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

It's not related. The recent result states that you can pick any integer m > 1 and find a scaling factor λ for a given path such that after m repeats of that path you will return to the starting point (except for some infinitesimal number of paths that have a specific structure).

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.

Damn, that's beautiful. I hope that Mr. Adams mentiond in the article got a good return from his patent.

I see it, yet I can barely believe it.

Always happy to share! I came across this while planning a 3D scanning (photogrammetry) rig. Perhaps you'll be the one to figure out gravity can be modelled as a rotation around an axis in a fourth dimension, wrapping clingy spacetime around itself? ;) I'm not clever enough for that.

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.

And no axle to rotate on.

As meindnoch points out, the connection needs to loop over the rotating object. That is no problem if the only affect of the rotation that interests you is the centrifugal force.

When you give plasma (not whole blood) the nurses use a centrifuge machine that seems impossible: one tube goes from you to it (carrying whole blood), another tube goes from it back to you (carrying plasma depleted blood). The mechanism of Dale. A. Adams keeps the tubes from twisting. Search “antitwister mechanism patent” for a drawing of the mechanism. As for the principle behind the mechanism, see http://Antitwister.ariwatch.com for a PC program where you can adjust every variable imaginable.

Wouldn't a slip ring help here?

Huh, looking just at the link at the top of the box, and forgetting the remainder of the links, this cannot work. I tried it with a flat cable. If you rotate it like that, it becomes twisted.

I can't go into detail, but that's essentially my use case. I have a geodesic dome with a cable running up externally, and would like to run it through a hollow shaft coming in through the top which rotates like a carousel. I'm fairly certain this is precisely what I need.

There's some Youtube videos out there of people who have built practical versions that work, like this one (with flat cables, even): https://www.youtube.com/watch?v=1x_oQv_qj_U

Sure, but the animation of the wiki page is wrong. The cable that ends at the bottom of the picture is fixed there, while the other end twists. That will result in a twisted cable.

(update: I was wrong, not the wiki page)

I tried it and it works. The animation uses belts that are very flexible. With a real belt I needed to give it a shake to make it untwist itself, but it does work.

It is indeed easy to twist the belt until you have the hang of it.

I think the animation is a bit deceptive because even with elastic bands you'd have to provide some way for the correct untwisting to occur. In the animation it happens 'automagically'.

What a fascinating project. It looks a real labor of love, and I wish I understood it more deeply. I've been making my own visualization sandboxes like this to explore configuration spaces and groups - but for much simpler, more intuitive physical systems.

I went down a few rabbit holes on the site - is this program also written in Basic?

Yes, indeed, it can work, I can see it now. But I wonder if/how you can make it practical.

well, if you look at the animation, it surely seems to work, there is no place where it fakes the untwist. I can also replicate that with a belt, but not so smoothly. manually with the belt, the twist from 2 full rotations of the cube are undone by one rotation of the belt around the cube.

Yes, specifically the PowerBasic console compiler version 4 (later versions don’t do animation nearly as well). The PowerBasic compilers are no longer being sold and the company appears to be defunct. Anyway, you can do a lot with a good BASIC compiler.

The whole point of the anti-twister mechanism is that it doesn't use a slip ring.