## 5 Discussion  
As has been seen throughout this paper, the use of SysML in mechanical modeling is usually limited to showing the high-level functional structure of the system. Our proposed SysML central model is much more detailed, specifically in those aspects related to geometry (coordinate systems, invariance classes, MGRE, etc. ), that are involved in system functionality. This detailed model enriches communication between experts, applications, and tools from various fields of mechanical engineering. In addition, it should be noted that the proposal supports the quantitative representation of geometric deviations (although it does not support form errors), and the mathematical equations that govern the analysis from different approaches (statistical, worst case, etc.). This is an important advantage compared to other analyzed proposals, in which SysML is used for the functional description of the system, developing qualitative analyses of the physical structure like the proposal based on C&C-M [19; 20]. Even GERTRUDE profile [18], which is based on the TTRS model, does not exploit the mathematical definition of surfaces with the level of detail considered this paper. After developing the proposal and its application to a case study, we have concluded that SysML has adequate constructive elements to define analytical models. This language includes constructions for a mathematical definition of the system and diagrams for its graphical representation from different perspectives (mainly BDDs, IBDs, and PAR diagrams in this proposal). Given the generality of SysML, the SysML4 TA profile was developed as a DSML for tolerance analysis, integrating concepts from the TTRS model. Along with the definition of the proposed profile and library and their subsequent application to a case study, the validity of TTRS concepts for supporting the geometry modeling has been demonstrated, including the definition of deviated geometries by applying SDTs. Additionally, it should be noted that throughout the development of the proposal, some  
Figure 23: PAR diagram of the AnalysisSpecif_1 Block. difficulties have been overcome. For example, SysML associative blocks have limitations in representing non-binary relationships, so alternative modeling solutions were explored. Regarding representation through diagrams, the case study highlights the convenience of enriching formal SysML modeling with alternative graphical representations to facilitate the definition and interpretation of models related to a specific domain. Thus, the development of a specific profile could allow for the definition of additional diagrams, designed from the perspective of a particular domain. In the specific case of this proposal, it would be interesting to have diagrams closer to the sketches usually used by tolerance analysis and synthesis experts (e.g., Figure 20c), integrating different viewpoints that current SysML diagrams address separately. Regarding the use of OCL rules for consistency assurance, this study explored the definition of OCL rules in each stereotype of the SysML4 TA profile. These OCL rules restrict the use of handled concepts, detecting inconsistencies when any of these rules are not fulfilled during model validation. The developed rules, described in the appendixes, control various model aspects, such as its completeness, the use of admissible connections, or the Functional Chain correctness, among others. In order to test the proposed OCL rules, during the development of the case study, conceptual errors were intentionally introduced into the model, and the model validation processes successfully identified them. Moreover, other unintentional errors were also identified. This proves the potential of the use of OCL rules at the profile level, as well as the correct implementation and operation of these rules. However, some issues about the completeness of the analysis model could not be addressed by defining rules in the profile level, and their validation can only be supported with OCL rules defined in the system model.