Modeling and Verification for a Three-Degree-of-Freedom Flexure-Based Planar Parallel Micro Manipulator

Micro positioning systems are popular devices to achieve ultrahigh precision motion. In this paper, a three-degree-of-freedom (3-DOF) flexure-based planar parallel micro manipulator is presented. The existing literature focusing on the modeling of micro manipulator is difficult to fully reflect the real internal physical characteristic in the relationship between the input voltage and output pose. A new comprehensive nonlinear model for a three-DOF flexure-based planar parallel micro manipulator considering the errors of compliant joint in multiple non-functional directions, inherent force, moment, and nonlinear properties of the piezoelectric actuator is proposed. The ideal kinematic model and stiffness model are derived for comparison to verify the comprehensive nonlinear model. The simulation results show that the accuracy of the comprehensive nonlinear model is higher than that of other two models. Finally, the experimental results demonstrate that the average accuracy of the proposed modeling method in the translational direction is 26.35% better than that of the ideal kinematic model. The average accuracy in the rotational direction is 27.49% better than that of the ideal kinematic model. The proposed comprehensive nonlinear model can improve the modeling accuracy. It can be applied to other types of flexure-based micro manipulator.