Predicting bearing states in three dimensions

Bichromatic bearings have an in nite number of sliding-free states, so called bearing states. For three-dimensional bichromatic bearings whose bearing states have four degrees of freedom, we show how the bearing state can be analytically predicted from the initial state without any information about the nature of the contact forces. We provide a systematic way of constructing such bearings and also show how the bearing state is modi ed by blocking a single sphere and that any bearing state can be induced by controlling the angular velocities of only two spheres. Furthermore, we show that it is possible to determine the total mass and the center of mass of the bearing by analyzing its response to changes of the angular velocities of at most two spheres.

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