  The quantum mechanics of a simple mechanical system is considered. A group of
gears can serve as a model for several different systems such as an artifically
constructed nanomechanical device or a group of ring molecules. It is shown
that the classical motion of the gears in which the angular velocities are
locked together does not correspond to a solution of the quantum problem. The
general solution for several gears is discussed and the correspondence to the
classical behaviour established.
