Robotic system with viscoelastic element modeled via fractional Zener model

Abstract

In this communication, we propose a four-parameter fractional derivative Zener model for modeling of a viscoelastic element connected into a robotic system. We used force-displacement relation in order to obtain generalized forces of the element connected to two different bodies in the system. Generalized forces of the element are derived using the principle of virtual work. In order to obtain numerical results, we suggested a robotic system with three degrees of freedom. Behavior of generalized forces is examined for changes of fractional order parameter and relaxation time.