I was just watching a YouTube video by James Bruton of xrobots.tech on spherical wheels composed of independently rotating hemispheres in order to be able to roll in one direction controlled by a drive axle and a second direction freely; he built a vehicle with three such wheels that could move in any direction. In the center of each hemisphere he included an additional wheel, copied from a design at Osaka University. And it occurred to me: what about a toroidal wheel to be able to do the same trick?
Not such a novel idea, I guess, with the diagonal rollers. But what if the rollers around the edge of the wheel simply rotate perpendicular to the torus’s axis? The torus can be driven on that axis and consist of four or more rollers around the outside whose axes of rotation form a regular polygon. Perhaps if there are many of them they can even overlap one another. Bruton’s spheres contain sort of a degenerate version of this: the torus has been stripped of all but two rollers, and the rest of the torus is covered with the hemispheres.