Dynamic analysis of microrobots with Coulomb friction using harmonic balance method

In this paper, we investigate the dynamic analysis of a strongly nonlinear microrobot using a three-term harmonic balance method. The employed locomotion concept, namely “friction drive principle,” is based on the superposition of a horizontal vibration at the interface between the robot and work floor and an active variation of friction force, obtained by the vertical vibration of the base at the same interface. The equation of motion for the system reveals a parametrically excited oscillator with discontinuity for which the elastic force term is proportional to a signum function. The obtained periodic solution not only is of high accuracy, but also can predict the contribution of the friction coefficient in the average velocity of the slider. Results show that the velocity and the step efficiency of motion depend almost sinusoidally on the phase shift between the horizontal and the vertical vibration. Unlike traditional analytical techniques and in agreement with both numerical simulations and experimental results reported in the literature, the utilized method demonstrates that the maximum average velocity occurs at a phase shift that varies with respect to system’s configuration parameters. Besides, the effect of variation of different configuration parameters on the behavior of this type of microrobots has been studied and the maximum achievable performance in terms of velocity and the step efficiency has been evaluated.