Involute of a circle

The path of the end of a taut thread unwound from a circle, so that every normal to the curve touches the circle. Its turns are evenly spaced. Most gear teeth are cut to it, since two such teeth press on each other along one fixed line.

x = r(cos(t + a) + t sin(t + a)), y = r(sin(t + a) - t cos(t + a))

On mathcurve.com as Développante de cercle