A Perturbation Method for Dynamic Analysis and Simulation of Flexible Manipulators

This paper presents a perturbation method for the dynamic simulation of flexible manipulators. In this method the vibrational motion of the manipulator is modeled as a first-order perturbation of the nominal rigid link motion. For that purpose the flexible dynamic model is split into two parts. A rigidified system describes the nominal rigid link motion of the manipulator. A linear system linearized about the nominal trajectory describes the vibrational motion. These equations are computationally more efficient than the non-linear dynamic equations and offer more insight in the dynamic phenomena of the system. The method is based on a full non-linear finite element formulation which treats the general case of coupled large displacements motion and small elastic motion. A planar one link manipulator and a spatial two link manipulator with flexible links are used for case studies. A comparison is made between the non-linear and the perturbation analyzes. The perturbation method appears to be a very efficient approach for dynamic analyzes of flexible manipulators and yields accurate results even for systems with low frequency elastic modes.