# Topology Optimization of Multi-Materials Compliant Mechanisms
## 1 Introduction  
A compliant mechanism is a new type of hingeless mechanism that relies on the elastic deformation of the whole or part of the mechanism itself to obtain movement. Due to the characteristics of low noise and vibration, no lubrication, compliant mechanisms are gaining interest in the fields of micro-electro-mechanical systems, medical devices and aerospace [1, 2]. Topology optimization method is the most widely used and effective tool for designing compliant mechanism [3]. [PERSON] et al. [4] introduced the concept of topology optimisation to the design of compliant mechanisms for the first time using the homogenisation method proposed by [PERSON]. Topology optimization is a kind of design method in engineering, which is based on certain external forces and other constraints to seek the best material layout and obtain the structure that meets the specific output requirements. The most important innovation of topology optimization is to find the optimal distribution form in a given design area from a higher dimensional point of view. The variable density method represented by solid isotropic material with penalization (SIMP) has become the mainstream method of topology optimisation due to the great simplification of the design variables and improved computational efficiency and has achieved good results in the design of compliant mechanisms [5, 6, 7, 8]. [PERSON] et al. used mechanical advantage as an objective function for the design of compliant mechanism [9]. [PERSON] [10] proposed geometric advantage as a design objective for the variable density method. [PERSON] et al. [11] proposed the idea of using the ratio of mutual potential energy to strain energy for the design of compliant mechanisms. [PERSON] proposed a design method for compliant mechanisms with mechanical efficiency as the design objective [12]. [PERSON] started the nonlinear problems in the design of compliant mechanisms [13]. [PERSON] et al. [14] tries to use the maximum output displacement with error constraints. [PERSON] [15] proposed that displacement load can be used to replace force load in optimization, which can improve the convergence rate and obtain the convergence solution easily. [PERSON] et al. proposed the design of large displacement compliant mechanisms considering path planning [16, 17]. [PERSON] et al. used compliant structural element to improve the solution speed [18]. [PERSON] takes the maximum energy efficiency as the goal of compliant mechanisms [19]. The design of compliant mechanisms with maximum flexibility and minimum stiffness was optimized by [PERSON] et al. [20]. [PERSON] et al. [21] proposed a multi-physics field topology optimization method for compliant mechanisms with functional gradients. [PERSON] proposed an optimization method that includes different virtual spring stiffnesses in the topology optimisation of compliant mechanisms [22]. [PERSON] proposed a sub-region partitioning design method in order to reduce the computational complexity of the compliant mechanism design [23]. [PERSON] et al., proposed a volume self-adjusting algorithm to solve the problem of artificially setting the volume fraction in topology optimization [24]. [PERSON] et al. [25], [PERSON] et al. [26] used a linear incremental method to reduce the computational complexity by replacing the non-linear problem with a series of linear problems. [PERSON] proposed the method of using standardized elements in compliant mechanisms design [27]. [PERSON] et al. conducted an in-depth study of multiple input-output and fatigue reliability problems for compliant mechanisms [28; 29; 30; 31; 32]. [PERSON] has done a lot of research work on pseudo-rigid body models and flexible hinges for compliant mechanisms [33; 34; 35; 36]. The essence of topology optimisation for compliant mechanisms is to find the best layout of materials in the design domain that satisfies the boundaries and constraints, and the properties of the material itself have a significant impact on the design results.