Hexagonal element-based topology optimization of dual-axial compliant mechanisms with decoupled kinematics

Compliant mechanisms are widely applied in fast-tool-servo machining and micro/nano-positioning devices. However, for multi-degree-of-freedom mechanisms, designing them is a multi-objective, multi-constraint problem where multiple factors need to be considered, such as large stroke, nanometer-level positioning accuracy, and static failure. Currently, traditional design methods may not be able to comprehensively address these factors. To solve these problems, this study proposes a topology optimization-based design method to develop a compliant mechanism with fully decoupled kinematics and two degrees of freedom, where a hexagonal element mesh with Wachspress shape functions is utilized. Besides, a coupling constraint formulation is designed to avoid the motion coupling in the input end and output end of the compliant mechanism and enhance positioning accuracy. Furthermore, a normalized p-norm stress method is used to restrict the compliant mechanism's maximum stress, which aims to prevent static failure and enhance its reliability. Finally, a dual-axial compliant mechanism with decoupled kinematics, as the numerical example, is designed by the proposed topology optimization method, and its performance specifications are verified by the finite element simulation, which demonstrates the effectiveness and superiority of the proposed topology optimization method on the design of the compliant mechanism.