Kinematic Calibration Of Parallel Mechanisms Based On Finite And Instantaneous Screw Theory

Accuracy is the primary key index for the extension of parallel mechanism from design to application.Kinematic calibration is an efficient and low-cost solution to improve the accuracy of parallel mechanism.Due to the diversity and complexity of closed-loop topology,it is very important to fully reveal the error transmission and accumulation law of parallel mechanism,realize high-precision error identification and complete high-efficiency kinematic calibration.Taking the finite and instantaneous screw as the mathematical tool,this thesis deeply studies the error modeling,error identification,compensation and calibration auxiliary software system development of parallel mechanism.The full text has achieved the following results:(1)Kinematic error modeling based on finite and instantaneous screw theory.Starting with the continuous motion representation of the single degree of freedom joint with finite screw,the error model of the joint is obtained by finite screw total differential operation.Based on the single joint error model,the error model of the limb is obtained by using the finite instantaneous screw differential mapping.Then,the error model of the mechanism is obtained by aggregating the error model of the limb.The influence of the motion error of the passive joint is removed by the reciprocity between the force screw and the motion screw,and the error model of the parallel mechanism satisfying the conditions of completeness and continuity is established.The error modeling method of parallel mechanism based on FIS theory clearly and intuitively shows the law of error traceability,transmission and accumulation,which lays a theoretical foundation for high-precision kinematic calibration method.(2)Error identification and compensation based on separation of redundant errors.It is found that the redundancy error is the main cause of the singularity of error identification.The redundancy error of parallel mechanism is divided into inter chain and intra chain redundancy errors.Through the correlation analysis of matrix,the mathematical and physical essence of two kinds of redundant errors are revealed.Based on this,a step-by-step elimination method of redundant errors is proposed,and it is proved that the minimum identifiable error number of parallel mechanism is4r(10)2 p(10)6.The method of equivalent conversion of joint axis error into mechanism input is proposed to realize efficient error compensation without changing controller parameters.For the parallel mechanism with passive limb,it is proved that the passive limb error does not affect the calibration results.Taking the 6-DOF Stewart platform as the object,the numerical simulation is carried out to verify the correctness of the proposed kinematic calibration method.(3)Design kinematics calibration software and experiments.Carry out the demand analysis and module division of kinematics calibration process,carry out the digital design of kinematics calibration based on QT,Eigen and My SQL,and complete the development of kinematics calibration C++ desktop software.Comparing the complete error model of helix parallel mechanism with the error model without passive limb,there is no difference between the two calibration results,which shows that the passive limb error does not affect the overall calibration results of parallel mechanism under the framework of step-by-step error identification.Based on the FIS theory,this thesis proposes a complete,continuous,clear and intuitive error modeling method,carries out high-precision error identification based on the analytical elimination of inter chain and intra chain redundant errors,develops the kinematics calibration auxiliary software,and forms a high-precision,efficient and universal parallel kinematics calibration process,It is of great significance to promote the engineering application of parallel mechanism.