###### Abstract  
A new multi-constraint optimization model with the weighted objective function is proposed to design the multi-input-multi-output (MIMO) compliant mechanisms. The main feature of this work is that both the two notable problems related to the de facto hinge and the movement coupling are tackled simultaneously in the topological synthesis of MIMO compliant mechanisms. To be specific, the first problem is the severe stress concentration in the flexible hinge areas, and it is solved by the introduction of input and output compliances into the objective function, which could facilitate the optimization to strike a good balance between structural flexibility and stiffness. The second problem is the high degree of control complexity caused by the coupled outputs and inputs, and it is addressed by achieving the complete decoupling with two groups of extra constraints that are used to suppress the input coupling and the output coupling, respectively. As the most common and effective topology optimization method, the Solid Isotropic Material with Penalization (SIMP)-based density method is adopted here to obtain the optimized configurations. After the analytical sensitivity deduction related to the weighted objective function and constraints, two typical numerical examples are presented to demonstrate the validity of the proposed topology optimization framework in designing the hinge-free and completely decoupled MIMO compliant mechanisms. topology optimization; compliant mechanism; de facto hinge; movement coupling; multiple inputs; multiple outputs +
Footnote †: journal: Medical  
method [35; 36; 37] and several others [38; 39; 40; 41; 42; 43; 44]. It is worth noting that the Evolutionary Topology Optimization (ETO) approach [22] not only belongs to the evolutionary method, but also is an elemental volume fraction-based method proposed for the first time, which also includes the Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT) algorithm [45]. Among the various topology optimization approaches, the density method with Solid Isotropic Material with Penalization (SIMP) interpolation scheme is the most widely used one, mainly because of its clear physical conception, simple formula, excellent numerical stability and convergence. In this paper, the SIMP approach is adopted to synthesize compliant mechanisms, and the corresponding compliant mechanism design problem is converted into the problem of seeking the optimal material distribution within a given design domain [2]. In the topology optimization design of compliant mechanisms, there are some challenging problems that prevent optimized results from being widely applied to the engineering practice, and the present work focuses on solving the two most common and important problems: de facto hinges and movement coupling. The former problem is reflected in Figure 1; de facto hinges (i.e., flexure points [46]) make the resulting mechanism not actually compliant but function as the rigid-body one with revolute joints [47; 48]. To be more specific, if the compliant mechanism is loaded, its major part will essentially undergo the rigid-body motion, and the mechanical deflection can only be realized by the bending deformations around its de facto hinges. Consequently, energy and force are mainly transmitted through the bending of flexible hinges, where the severe local stress concentration occurs unavoidably and may significantly shorten the mechanical life span [4; 5; 6; 7; 49; 50; 51]. In order to eliminate de facto hinges and obtain the virtually distributed compliant mechanism [52; 53], varieties of methods have been developed and some characteristic ones are described below. [PERSON] et al.