On the rectification of vibratory motion

This paper establishes a theoretical framework for analyzing and classifying actuators that generate their output by rectifying small-amplitude mechanical vibrations, such as might be generated by piezoelectric elements. These ideas are of special interest when designing for microfabrication, because motors based on these principles: (a) can generate translational output directly without use of rotary bearings; (b) appear to be scalable over several orders of magnitude of the length scale; and (c) appear to be capable of generating mechanical power proportional to driving frequency over one to two orders of magnitude of frequency. In order to achieve this performance, it is necessary to be able to farbricate features, or at least control surface irregularities, on the scale v/w where v is velocity of the actuator and w is the operating frequency.