Effects of joint flexibility on the motion of a flexible-arm robot

Abstract

Once flexibility is introduced into the arm of the robot severe problems in the accuracy and stability are likely to occur which make control a critical issue. These problems could amplify drastically once the joint flexibility is also added to the system. A more successful control algorithm can be developed if the nonhnear dynamics associated with the flexible joint-arm is properly accounted for In this paper we study the behaviour of a three degree of freedom flexible joint-arm. Robot with quadratic and cubic nonlinearities. The symibolic manipulator language MAPLE is used to develop a simplified mathematical model of the system and to perform the analytical study. The two-variable expansion perturbation method is used to show the existence of various nonlinear resonances. If the system natural frequencies are defined as ω1,ω2 and ω$inf;2 internal resonance occurs when omega;2$einf; = 2ω 1ω3/(ω2 1 + ω2 3)½. Moreover, once subjected to harmonic forcing with frequency Ω a nonlinear forced resonance occurs at Ω ≈ ω2 the system undergoes a jump phenomenon Numerical simulation concurs with the analytical results for small motions. However, at higher amplitudes of forcing, numerical studies indicate the existence of a chaotic solution in the resonance region. The route to chaos contains subharmonic bifurcations