The question is triggered by the wonderful animations by Jason Hise:

https://www.youtube.com/watch?v=LLw3BaliDUQ

https://www.youtube.com/watch?v=aYVt1UiERIQ

All these animations are based on the belt trick and suggest that a solid sphere that is glued into a soft mattress can rotate continuously, if the mattress performs certain appropriate motions around the sphere. Is this correct? Are there papers on this very counter-intuitive issue?