Fun with Excel and mathematics

I wrote this algorithm some years ago for a pure mechanical machine I've designed.  The objective was to convert the movement of the tip of an rotating arm into a square output trajectory, while the opposite end of the arm is attached to a rotating shaft.

In the video below, there is a cell named "Crank arm ratio" and when set to the value 3 the output graph forms a square.  Entering other values (in this demo from 0 to 20) shows interesting patterns developing.