###### Abstract
[54] address the de facto hinge problem by introducing a quadratic energy functional used in image analysis in the level set method; [PERSON] and [PERSON] [55] study the joint use of local stress constraints and proper filter radius to design distributed compliant mechanisms; [PERSON] [56] removes de facto hinges by applying minimum length-scale constraints to both structure and void regions; [PERSON] and [PERSON] [57] prevent the formation of flexible hinges by means of the robust topology optimization considering material uncertainties. In our work, a relatively popular method with the weighted objective function is adopted, in which the optimization objective includes geometric and mechanical advantages [46; 47]. The geometric advantage usually represented by the desired output displacement or the mutual compliance is employed to quantify the mechanical performance and enhance the output motion. The mechanical  
Figure 1: Drawings related to the de facto hinge phenomenon: (**a**) the revolute joint of two rigid bodies; (**b**) the flexure point of a structure; (**c**) the distributed compliant mechanism. advantage that could be simply defined by the mean compliance is used to ensure adequate structural stiffness and hence has the effect of eliminating de facto hinges [58; 59]. The latter problem is the coupling issue of outputs and inputs existing in the operational process of multi-input-multi-output (MIMO) compliant mechanisms [60; 61; 62; 63; 64; 65]. The output coupling always results in complex kinematic models, and the input coupling would lead to undesired loads on actuators. Both of them could cause serious difficulty in motion control, so the decoupling property is a crucial factor needing to be considered in the process of designing precision MIMO compliant mechanisms. In the current study, we aim to develop fully decoupled mechanisms with both output and input decoupling properties. Generally, the output decoupling means one actuator produced only one axial output motion without affecting the motion of other axes [61], and the input decoupling emphasizes on the isolation of actuations [62]. In order to obtain the fully decoupled compliant mechanism, many effective kinematic-based approaches have already been proposed [63; 64; 65], but they often lead to complicated structures that are not convenient for control implementation and prototype fabrication. To solve this problem, [PERSON] et al. [60] adopted the topology optimization method to design the fully decoupled compliant mechanism, and relatively simple structures with de facto hinges were obtained. The present study is conducted to design hinge-free and fully-decoupled MIMO compliant mechanisms, by addressing both the de facto hinge and the movement coupling problems at the same time. To achieve this end, a new multi-objective-multi-constraint optimization model is proposed. Specifically, the multi-objective function consists of desired output displacements as well as input and output compliances, and corresponding weighting factors are updated adaptively to make the optimization strike a good balance between structural flexibility and stiffness. The multi-constraint conditions could be classified into output decoupling and input decoupling constraints, which are employed to restrict the undesired displacements at output and input ports, respectively. In order to solve the above-described optimization model, analytical sensitivities related to multi-objective and constraint functions are deduced and the Method of Moving Asymptotes (MMA) [66] is used as the optimizer. It should be noted that the proposed method is quite convenient as it possesses a self-adaptive ability and does not need the setting of many empirical parameters, such as stiffness coefficients of connecting springs. The remainder of the paper is organized as follows. MIMO compliant mechanism design problems regarding the de facto hinge and the movement coupling are introduced in Section 2, where the integrated mathematical model of concerned optimization problems is built.