Abstract: Multiple degree-of-freedom compliant mechanisms are widely used in the fields of micro-positioning and micro-manipulation, and the topology optimization of compliant mechanisms is actually a geometrically nonlinear problem. So it is very necessary to study the topology optimization of multiple inputs and outputs compliant mechanisms undergoing large deformation. A new topology optimization method of multiple inputs and multiple outputs compliant mechanisms with geometrical nonlinearity is presented. The multi-objective function is developed by the minimum compliance and maximum geometric advantage to design a mechanism which meets both stiffness and flexibility requirements, respectively. The suppression strategy of input and output coupling terms is studied, and the expression of the output coupling terms is further developed. The weighted sum of conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions, and the decision function is set to select the preferred solution. Geometrically nonlinear structural response is calculated by using a total Lagrange finite element formulation and the equilibrium is found by using an incremental scheme combined with Newton-Raphson iterations. The solid isotropic material interpolation method is used in design of compliant mechanisms. The sensitivity of objective functions is analyzed by using the adjoint solution technique and the optimization problem is solved by using the method of moving approximation algorithm. These methods are further investigated and realized with the numerical examples, which are simulated to show the availability of this approach.

Key words: Compliant mechanism, Geometrical nonlinearity, Multiple inputs and outputs, Output coupling, Sensitivity analysis, Topology optimization