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The mapping matrix cannot be given in advance when using traditional topology optimization method (TOM) to design compliant mechanism (CM), which makes the CM unable to accurately establish model and affects the mechanism precise control. In this paper, a design method for CM is proposed based on planar parallel prototype mechanism with optimal structural parameters, the mapping matrix under the optimal structural parameter reasonably modified as the desired mapping matrix of CM in the process of topology optimization. Based on the idea of linear regression, the difference between the actual mapping matrix of the CM and the expected mapping matrix is constrained to makes the actual mapping matrix of the CM approach the expected mapping matrix gradually in the optimization process, take the low order modal frequency of the mechanism as objective, and finally obtains the CM that meets the design requirements. Experimental and simulation results show that take the mapping matrix as constraint in CM design process can achieve the consistency of differential motion between the CM and the parallel prototype mechanism within a range of deviation, which indicates that the method is effective for the design of CM and provides a foundation for the follow-up research of CM.

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.