Casimir rack and pinion: Mechanical rectification of periodic multi-harmonic signals

We study noncontact rack and pinion composed of a corrugated plate and a corrugated cylinder intermeshed via the lateral Casimir force. We assume that the rack position versus time is a periodic multi-harmonic signal. We show that in a large domain of parameter space and at room temperature, the device acts as a mechanical rectifier: The pinion rotates with a nonzero average velocity and lifts up an external load. The thermal noise may even facilitate the device operation.