## 3 Results and Discussion
### Static Analysis  
As can be supposed, the results of the static analysis also vary depending on the situation in which the mechanism is studied. In the blockage situation, the maximum stresses are located on the supports of the horizontal axles. At these points, the von Mises stress reaches a maximum at the insertion of the DD axle with the inertia flywheel with a value of 186.9 MPa (Figure 18a). Similarly, for the rest of the contacts between the axles and the supports, there also appear high stress values: the support of the AA axle is subjected to a stress of 169.5 MPa (Figure 19a), and the support of the intermediate BB axle to a stress of 77.8 MPa (Figure 20a). Outside of these points, stresses are generally low. In the braking situation, the maximum stress is located at the point of attachment of the support bar of the first brake, with a value of 1025 MPa (Figure 18b). This stress, as was observed in the previous sections, could not be achieved, since the operator would need to use a force equivalent to 2 tons to be able to stop the loaded tugboat. Therefore, the support bar of the first brake would break. However, it should be emphasized that the rest of the structural elements would be subject to  
Figure 17: Convergence curve: (**a**) blockage situation and (**b**) braking situation. reasonable stress. Thus, the second highest stress value would be reached in the support of the bar with a value of 390.7 MPa (Figure 19b), and the third highest value (287.1 MPa), would be reached at one part of the drive shaft, and would be located at the point of contact between the shaft of the largest gear of the DD shaft and that of the BB shaft gear (Figure 20b). Another result of the static analysis is that relative to the safety coefficient. The safety coefficient at a given point in the model is calculated as the ratio between the von Mises stress and the elastic  
Figure 19: Location of the second highest von Mises stress: (**a**) blocking situation and (**b**) braking situation. Figure 20: Location of the third highest von Mises stress: (**a**) blocking situation and (**b**) braking situation. limit of a material for that point. In other words, the safety coefficient shows graphically whether the material from which a piece is made is capable of supporting a certain stress or not. In principle, a safety factor close to one unit would indicate that the material is working very close to its elastic limit; if it is less than one, it would indicate that the material exceeds this limit and would break, and if it is greater than one, it would indicate that it works without problems when subjected to said stress. Nowadays, the materials and their elastic limits are much better known than at the end of the 18 th century, and for this reason, engineers aim for the elements to work within a range of safety coefficient of 2 to 4 units. At the time of the _Hay inclined plane_, on the contrary, machines tended to be oversized, since those limits were unknown. For this reason, it is not surprising that, in general, almost the entire model works well above the elastic limit of the materials. In the blockage situation, it can be observed, however, that the axle supports work with a value of 3.51 (Figure 21a). These elements have in common that they are in contact with the most stressed elements, and therefore, [PERSON] used wooden supports, because they are elements that can be easily replaced, since there was much wear due to the excessive friction of the axles (the bearing had not yet been invented). However, in the braking situation, the point of maximum stress (point of union of the support bar of the first brake) coincides with the one with the lowest safety factor, with a value of 0.74 (Figure 21b). Outside this bar, the points that have the lowest safety coefficient are located at the joints between the links that form the brake, with a value of 1.7 in the tenth link (Figure 22b). The rest of the links have somewhat higher values, also around 2.