Abstract: In order to match the large-displacement character of compliant mechanisms, a nonlinear optimization method for designing inverter mechanisms is presented by combining the theory of the Element-free Galerkin method and topology optimization. The performance of the inverter produced according to the design result is tested. The structural response analysis and sensitivity analysis are carried out by using EFGM, which matches the natural geometrical nonlinear behavior of the inverter mechanisms. According to the topologies designed by linear and nonlinear meshless methods, two kinds of inverters are produced. The load-displacement responses of the inverters are tested. And the result is demonstrated that the non-linear EFGM is better for designing compliant inverter mechanisms than the linear EFGM.