A novel mechanical model based on the dynamic stiffness matrix for unified dynamic and static modeling of planar compliant mechanisms

Abstract

This paper presents a dynamic and static modeling method for compliant mechanisms based on the dynamic stiffness matrix. Its advantage is that accurate dynamic and static modeling can be established simultaneously in frequency domain. Firstly, the dynamic stiffness matrices of flexure beams/hinges are introduced in detail. To ensure modeling accuracy, the nodes of flexible elements are translated to the research nodes, and the local coordinate system is rotated to make it consistent with the global coordinate system. The translation matrix and the rotation matrix are derived, and then the extended dynamic stiffness matrix of flexible elements is also obtained. Then the displacement of the discrete node and the displacement of the research node are taken as the hybrid state variables, and the dynamic model of the whole mechanism is established in frequency domain. The static model of the whole mechanism can be established by changing the angular frequency value. Eventually, two examples are given, and the proposed method is compared with other theoretical models and finite element analysis (FEA). The results show that this method has high modeling accuracy. It provides a reliable modeling method for dynamic and static performance analysis of compliant mechanisms.