Optimal design method for 3-DOF planar compliant mechanisms based on mapping matrix constraints

Abstract

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.