involute Curve. An infinite number of curves can be developed to satisfy the law of gearing. Due to three advantages of involute curve, modern gearing (except for clock gears) is based on it.

• Conjugate action is independent of changes in center distance.
• The form of the basic rack tooth is straight-sided, and therefore is relatively simple and can be accurately made; as a generating tool it imparts high accuracy to the cut gear tooth.
• One cutter can generate all gear teeth numbers of the same pitch.

The development and action of mating teeth can be visualized by imagining the taut string as being unwound from one base circle and wound on to the other. Thus, a single point on the string simultaneously traces an involute on each base circle's rotating plane. This pair of involutes is conjugate, since at all points of contact the common normal is the common tangent which passes through a fixed point on the line-of-centers. If a second winding/unwinding taut string is wound around the base circles in the opposite direction, oppositely curved involutes are generated which can accommodate motion reversal. When the involute pairs are properly spaced, the result is the involute gear tooth.