Spirograph (rotation angle of the inner circle)

Description

Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.
A circle is rolling inside a fixed circle of longer radius and is continuously tangent to it. The angle by which the inner circle rotates (in the relative system of coordinates) is related to the circles’ radii and the angle by which a tangent point of the inner circle rotates on the outer circle. A counterclockwise motion corresponds to a positive change of angle and a clockwise one to a negative change of angle.

Related formulas

Variables

θiAngle by which inner circle rotates (radians)
RRadius of the larger fixed circle (m)
rRadius of the smaller inner circle (m)
θ0Angle by which the tangent point rotates on the fixed circle (radians)