Effect of Joint Flexibilty on the Motion of Flexible Arm Robots Authors Singh, T., Golnarahi, M. F., & Dubey, R. N. Source
International Journal for Dynamics and Stability of Systems,
Abstract Once flexibility is introduced into the arm of the robot, severe oroblems in the accuracy and stability are likely to occur which make control a crictical 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 nonlinear dynmaics 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 subic nonlinearities. The symbolic 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 existance of various nonlinear resonances. If the system natural frequencies are defined as omega_1, omega_2 and omega_3, internal resonance occurs when omega_2 = 2*omega_1*omega_2/(omega_1*omega_1+omega_2*omega_2). Moreover, once subjected to harmonic forcing with frequency Omega, a nonlinear forced resonance occurs at Omega = omega_2; the system undergoes a jump phenomenon. Numerical simulations 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. @article{Singh91_DSS, Author = {T. Singh, M. F. Golnaraghi and R. N. Dubey}, Journal = {International Journal for Dynamics and Stability of Systems}, Month = {}, Pages = {235-254}, Title = {Effects of Joint Flexibility on the Motion of a Flexible Arm Robot}, Volume = {6}, Number = {3}, Year = {1991} } |