Topology optimization of a 6-DOF spatial compliant mechanism based on Stewart propotype platform

Abstract

To improve the global stiffness and conveniently build a model of a compliant mechanism with spatial multiple degrees of freedom (DOF), the topology optimization method, combined with the isomorphic mapping matrix, is proposed in this paper for structure synthesis of a 6-DOF spatial compliant mechanism. By using the differential approximation method, the Jacobian matrix of the Stewart prototype platform is calculated as the isomorphic mapping matrix, and its eigenvalues and eigenvectors are considered. Combining the isomorphic mapping matrix with the solid isotropic material with the penalization topology optimization method, the topological model of the 6-DOF spatial compliant mechanism is constructed, and a topological structure of the 6-DOF spatial compliant mechanism is derived which has the same differential kinematic characteristics as the Gough–Stewart prototype platform. Piezoelectric actuators are mounted inside the topological structure during the three-dimensional printing manufacturing process, and its driver directions are in accordance with the driver configuration directions of the Gough–Stewart prototype platform. The effectiveness of the proposed method for topological structure synthesis of the 6-DOF spatial compliant mechanism is demonstrated through several numerical examples and experimental studies.