Epicycloid (The ordinate of a point)

Description

In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle — called an epicycle — which rolls without slipping around a fixed circle. It is a particular kind of roulette.
The ordinate of a moving point is given in relation to the radii of the two unequal circles, the radian from the tangential point to the moving point and the radian from the starting point to the tangential point.

Related formulas

Variables

yY-Coordinate of the point (ordinate) (dimensionless)
RRadius of the larger circle (dimensionless)
rRadius of the smaller circle (dimensionless)
θTthe radian from the starting point to the tangential point. (dimensionless)
aThe radian from the tangential point to the moving point (dimensionless)