Development of a 3-DOF flexible micro-motion platform based on a symmetrical two-stage magnifying mechanism

Abstract

A symmetrical 3-PRR flexible motion platform kinematic dynamic model is built. The natural frequency analysis of the platform is studied in this paper. Firstly, a flexible lever displacement two-stage amplification mechanism is proposed. A pseudo-rigid body model is established. A kinematics model is established by using the vector closed-loop method. The relationship between the input and output of the flexible lever displacement two-stage amplification mechanism is obtained. Secondly, based on the two-stage amplification mechanism of flexible lever displacement, a 3-PRR flexible motion platform is designed. The Jacobian matrix of input displacement of piezoelectric ceramics and output displacement of flexible motion platform is obtained by using coordinate transformation method and vector equation closed-loop method. Considering the elastic potential energy of flexible hinge and biaxial hinge, the Lagrange equation is established, and the expression of the natural frequency of 3-PRR flexible motion platform is obtained. Finally, the correctness of the theoretical dynamic model is verified by theoretical calculation and finite element software simulation. The numerical calculation and simulation results show that the maximum relative difference of the natural frequency is 17.6%, and the maximum relative difference of the output displacement of the two-stage amplification mechanism of flexible lever displacement is 13.4%.