Entrainment property analysis of Van der Pol oscillator driving a spring-mass system for large force generation by averaging method

Abstract

This paper presents a mathematical proof of the entrainment property of Van der Pol (VDP) oscillator driving a spring-mass system for large force generation. The entrainment property enables the mechanical system to generate a large force despite smaller amount of driving torques. Although it has been already confirmed by simulations using a manipulator model that a method with the VDP oscillator is effective in efficient large force generation, any mathematical proof that supports the simulation results has not been provided yet. In this paper, using an averaging method, which is a technique for nonlinear system analysis, we derive an approximated model of a spring-mass system driven by the VDP oscillator, and then prove the entrainment property of the VDP oscillator that realizes efficient large force generation based on the model.