Sphere-based drive trains

During a recent idle moment, I started thinking about spherical wheels, spherical gears (I think that one might want to use 3 spheres in order to transmit rotational motion from one sphere to another, as opposed to 1 conventional gear for the same purpose) and (most interestingly) omni-directional electromagnetic motors with spherical (rather than cylindrical) shafts.

Here is (roughly) how the motor would work :

 Make the "shaft" a sphere (d'uh) and cover the surface with a pseudo-random pattern of permanent magnets.

 Put the sphere-shaft in spherical bearings, and surround it with a regular pattern of controllable electromagnets.

 At every time-step, solve for the set of magnetic fluxes (or electric currents) on the pattern of electromagnets to best apply the appropriate delta rotation to the shaft. Or, simpler yet, render (draw) the pseudo-random pattern of magnets on the shaft, rotated by the desired amount, using the controllable electromagnets.

Presumably some clever electrical engineering could measure and/or estimate the orientation of the spherical-shaft by the induced current on the outer electromagnet coils (at least while the shaft is moving). Or, hey, one could just draw a recognizable pattern on the sphere-shaft and use light sensors/emitters to estimate shaft orientation.

SIAM paper

I had forgotten to post this earlier...
Distributed Tree Rearrangements for Reachability and Robust Connectivity
published in : SIAM Journal on Control and Optimization