Based on the differential kinematics of parallel mechanism displacement vector differential mapping relation between input and output,through establishing a planar 3-RPR topology optimization model of fully compliant parallel mechanism（ SIMP interpolation model）,the solution is optimized by using the optimization criterion method（ OC） algorithm,and by using the Heaviside filtering technology,the checkerboard phenomenon is restrained and processed. Combining with quadratic interpolation method of topology optimization,the curve fitting of the model is carried out,and the 3D model is created in the Solidworks,the model is imported into Hyperworks for second meshing and its statics comparison and analysis are carried out,the results show that,the manipulator which based on the mapping relation of topology optimization not only has the same movement characteristic with the traditional parallel mechanism,but also the structure is more compact,lightweight,and the method provides a theoretical reference for the configuration synthesis of this kind of plane compliant parallel mechanism.