Static and Dynamic Analysis of Flexure-based Compliant Mechanism by Matrix Displacement Method

This paper proposed a novel analytical modeling method for the static and dynamic analysis for the flexure-based compliant mechanisms based on the matrix displacement method. Firstly, the theoretical compliance characteristics of a flexure element is transformed into its elemental stiffness matrix. Then, based on the elemental stiffness matrix, the new elemental stiffness matrix for two connected rigid bodies is derived by considering two points on rigid bodies and the forces applied on them as the nodal displacement and nodal forces. Finally, by expanding each new elemental stiffness matrix into contribution matrix and superimposing all of the contribution matrices, the global stiffness matrix can be obtained. The comparisons between the analytical method and the finite element analysis for two specific compliant mechanisms are conducted. The maximum differences of the analytical results with respect to the finite element analysis results are less than 5%, which demonstrate the high accuracy and effectiveness of the analytical model..