Analysis of three nodes flexure hinge element in ultra-precision positioning stage

The ultra-precision positioning stages are generally used in high precision positioning engineering fields, such as in biomedical genetic engineering, precision optical engineering, MEMS manufacturing and other fields. In this paper, an ultra-precision positioning stage is introduced. The flexure hinge is treated as a three nodes element with varying cross-section, in which each node has three degrees of freedom, and the center offset can be calculated. The cosine functions with high-order terms are introduced, and based on Castigliano´s theorem, the analytic solution of the element stiffness matrices and the mass matrices for the flexure hinge are obtained, and its results are compared with that of numerical integrations. Numerical analysis shows that the analytic results and ANSYS results match each other very well. Finally, analytic and experimental analyses are carried out to the stage. The analytic results match with that of the experimental results and ANSYS results, which indicate that the analytic method developed in this paper is accurate.