Nonlinear modelling and dynamics of spatial multi-link rigid-flexible manipulator with moving platform

Abstract

The demand for developing lighter manipulators, particularly in various long-reach applications, has surged significantly. In many of these applications, inherent structural flexibilities are unavoidable and lead to vibrations. Consequently, these residual vibrations detrimentally affect working efficiency and positioning accuracy. The present work introduces a novel approach by formulating a nonlinear dynamical model of a spatial multi-link manipulator mounted on a mobile platform. This model incorporates both rigid and flexible links, as well as the payload, enabling a comprehensive study of end-point residual vibration characteristics. The dynamic modeling employed in this study accounts for the interplay of coupled geometric and inertial nonlinearities arising from motion interactions among joints, actuators, and elastic link deflections. The manipulator configuration comprises rigid components and two 3D-flexible links actuated by prismatic and revolute joints, respectively. The flexible links are modelled using Euler–Bernoulli beam elements, while time-dependent in-plane motion is imparted to the rigid link. Utilizing Hamilton’s variational principle, a set of nonlinear governing equations of motion is analytically derived. Subsequently, an independent generalized coordinates system is adopted to transform the equations of motion into a nonlinear reduced form. This is achieved through discretization of the spatio-temporal equations, facilitating the analysis of trajectory dynamics for the robotic manipulator. The residual vibration characteristics at the payload end were explored graphically by applying generalized sinusoidal and bang-bang torque profiles to their respective joints. Nonlinear structural flexibility and material properties emerge as pivotal factors influencing these residual end-point vibrations. It has been observed that the bang-bang torque profile extends the settling period in residual vibration due to its intricate transition characteristics, in contrast to the sinusoidal motion profile with a specific torque duty cycle. Numerical simulations highlight that variations in physical and geometric variables significantly impact end-point residual vibrations and joint deflections, potentially leading to positioning errors in the control of spatial flexible manipulators.