Free Vibrations of a Flexible Arm Attached to a Compliant Finite Hub

Abstract

A single-joint flexible robot arm consisting of one link and carrying an end effector is modeled by a continuous, uniform, clamped-free beam having a concentrated mass at the free end and being clamped at the other end to a compliant finite hub. The first six natural frequencies are given for various ratios of physical parameters. The modal shapes are also presented along with their orthogonality relationship. The limiting cases of some of the physical parameters are discussed.