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

Abstract

The demand of developing lighter manipulators especially in various long-reach applications has been immensely escalated and in most of these applications, the presence of inherent structural flexibilities is more inevitable that causes vibration. As a result, this undesirable residual vibration reduces the working efficiency and positioning accuracy. For the first time, the present work formulates a nonlinear dynamical model of a spatial multi-link manipulator mounted on a mobile platform incorporating rigid and flexible links, and payload to study the end-point residual vibration characteristics. The dynamic modelling takes into account of coupled geometric and inertial nonlinearities due to impinging motion quality between joints, actuators, and elastic link deflections. The manipulator consists of rigid and two threedimensional flexible links driven by prismatic joint and revolute joints, respectively. The flexible links assume the Euler-Bernoulli beam elements and time-dependent in-plane motion is provided to the rigid link. Sets of nonlinear governing equations of motion have been developed analytically using Hamilton's variational principle. An independent generalized coordinates system is then used to obtain a nonlinear reduced form by discretizing the spatiotemporal equations of motion and study the trajectory dynamics of the robotic manipulator. The residual vibration characteristics at the payload end have been graphically investigated by imparting generalized sinusoidal and bang-bang torque profiles at respective joints. Nonlinear structural flexibility and material's class can play key factors that influence the residual end-point vibration. It is proven that Bang-Bang torque profile widens the settling period in residual vibration due to its complex transition characteristics as compared to sinusoidal motion profile for a specific torque duty cycle. The numerical simulations demonstrate that the end-point residual vibrations and joint deflections are significantly influenced by the changes in physical and geometric variables which may lead to positioning errors and control of spatial flexible manipulators.