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Tip Trajectory Characteristics and Nonlinear Stability Analysis of Robotic Manipulator With Flexible Links-joints


 An efficient and new dynamic model of two-link flexible manipulator connected and controlled by flexible joints i.e., prismatic and revolute pairs has been developed to explore the modal analysis to study tip-trajectory characteristics and subsequently investigate the nonlinear steady-state responses under harmonic motion at flexible joints. The governing equations including joint dynamics have been derived using extended Hamilton’s principle. Modal parameters have been graphically presented to highlight the influences of various system parameters on the determination of eigenfrequencies and eigenspectrums. Obtained reduced order equations have then used to study the trajectory characteristics of tip displacements, angular and actuator positions by imparting the appropriate actuator force and joint torque. Further, nonlinear studies have been carried out to compute the steady state responses and their stability and local bifurcation by using 2nd order method of multiple scales. Investigation of the influences of various design parameters on the nonlinear stability and local bifurcation of steady state responses have been demonstrated and those results have been found to be in good agreement with numerically obtained findings. The obtained results find very useful in the applications of long-reach robot manipulators performing complex operations assigning with translating and rotary motion together.