Nonlinear modeling and vibration analysis of a two-link flexible manipulator coupled with harmonically driven flexible joints

The present paper deals with the theoretical studies to determine the modal parameters and investigate the dynamic instability of a harmonically driven planar two-link manipulator with flexible joints. An appropriate dynamic model incorporating both link and joint flexibilities subjected to a harmonic motion has been developed while joint flexibility has been modeled as a combination of torsional spring-inertia elements. Modal parameters for various modes of vibration have been evaluated and graphically demonstrated. Then, method of multiple scales has been employed to further analyze the vibration attributes of steady state responses and their stability under resonance condition. The comparative mode shapes and bifurcation diagrams those describe the vibrating system have been illustrated to demonstrate the dynamics of the flexible manipulator. The effect of geometric and inertial coupling existing between the flexible arms on bifurcation states and stability of the obtained solutions has been thoroughly investigated. Analytically obtained results have been verified numerically and found to be in good agreement. The present theoretical results deliver a useful insight into the attributes of vibration characteristics along with the nonlinear dynamic behavior and operational stability of two-link flexible manipulator under joint motion.