My proposal was for a kinetic sculpture/s that were driven from a single point. Each would be a basic shape with a track hidden on the rear. A wall-mounted motor would drive the shape along the track without rotating it.
The idea started with the square. But it turns out that that’s a difficult problem. So I broke it down into trying to just drive a square piece along a square track.
Also a difficult problem.
While prototyping I figured that a rod fixed at one end, rotating at the same rate as the small square in the track would (depending on the length of the drive-arm) describe a clover-like shape.
After talking to some more mathematically inclined friends I got my hands on a processing sketch that helped describe the shape. As the rod rotates, the small ellipse will draw the clover onto the moving square.
This is that shape.
I wasn’t able to determine an exact equation for the measurements of the shape, so I guesstimated how far the free end of the drive needs to move. That gave me enough movement to test. But it became very clear very quickly that the measurements of all of the pieces needed to be way more exact than I was able to cut for this to work.