Considering that the Jacobian matrix maps the velocity of the joint space of the robot to the end velocity of the Cartesian space, a novel topology optimization approach is proposed in this article for the design of three-translational degree-of-freedom spatial compliant mechanisms by combining the optimized Jacobian mapping matrix with the solid isotropic material with penalization topological method. First, by using the condition number method, the structural parameters of Universal-Prismatic-Universal (UPU)-type parallel prototype manipulator are optimized, and then, the differential Jacobian mapping matrix is calculated by using equivalent infinitesimal method. Second, comparing with the driver configuration and twist/wrench constraint conditions of the UPU-type parallel prototype manipulator, the topological algorithm combining solid isotropic material with penalization with optimized Jacobian mapping matrix is proposed. Finally, a novel spatial compliant mechanism with three-translational degree-of-freedom is derived, and numerical simulation results are reported to demonstrate the effectiveness of the proposed method.

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.

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