## 2 Materials and Methods
### Computer-Aided Engineering (CAE)
#### 2.2.5 Meshing  
The last step before beginning the static analysis consists of the geometric discretization or meshing of the engine. Most software that performs an FEA uses tetrahedral elements, type tetra 10 (4 physical points and 10 nodes). If the simulation is more complex, for example, in dynamic analysis or in static analysis of complex geometries, some software uses hexahedral volumes, such as hexa 8, hexa 20 or hexa 27 for meshing. The use of the hexahedron allows the mesh to be formed by elements of greater volume, and therefore it needs a smaller number of elements to generate all of the geometry of the model. The choice of hexahedral meshes decreases the computational requirements and saves time, but results in less accurate results, since the total number of nodes is reduced and the mesh is less suited to the real geometry. In an analysis such as the present study, there is no problem in using tetra 10, since the total number of elements to analyze is not excessive. Therefore, in FEA analysis, the elements used were tetrahedrons with 4 nodes and first order integration (constant interpolation of the stress and strain). The elements are formulated in a 3D scheme with three degrees of freedom per node (translational in X, Y and Z directions). However, a sensitivity analysis of the size of the element has not been carried out, since the structure is oversized. On the other hand, the specific software used in the analysis of thermal parameters or lighting uses bar elements or shell elements. These elements of lower order than those used in the present study could also be used for the static or modal analysis of a mechanism, but it would require a much larger number of nodes to simulate its geometry, and therefore for a computer with a standard processor, these meshes would need an excessive time in their calculations. Regarding the shell elements, although they are capable of capturing the stress gradients in a more efficient way, they have not been used in  
Figure 13: Force exerted on the braking bar in the situation of emergency braking. this study, since the mechanism is oversized, and because it would provide an accuracy that would not change the conclusions in a significant way. Autodesk Inventor Professional can automatically generate a mesh based on the size of the element to be discretized. By default, it generates tetrahedra whose average size is 10% of the length of the element, a minimum size of the tetrahedron of 20% of the average size, a maximum variation between tetrahedra of 1.5 and a maximum angle of rotation of 60\({}^{\circ}\). However, it is advisable to pay more attention to the places where the geometry is complex, since in these parts, the mesh usually gives results that differ greatly from the actual geometry of the element. For these singular places, the software offers the possibility of carrying out a manual meshing of the element in which the mesh size is determined. In addition, in general lines, it should be mentioned that in places where the concentration of stress is greater, it is also convenient to increase the density of the mesh. Figure 14 shows the meshing result that is generated automatically by Autodesk Inventor Professional. In the present research, it was also necessary to modify the discretization in some places, performing a refinement of the mesh. Specifically, this was done in the contacts between the teeth of adjacent gears (Figure 15) and on the surfaces of the ends of the axles in contact with their supports (Figure 16). In the first case, the reason for this intervention was the complicated geometry of the tooth of the gear, while in the second case, the reason lay in the concentration of the stresses. Figure 14: Automatic mesh obtained from the Hay inclined plane. Figure 15: Refinement of the mesh in the teeth of the gears. To conclude this section, it must be emphasized that for static analysis, it is necessary to establish a convergence criterion since iterative processes are used in this analysis.