Slide-glide cyclides

This design is made out of shapes called cyclides. In this mechanism the cyclides rotate against each other, opening out while staying in contact so that the overall shape transforms from a sphere to a disk. 

This design was discovered by Andrew Kepert when investigating ways to “see” why the area of a sphere is four times the area of a disk of the same radius. I added the gears and the base.

The cyclides (eight of them) are printed in two parts that are superglued together (with little pegs to slot in for alignment). This minimizes the amount of overhang when printing, but the print will still need support around the gear teeth. (I also uploaded a version which is not cut into two parts, in case you are printing with some other technology.)

There are three other parts - two base parts and one crown gear part. The frame base only needs support for the main central bridge, while the crown gear base only needs it for the channels where the nuts sit. The crown gear shouldn't need any support.

The design is put together with M3 nuts and bolts. It uses four 30mm M3 bolts to attach the crown gear onto its base, and eight 25mm (or maybe slightly longer would work better) M3 bolts as axles for the cyclides through the frame base. 

I also included step files for easier remixing.

Mathologer video:

Andrew Kepert's playlist on lunes and cyclides: https://www.youtube.com/playlist?list=PL9JP5WCX_XJY9GmMO-kotRR5bRYOPOtn9