https://archive.is/08ig5
Thank you!
Mathematicians have found a hidden 'reset button' for undoing rotation
91–100 of 125 posts
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#92Earlier quoted context omitted.
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 co…
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.
Wouldn't a slip ring help here?
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#93I don't entirely understand why they're framing rotations as so complex, outside of a play on words that I don't think they're making. Most rotations just use quaternions which are relatively simple. Their example of robotics uses quaternions and getting the inverse of any rotation is trivial - you literally just flip the signs of the 3 imaginary components of quaternions. For non-unit quaternions, you just then just renormalize the result (divide by the sum of the squares of the components).
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#94I 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
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.
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#95Earlier quoted context omitted.
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…
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.
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#96The final paragraph: The work could also lead to advances in robotics, says Josie Hughes at the Federal Polytechnic School of Lausanne in Switzerland. For example, a rolling robot could be made to follow a path of repeating segments, comprising a reliable roll-reset-roll motion that could, in theory, go on forever. “Imagine if we had a robot that could morph between any solid body shape, it could then follow any desired path simply through morphing of shape,” she says.
Interestingly, that didn't come from the PR department. Hughes is a tenure-track professor whose lab builds unusual flexible robots. They're trying to use LLMs to design special-purpose grippers.[1] That's an interesting idea. Most of the cost in industrial robots is special-purpose end effector tooling. Something that could bang out a design, given "we want to put this thing in there", would be very useful.
Here are some examples of end of arm tooling.[2] Auto plants are full of this stuff, and it's all custom. An automated design system for designing all those one-off items would really speed up retooling assembly lines for a new product. Much of the research in robots involves trying to make more human-like grippers. That may be approaching the problem from the wrong end. Cheap custom tooling designed by AIs and maybe 3D printed may be the way to go.
That an LLM can do something like that is a surprise, but apparently there's been progress.
There's a YC-sized startup opportunity in this.
[1] https://www.epfl.ch/labs/create/
[2] https://eoat.net/tooling/?device=c&keyword=End Of Arm Tooling Grippers
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#97I 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
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.
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
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#98Earlier quoted context omitted.
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.
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)
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#99A series of rotations – a discrete walk (or continuous path) in the manifold of the rotation group SO(3) or SU(2) – can of course be inverted (starting from the end, find a walk that returns to the beginning) by performing the steps in reverse. Eckmann et alshow that, for almost all walks, there is another way: starting at the end, perform the steps in the original order (1) twice, and (2) uniformly scaled by a facto…
The article is here. https://arxiv.org/abs/2502.14367 Sorry, but the existence of such an inversion still is interesting from a mathematical perspective. It isn't "of much use" practically without the inversion formula/calculation, but that's ok. "There exists" is still a fascinating fact.
Completely agree. Beyond being of interest in its own right, "There exists" is a prerequisite for further work in finding a practical approach to find the path.
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#100Earlier quoted context omitted.
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'.