Involutes

Involutes :

It is the curve traced out by a point on a cord as it unwinds (but remains taut) around a circle or polygon

Alternatively an involute may be defined as the curve traced out by a point on a straight line which rolls around a circle or polygon without slip. Depending upon plane shape around which the line rolls, the involutes are named as involute of a triangle, involute of a square, involute of a polygon, involute of a circle etc.

The most common application of involute is seen in the manufacture of gears. The profile of a gear tooth is the shape of involute.