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In order to ensure optimal optical performance, primary mirror assembly must be impervious to environmental influences. These environmental influences include gravity, assembly error, and thermal change, under which external loads are imposed on the mirror. The external loads degrade the mirror surface accuracy and cause misalignment between mirrors. In this paper, a tripod flexure with a flexible hinge is designed to alleviate the influence of the external load on the surface accuracy of a 2 m primary mirror. This structure can effectively release the rotational freedom, provide a certain translational flexibility, and yield high axial stiffness. The axial stiffness is used to increase the frequency of the primary mirror assembly. According to the fast optimization model, the derivation of close form compliance equations is developed to characterize the flexibility, and parameter optimization is done to achieve the maximum performance. Then a finite element analysis and test are used to verify the final design. The results show that the index requirements of the 2 m primary mirror have been met.