3D dynamic modelling of a rigid manipulator mounted on a rectangular plate based on Hamilton principle

Abstract

This paper proposes a comprehensive model to predict the dynamical coupling behaviors of a rotating rigid manipulator mounted on a rectangular plate, which represents real applications such as on-orbit array installation of solar panels. The three-dimensional relationship of displacement field between the end-effector, with arbitrary installation position and azimuth, and the rectangular plate is first established based on spatial descriptions and transformations method. Galerkin’s method is employed and extended to treat the spatial partial derivatives. Then, the governing equation of motion is derived using the Hamilton principle. The dynamic behavior of the system with respect to torque input, the variation of structural parameters as well as installation position and azimuth of the manipulator, is analyzed by simulation, which may provide some principles to control the vibration amplitude of plate and oscillating value of end-effector. Simulation results show that the presented three-dimensional dynamic model is more proper and accurate to describe the dynamic behaviors of system through comparison with two conventional dynamic models, and especially the large structure parameter manipulator is mounted on a rectangular plate.