Simultaneous optimal design of topology and size for a flexure-hinge-based guiding mechanism to minimize mass under stiffness and frequency constraints

The guiding mechanism based on flexure hinges (FHs) is widely used in micro/nano-manufacturing technology. Both the stiffness and the frequency of FHs play significant roles in their dynamic performance, so the design task of such a structure is to find the optimal topology and corresponding size of FHs under stiffness and frequency constraints. However, the existing optimization methods pay more attention to the stiffness than to the frequency constraint owing to difficulties in dynamic topology optimization. In this article, with the symmetrical layout assumption of FHs and the analytical equivalent stiffness and mass expression of a single FH, the simultaneous topology and size optimization problem is converted to an analytical optimization formula with both discrete and continuous variables. Finally, the tension stiffening effect is used to compensate for manufacturing errors. A design case is used to illustrate the efficiency of the proposed method.