A semi-analytical modeling method for the static and dynamic analysis of complex compliant mechanism

A semi-analytical modeling method towards the static and dynamic analyses for a class of flexure hinge-based compliant mechanisms or their composed systems is presented to provide accurate and efficient solutions. It is realized by firstly transforming the theoretical compliance matrix of a flexure hinge into a unified elemental stiffness matrix of a variable cross-section beam. Then, the semi-analytical finite element model of complex compliant mechanisms is established based on Lagrange's equation taking the flexure hinge, the flexible beam and the lumped mass as the minimum elements. Shearing effects of the flexure hinge and rotary inertia of the flexible beam are included to enhance the modeling accuracy. A comparison of the method with another existing theoretical method and the finite element software ANSYS for two exemplary compliant mechanisms reveals a maximum deviation of less than 8% regarding the static displacement and the fundamental frequency but with a much substantial reduction of degrees of freedom. The results suggest the presented method is applicable to time-critical scenarios such as dynamic topology optimization and real-time feedback control simulation for complex compliant mechanisms.