Hypotrochoid

The discs of a Spirograph draw these curves: a wheel rolls inside a fixed ring, and a pen held in the wheel at some distance from its centre traces the hypotrochoid. With the pen on the rim it is a hypocycloid, and with the pen off the rim and a ring twice the size of the wheel, an ellipse.

x = (R - r) cos θ + d cos((R - r)θ/r), y = (R - r) sin θ - d sin((R - r)θ/r)

On mathcurve.com as Hypotrochoïde