Mathematicians have found a hidden 'reset button' for undoing rotation

I was immediately reminded of the anti-twist mechanism, perhaps unrelated but "reset rotation, twice/half" comes up there as well.

https://en.wikipedia.org/wiki/Anti-twister_mechanism

What?!

Thank you! I'm working on a robot with a very expensive slip ring, and need to send high fidelity data through it with shielding. I had no idea this was possible this will make things so much easier!

I found a related video you might find interesting.

https://www.youtube.com/watch?v=gZvimEf6DFw

I'm currently studying group theory and SO3 rotations (quaternions & matrix groups) and I'm also curious about the connection. I still have a lot to learn but I wouldn't be surprised if the reset rotation is unique, if we abstract away variation.

There's a bit of a caveat with the anti-twister mechanism, namely, that the wiring must be loose enough to pass around the supplied rotating part.

This is important. The mechanism doesn't really work the way you want most of the time. I occasionally see a claim that you can power a carousel with this method, but it doesn't work. You would have to have the cable go out and around the carousel structure, and then into the top. And the cable would still move relative to the ground and the carousel.

You could, in principle, have a totally internal system, but with arms that grab and release the cable at intervals so that the looped portion can pass by them. You could arrange the timing so that electrical contact is never lost. But you are still making/breaking contact and it starts to lose some apparent advantages compared to a slip ring.

That's not to say it isn't still useful for some purposes, like maybe a radio antenna that isn't too impacted by a cable moving in front on occasion. But it doesn't eliminate all uses for a slip ring.