## 2 State-of-the-Art and Related Work
### Tolerance Analysis of Systems in Motion Considering Joint Clearance and Geometric Deviations  
Various approaches for computer-aided tolerance analysis have been developed during the last decades, whereby the three major approaches are tolerance stacks, tolerance analysis based on the Small Displacement Torsor and vector loops [6]. Gaps between parts resulting from their geometric part deviations can thereby be considered using the vector loops approach. Therefore, the assembly is modelled as a chain of vectors, whereby each part is represented as a vector. For the integration of joint clearance, the clearance vector is introduced. The vector loop is thus enhanced through a virtual massless link connecting the two centre points of the joint-pair. This clearance vector can be defined according to worst-case or stochastic scenarios or due to a certain joint force [9]. The tolerance analysis of systems in motion considering joint clearance and geometric deviations has been a constant topic of research in the field of conventionally manufactured  
Figure 1: Additively manufactured non-assembly 4-bar mechanism after the Fused Deposition Modelling (FDM)-process and after the support removal [8].  
and assembled mechanisms [7; 10]. However, [PERSON] et al. propose an approach for the tolerance analysis of 3D-printed mechanisms. Tolerance values are hereby chosen based on experience and the influence of varying process parameters is thus neglected [11]. [PERSON] and [PERSON] introduced the \"integrated tolerance analysis of systems in motion\". This methodology can be used for the tolerance analysis of mechanisms with deviations from both, manufacturing and operating [9]. [PERSON] et al. extended this methodology by the consideration of interactions between deviations for systems in motion using meta-modelling techniques for representing affected deviations. The methodology was thereby applied to a non-ideal crank-mechanism [7]. According to [PERSON] et al., there are three main approaches for modelling the mechanisms in motion affected by joint clearance--the massless link approach, the spring-damper approach and the momentum exchange approach [12]. In order to enhance the tolerance analysis of systems in motion affected by clearance, an MBS can be used to derive the missing joint forces [12]. For modelling the impact of journal and bearing in an MBS, two approaches are firmly established, namely the continuous and the discontinuous approach. In the continuous contact model approach, the forces arising from the impact act perpendicular to the impact zone. This model can either be linear (Kelvin-Voigt model) or non-linear (Hertz law) [12]. [PERSON] and [PERSON] presented an approach of a force model for the simulation of joint clearance in which both elastic and damping effects are considered. The damping effect is hereby directly linked to the energy dissipated during the impact process. With the help of this approach, the dynamics of mechanisms including planar revolute clearance joints can be modelled for tolerance analysis [13]. [PERSON] and [PERSON] proposed an optimisation approach for designing mechanisms in which tolerances and joint clearances were considered, which was later applied to a planar four-bar mechanism including kinematic joints affected by clearance [14].