Research On Compliant Force Control Of A 3-PRR Compliant Parallel Platform Based On Cross-spring Flexure Pivots With Variable Cross-thickness

The compliant parallel platform combines the advantages of flexible hinges and parallel platforms and is widely used in precision platforms.However,the flexible hinge in the platform generally has a small range of motion and may have a parasitic motion,which limits the motion space of the compliant parallel platform.In this paper,based on the analysis of traditional cross-reinforced flexible hinges,a cross-spring flexure pivot with variable cross-thickness with large stroke and low axial drift was studied and applied to the 3-PRR parallel platform.Then the force-flexible control study was performed on the 3-PRR flexible parallel platform.In this paper,the concept of the cross-spring flexure pivots with variable crossthickness is introduced firstly,and the relationship between the variable cross-section coefficient of the spring leaves and the rotation angle of the flexure pivot is analyzed through finite element simulation,and the appropriate variable cross-section coefficient is selected.Based on the modified Awart constraint beam model,the load-displacement relationship was derived for the selected cross-spring.The mechanical model of the flexure pivots was further established.The results were compared with the finite element simulation,which verified.the correctness of the deformation model of the flexure pivots established in this paper.Then,a 3-PRR compliant parallel platform was designed by combining the flexure pivots and a 3-PRR planar parallel platform.The inverse kinematics and positive kinematics of the rigid platform are solved by the closed loop vector method and the velocity Jacobian matrix iterative method,respectively.Deformation equations of simultaneous hinges,displacement coordination equations and static equilibrium equations of compliant parallel platforms are jointly solved for kinematic models of compliant parallel platforms.Comparing the kinematic model of the rigid and compliant parallel platform with the finite element simulation results,the accuracy and necessity of the kinematics modeling of the compliant parallel platform are verified.However,because the kinematics model of the compliant platform is complex and the computing speed is slow,so the BP neural network is used to solve the kinematics model of the compliant parallel platform.Then the position control experiment was performed with the aid of a laser displacement sensor and the accuracy of the position control was verified.Finally,for the problem of force compliance of 3-PRR compliant parallel platform,firstly,the classical position-based impedance control is studied.The simulation system is designed and constructed.The influence of impedance parameters on control performance is analyzed through simulation.Then by analyzing the steady-state error of impedance control,the limitations of impedance control are discovered.The adaptive impedance controller is designed through Lyapunov stability theory,and simulations are performed for different situations.The force compliance control experiment was performed using a force sensor mounted on a moving platform as a force feedback element to verify the correctness of the force compliance control strategy.