I saw a demo where a foam cube had a knitting needle inserted along the long diagonal, and was rotated by spinning the needle between the palms of the hands.
The sides of the cube formed a curve... in fact a portion of a hyperbola, as this video illustrates.
Archimedes trammel draws an ellipse if you fix the base and move the handle.
What happens if you fix the handle and move the base?
Drag point D to find out.
See the curve.