Effect of Joint Flexibilty on the Motion of Flexible Arm Robots


Singh, T., Golnarahi, M. F., & Dubey, R. N.


International Journal for Dynamics and Stability of Systems, 6(3), 235-254, 1991.


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.

   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}