Modeling and simulation of flexible robot manipulator with a prismatic joint

This correspondence investigates the modeling and simulation of a single link flexible robot arm (beam) having both rotational and translation motions, and the effects of higher-order dynamics on the response of the arm. The model is suitable for the development of control strategy to suppress the vibration of the arm. Assumed modes techniques have been reported in the literature where only two or three modes are retained and the rest are truncated which in many cases is inadequate for high performance control system development. In this study, an analytical model of the manipulator, characterized by an infinite number of modes, is developed using Euler-Bernoulli beam equation and modal expansion method. The infinite-dimensional transcendental transfer function for the robot arm is formulated without modal approximation that is conveniently transformed into state-space form. The effects of higher-order dynamics are demonstrated through computer simulations using National Instrument's LabVIEW software package. In this approach, adding modes or increasing the order of transfer function is straightforward and provides a straightforward check of the effect of ignoring higher-order terms. The results are illustrated for different modes through an example.