3-Dimensional vibration analysis of multi-link flexible robot arms.

Abstract

This paper is concerned with a study of the 3-dimensional vibration analysis of multi-link flexible robot arms. The diformation of the arm is discussed on the basis of the Bernoulli-Euler beam theory. The 3-dimensional matrix equations are obtained for the beam element, the supported edge with elastic constraints, the free tip with payload, and the elbow composed of two joints connected together by a spring and a dashpot. The matrices are constructed by taking into acceunt the equilibriums of the displacements, the rotation angles, the bending and torsional moments, and the axial and lateral shear forces in the x^-, y^- and z^- directions. Numerical results are given for a two-Link flexible arm. It is shown that the vibration modes are separated into two groups, i.e., the in-plane modes and the out-of-plane vibration modes. In the in-plane mode both the in-plane bending deformation and the axial elongation are coupled, while in the out-of-plane mode the out-of-plane bending and the torsional deformations are coupled. This leads to the conclusion that the control of the out-of-plane vibration of two-link flexible arms can be discussed without referring to the effect of the in-plane vibration and vice versa.