Modeling of a rigid-flexible manipulator using Hamilton’s principle

Abstract

This paper presents a mathematical model of a two-link rigid-flexible manipulator, derived by Hamilton’s principle. The paper shows how the dynamic equations of motion can be simplified and converted to a form suitable for time-step integration. The equation describing deflection of the flexible end-link is discretized using the assumed modes method and a finite number of low frequency modes retained in the conversion to state-space form. A set of simulation results showing behavior of the model is presented. With the inclusion of a simple damping model, the simulation model gives physically realistic motion behavior and is therefore considered suitable for predicting vibration behavior of a rigid-flexible manipulator and as a tool for designing and testing controllers for reduction of flexible link vibration.