Hypotrochoid
Instructions:
Move sliders \(d\) (point from a certain internal circle center distance), \(R\) (external circle radius) or \(r\) (internal circle radius) to change the hypotrochoid. 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.
$$ x \left(\theta\right)= \left(R - r\right)\cos \theta + d \cos \left(\frac{R - r}{r} \theta \right) $$
$$ y \left(\theta\right)= \left(R - r\right)\sin \theta - d \sin \left(\frac{R - r}{r} \theta \right) $$