nickpang — "There's no way the mobius strip answer would work. The belt would not rotate around leaving the twist in one spot between pulleys, but the tiwst would rotate with the belt and go over the pulleys"And you know this how? Gut feel?
Twisted belts were often used on old farm equipment, either for reversing direction, to reduce effects of wind whip, or to increase friction.I have seen this at antique farm equipment shows. Google tractor thresher twisted belt for some YouTube videos.
One fellow in Maine had a 6 hp gasoline engine attached by a flat belt to a table saw. (Apparently it was a short belt.) While applying belt dressing to the inside surface, a dangerous job, he wondered if he could turn the belt into a Mobius strip and apply belt dressing only to the upper surface. It is easy to do this by removing the belt lacing pin and giving the belt a half-turn before reinserting the pin…
Read his story here
Either that guy is lying, or the twist does not “walk around” even a short belt as you claim.