On the flexural vibrations of elastic manipulators with prismatic joints

Abstract The aim of this paper is to investigate the flexural vibrations of an axially moving robotic arm sliding through a prismatic joint while the joint is undergoing both vertical translation and rotary motion. Considering not only Euler-Bernoulli beam assumption but also the effects of gravitation, rotary inertia and axial force, the equations of motion and associated boundary conditions of the dynamic model are derived by using the extended Hamilton's principle. Since they form a complex boundary value problem which cannot be solved analytically, the assumed modes method is utilized to obtain an approximate solution. Simulation results are presented for some typical kinematical inputs.