Epitrochoid
Instructions:
Move sliders \(d\) (point from a certain external circle center distance), \(R\) (internal circle radius) or \(r\) (external circle radius) to change the epitrochoid. Press the "Start" button to watch the animation, this will move the \(t\) (time) slider. Press the "Stop" button to interrupt the animation and press the "Reset" button to reboot the starting values.
$$ x \left(\theta\right) = \left(R + r\right)\cos \theta - d \cos \left(\frac{R + r}{r} \theta \right) $$
$$ y \left(\theta\right) = \left(R + r\right)\sin \theta - d \sin \left(\frac{R + r}{r} \theta \right) $$