Interesting. But I think the clearest mechanical realization of a 3-torus would be three independently rotating rods. The configuration space is then all ordered triples of angles, which is immediately S^1 x S^1 x S^1 = T^3. This still leaves a wide variety of possibilities for how this could be realized in the plane or 3-space. One possibility is to connect the ends of the rods by elastic bands of 3 different colors, so that the configuration space is displayed as all the resulting triangles. The rods could be set to mechanically rotate at three linearly independent speeds, so that the 3 angles trace out a curve in T^3 that's eventually arbitrarily close to every point of it. (There are many ways to do this so the elastic bands don't get tangled up.) --Dan Jim wrote: << Note that one could describe this linkage simply as a mechanical realization of a 3-torus (hence the title of this post).

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_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele