Dynamic Modeling and Optimization Analysis of Rigid-Flexible Coupling Manipulator Based on Assumed Mode Method

Lightweight robotic arms are one of the main technologies to improve the working performance of robotic arms in the future. Focusing on the spatial vibrations issue brought about by the light-weighting of a space robotic arm in this paper, a rigid-flexible coupling dynamics model of a space robotic arm system was established based on the assumed mode method and Lagrange method. Based on the lightweight flexible robotic arm structure, a comparative analysis of the first four mode functions was conducted under different fixed constraints and physical properties to determine the mode order that matches the simulation analysis of this robotic arm, thus, further simplifying the rigid-flexible coupling dynamics equations of the system. The overall rigid model and simplified dynamic model of the robotic arm system were solved by using MATLAB, resulting in a motion trajectory of the flexible arm end in space. The three-dimensional model was validated and simulated using virtual prototype technology under the same joint inputs as the model in MATLAB. The simulation results demonstrated that the trajectory of the end of the flexible arm was basically the same between simplified dynamics model simulation and virtual prototype simulation, and the maximum deviation of the end trajectories of the flexible connecting rods L1 and L2 was less than 18mm and 58mm, respectively. Meanwhile, the trajectory trend of the end of the flexible arm in the two aforementioned models was the same as the simulation results of the ideal model (overall rigid model). The above conclusions can verify the correctness of the mathematical model of dynamics obtained from the calculations in this paper. In addition, the research data showed that the maximum vibration deviation of the flexible arm was stabilized within a certain value range under different joint inputs, and this research also provided theoretical support for the late vibration suppression control of the spatial rigid-flexible coupled robotic arm.