Modal characterization with nonlinear behaviors of a two-link flexible manipulator

TLDR: An appropriate and realistic dynamic modeling of the two-link manipulator taking into account of inertia coupling and geometry compatibility between equations of motion and boundary conditions has been derived using the extended Hamilton’s principle.

Abstract: This present work has made a noteworthy attempt to demonstrate brief modeling of N-link manipulator and subsequent modal characterization along with the determination of static deflection of a two-link flexible manipulator with a payload. In addition, investigation of nonlinear phenomena of dynamic responses under 3:1 internal resonance has also been accomplished considering geometric nonlinearities. An appropriate and realistic dynamic modeling of the two-link manipulator taking into account of inertia coupling and geometry compatibility between equations of motion and boundary conditions has been derived using the extended Hamilton’s principle. The effect of parametric variation on system eigenfrequencies is well tabulated, and the corresponding eigenspectrums are illustrated graphically. Further, the nonlinear phenomena of dynamic solutions have been demonstrated by using MMS of second order for its statutory effect onto the system instability for the existence of S-N bifurcations. The effect of nonlinearities and various design parameters on the dynamic responses and subsequent bifurcations for 3:1 internal resonance has also been demonstrated. The outcome of the present work enables new understanding into the design criterion and performance limitation of multi-link flexible robots.