## 1 Introduction
This review highlights the lack of literature in the field of topology optimization for compliant mechanisms with large deformation and stress constraints, which we address here. In the present work, two types of this design problem are considered, both introduced by [PERSON] et al. [14]:  
**Problem type I:**: The design of maximum-displacement mechanisms finds the topology for the largest displacement of predefined degrees of freedoms for a given load. **Problem type II:**: The design of path-generation mechanisms finds the topology in which certain degrees of freedom are designed to go through predefined points (also known as way points or precision points), which describe a trajectory or path. As large deformations--and therefore nonlinear strains--are desired in compliant mechanisms, nonlinear finite-element analysis is required for their design [14]. The nonlinear structural-mechanical analysis, which serves as the basis of the topology optimization, can be split into two general categories: static (including quasi-static) and transient analysis. A proposal for the categorization of the methods of topology optimization was introduced by [PERSON] et al. [15]. This categorization includes the replacement of the nonlinear behavior with a series of linear calculations via the update method from [PERSON] [16] or a single replacement load introduced by [PERSON] [17], [PERSON] and [PERSON] [18]. Other methods utilize efficient gradient-free rule-based methods, e.g., hybrid cellular automata by [PERSON] et al. [19], avoiding the challenge of deriving and implementing sensitivity analysis for nonlinear finite-element analysis. The behavior of compliant mechanisms in this work is considered quasi-static. Studies on path-generation compliant mechanisms by [PERSON] et al. [20] and [PERSON] et al. [21] include large deformations, yet neglect stress constraints. As compliant mechanisms are designed to avoid plastic behavior, the authors find the application of stress constrains necessary and therefore extend this study to include them in this work. The material may also exhibit nonlinear elasticity, though this will not be considered. Therefore, we will restrict our examples to topology optimization for stress-constrained compliant mechanisms using nonlinear quasi-static analysis considering linear-elastic material models and its sensitivity analysis. In order to obtain high-resolution topologies with the classical topology optimization approach, a high number of finite elements is required and with it a high computational cost. Nonlinear finite-element analysis exacerbates the high computational effort, as the case in this work. Standard topology optimization assigns a material density to each finite element and hence the element size defines the minimum length scale for the topology to be found. Multiple approaches were proposed to reduce computational effort in topology optimization e.g., adaptive mesh refinement [22; 23] or domain decomposition [24]. [PERSON] et al. [25; 26] introduced a multiresolution topology optimization (MTOP) scheme, which decouples the degree of detail of the topology from the finite-element size. Therefore, different discretizations for displacements, densities and design variables are used. By this means, it is possible to obtain detailed designs on a relatively coarse FE mesh. In this work, multiresolution topology optimization is extended with stress constraints and used for the synthesis of large-deformation path-generating compliant mechanisms. There are several challenges when considering stress constraints in topology optimization. Low density elements can show singular behavior resulting in exaggerated stresses, which then dominate the progression of the topology optimization. [PERSON] and [PERSON] [27] introduced a relaxed stress scheme to avoid this problem. [PERSON] et al. [28] as well as [PERSON] [29] implemented stress constraints in the synthesis of compliant mechanisms with topology optimization, albeit only for linear finite-element analysis.