Modeling And Experimental Study Of 2PRU-2UPR Redundantly-actuated Parallel Mechanism

With the further acceleration of my country’s industrialization process and the introduction of high-quality development tasks,the development,application and research of redundant parallel mechanisms will become more and more popular.Some performance defects of existing parallel mechanisms can be solved by introducing "redundancy",such as small non-singularity working space,insufficient rigidity,limited load capacity,etc.Kinematic analysis is the basis for subsequent control and optimization,and kinematic calibration can effectively improve the absolute positioning accuracy of the end.This paper mainly studies a kind of redundantly actuated parallel mechanism2PRU-2UPR with few degrees of freedom.The main contents are as follows:(1)For the 2PRU-2UPR redundantly drive parallel mechanism,describe the components of the mechanism and the branch coordinate system of each component are established.According to the constraint relationship between the three independent generalized coordinates of the moving platform at the end of the mechanism,the closedloop vector method is used to obtain the inverse solution expression of the mechanism’s position,and the kinematics simulation verification of the mechanism is carried out based on Sim Mechanics.The position and orientation relationship of the end point of the mechanism tool is analyzed,and the rotation matrix of each branch chain is obtained.(2)Analyze the velocity and acceleration of each component of the 2PRU-2UPR redundantly drive parallel mechanism,and establish the mapping relationship between it and the mechanism’s pose parameters.The inverse dynamic equation of the mechanism is obtained by using the principle of virtual work,and the optimal driving force distribution of the mechanism is obtained by the least square norm method.Comparing the results with Adams software and Matlab programming verifies the correctness of the built kinematic model.(3)Taking the 2PRU-2UPR redundantly driven parallel mechanism as the research target,analyze its error sources,determine the kinematic error parameters to be identified,and establish a kinematic model with error parameters.When the driving values of multiple branches cannot meet the motion state of the geometric constraints,the redundantly drive parallel mechanism is decomposed into four non-redundant drive submechanisms by removing unnecessary drives,and the numerical differentiation method is used to establish the sub-mechanisms error model.At the same time,the error mapping Jacobian matrix is further preprocessed,and then the error model of the redundant mechanism is obtained by linear accumulation and averaging.(4)Carry out external calibration numerical simulation of the mechanism,use the kinematics forward solution model with error parameters to simulate the actual error measurement,and then obtain the deviation between the theoretical position and the actual position of the end.The objective function to be optimized is constructed with this deviation,and the real kinematic error parameters of the mechanism are identified by the least square method.Compensate the identification result to the geometric dimension parameters of the mechanism,and further judge the absolute positioning accuracy of the front and rear ends of the calibration.(5)Build an experimental platform for kinematics calibration experiments and PD control experiments based on dynamics feedforward compensation.The calibration results show that the average position error of the tool end after compensation drops from6.7390 mm to 0.9106 mm,and the accuracy increases by 86.49%.At the same time,in order to prove the accuracy of the identification results,the actual identification results were replaced with the second set of test points.The position error decreased from the average value of 7.0373 mm before compensation to 0.9477 mm after compensation,and the accuracy increased by 86.53%.Obviously,the absolute positioning accuracy of the end of the mechanism has been significantly improved,which verifies the built error model correctness.At the same time,the control experiment results verify the feasibility and effectiveness of PD control based on dynamics feedforward compensation.In this paper,the modeling and experiments of a redundant drive parallel mechanism with few degrees of freedom(2R1T)are studied in detail,which provides an important theoretical and experimental basis for promoting the practical application and technological innovation of parallel robot engineering.