Dynamics of Elastic Manipulators With Prismatic Joints

Abstract

The purpose of this investigation is to study the formulation of equations of motion for flexible robots containing translationally moving elastic members that traverse a finite number of distinct support points. The specific system investigated is a two-degree-of-freedom manipulator whose configuration is similar to that of the Stanford Arm and whose translational member is regarded as an elastic beam. Equations of motion are formulated by treating the beam’s supports as kinematical constraints imposed on an unrestrained beam, by discretizing the beam by means of the assumed modes technique, and by applying an alternative form of Kane’s method which is particularly well suited for systems subject to constraints. The resulting equations are programmed and are used to simulate the system’s response when it performs tracking maneuvers. The results provide insights into some of the issues and problems involved in the dynamics and control of manipulators containing highly elastic members connected by prismatic joints.