Dynamics of noncontact rack-and-pinion device: Periodic back-and-forth motion of the rack

We study a nanoscale system composed of one corrugated cylinder (pinion) and one corrugated plate (rack). The pinion and rack have no mechanical contact, but are coupled via the lateral Casimir force. We consider the case where the rack position versus time is a periodic triangular signal. We find that the device can rectify the periodic but nonsinusoidal motion of the rack. Using the typical values of parameters, we find that the pinion rotates with an average angular velocity Omega = 1 similar to 100 Hz. Experimental observation of the pinion rotation will show that the quantum vacuum can intermesh the noncontact parts of nanomachines.