Dynamic analysis of vibration-driven systems moving based on frictional locomotion principles

In this article, we investigate the dynamic analysis of vibration-driven systems moving based on frictional locomotion principles. Symmetrically actuating particles with longitudinal harmonic forces or with longitudinal vibration of the base does not lead to the net motion, unless the generated slip varies during back and forth motion. Harmonically varying the normal contact force and employing asymmetric friction coefficients are two approaches for obtaining frictional locomotion principles. In order to study the simultaneous effect of these required conditions of generating net displacement, a mathematical model is developed, and the resulting non-linear equations of motion are analytically solved. We have shown that the proposed model can be simply generalized to many other frictional, vibration-induced principles, such as the friction drive and the directional friction concepts. The obtained results are in good agreement with those achieved from numerical integration and experiments, reported in the literature. The presented theoretical findings can be effectively used for the design and control of this type of oscillators.