Research On Stiffness And Vibration Control Of A Kinematically Redundancy Planar Parallel Mechanism

With the wide application of robot technology,the adaptability of robot to complex working environment has attracted more and more attention.The research background of this subject is the special equipment in the wind tunnel.The shaping mechanism contains flexible parts,and in the flow field environment with complex loads.In order to ensure the shaping accuracy and stability,a kinematically redundant parallel mechanism is proposed for the driving part of the planar parallel mechanism,and the research on kinematics,spatial stiffness,stiffness modulation and vibration suppression theory is carried out.The main research contents are as follows:To avoid singularity configuration,a joint trajectory planning method based on speed and position levels is proposed,considering the accuracy of end-effector position and the smoothness of joint trajectory.First,according to the geometric constraints of the 3-PRPR mechanism,the Jacobian matrix is obtained by establishing the vector equation.Then,the effect of the number of actuators on the non-singular workspace is explored,and the singularity function is established by geometry.Finally,the results obtained by the proposed method are compared with those obtained by the traditional method.The results show that the proposed method can guarantee the accuracy of the end-effector position,and the minimum singular value is improved compared with the traditional method in general.The mechanism is subjected to spatial six dimensional forces,the spatial stiffness of the mechanism is analyzed and calculated,and a stiffness index is proposed.First,the overall Jacobian matrices of the two non-redundant branch PRR and RPR are established by screw theory,the components stiffness are calculated from the active/constraint directions,and the subspace stiffness distribution under a desired trajectory is obtained by using the virtual work principle and overall Jacobian matrix.Second,the stiffness distributions in each direction and the proposed indexes for the two non-redundant mechanisms are compared,the results show that the 3-RPR mechanism has better stiffness performance,the active stiffness of the 3-PRR mechanism is more affected by the constraint stiffness.Finally,the stiffness distribution and stiffness coupling index of the 3-PRPR mechanism are calculated based on the instantaneous screw of 3-PRR mechanism and deformation transformation,which will provide a theoretical basis for subsequent optimization and design of the mechanism.Aiming at the requirement of a constant stiffness when the mobile platform moves along a desired trajectory,this paper employ the deep reinforcement learning approach to plan the joint trajectory of a kinematically redundant parallel mechanism for the first time.First,the converging direction stiffness was defined according to the virtual work principle and the minimum perturbation method.Then,considering the end-effector pose accuracy and desired stiffness,a continuous action space learning framework is designed based on TD3 algorithm,and the position level joint trajectory planning is completed Finally,the simulation results show that,compared with conventional algorithms,the stiffness obtained by deep reinforcement learning is closer to the desired stiffness,and the accuracy of end-effector pose can be guaranteed.To reduce the vibration of the mechanism,the response amplitude is reduced by joint trajectory planning based on two dynamic models and the excitation frequency.First,according to a simplified dynamical model and an external excitation signal,a joint trajectory planning method that modulate the natural frequencies of the mechanism is proposed.Second,by comparing the frequency response with that obtained from the trajectories without suppression,the results indicate that the proposed method can reduce the response amplitude.Then,to make the model closer to the real working condition,based on the elastic dynamics model and the complete excitation frequency signal,a vibration suppression strategy is designed based on deep reinforcement learning.Finally,by comparing with the frequency response obtained from the trajectories with the suppression effect,the results show that the proposed strategy can reduce the vibration to a certain extent.The experiment platform has set up,and the theoretical stiffness model and elastic dynamic model are verified through the stiffness experiment and free vibration experiment.To reduce the effects of parameters such as joint clearance,machining and assembly,stiffness experiments are accomplished by using spring stiffness as component equivalent stiffness,and the results show that the experiments are generally consistent with the theoretical stiffness.The elastic dynamic model validation was completed by the natural frequencies obtained from free vibration experiments,and the experimental results show that the first and second order natural frequency are consistent with theoretical results,which proved the correctness of the theoretical model.