## 4 Determination of the Most Loaded Component of the Platform  
The output shaft of the gearbox is the most loaded component. The drive-shaft of a drive-train mechanism is often the most loaded part, which is imposed not only by mechanical tension resulting from the loads, but also by dynamic loads and vibration occurring during its operation [30; 31]. The calculation of the electromotor has proven that the electromotor can be used even for greater loads, but it is necessary to analyse the output shaft (Figures 8b and 12). Individual loading forces are given by the following formulations:  
\[F_{t}=\frac{M_{o}}{\frac{g}{2}}, \tag{36}\]  
Figure 11: The dependence of the track slope angle on the electromotor power under individual platform loads \(m_{2}\). Figure 12: Scheme and distribution of the load of the output shaft: (**a**) \(z\)-\(y\) plane; (**b**) \(z\)-\(x\) plane. \[F_{r}=F_{t}\cdot\tan 20^{\circ}, \tag{37}\]  
\[\sum_{i}M_{iFR1}=0\to F_{R2}\cdot 63.5-(R_{lm}+F_{r})\cdot 26=0, \tag{38}\]  
\[\sum_{i}F_{iy}=0\to F_{R1}+F_{R2}-R_{lm}-F_{r}=0, \tag{39}\]  
\[\sum_{i}M_{iORy}=0\to M_{R}-F_{R2}\cdot 16.4-F_{R1}\cdot 79.9+F_{r}\cdot 53.9=0, \tag{40}\]  
\[M_{O1}=F_{R1}\cdot z_{1}, \tag{41}\]  
\[M_{O2}=F_{R1}\cdot(26+z_{2})-F_{r}\cdot z_{2}, \tag{42}\]  
\[M_{O3}=F_{R1}\cdot(63.5+z_{3})-F_{r}\cdot(37.5+z_{2})+F_{R2}\cdot z_{3}. \tag{43}\]  
We can assume that the maximal value of stress will be in the considered coupling, because the maximal value of the bending moment is at the shaft constraint end (diameter is \(d_{1}=25\) mm) and other diameters of the shaft are bigger as well as the bending moments in these locations being less. The corresponding bending modulus of section is:  
Figure 11:0  
The maximal stress in the \(z\)-\(y\) plane is given as the following:  
Figure 11:1  
The individual forces depicted in Figure 12 are the following: forces \(F_{R1}\) and \(F_{R2}\) are forces in rolling bearings, which transmit loads from the platform to a bottom trolley. The end of the shaft is mounted rigidly in a gearbox, which causes reaction forces \(R_{x}\), \(R_{y}\) and reaction torque \(M_{R}\). The drive force is decomposed in the contact to a radial component of a drive force \(F_{r}\) and a tangential component. Forces depicted in Figure 12 always act in the radial direction regarding the shaft axis. Furthermore, Figure 12 shows the tangential component of the drive force \(F_{t}\), the drive torque \(M_{h}\) (in the scheme, it is considered as the reaction torque due to the \(F_{t}\) force), the reaction force \(R_{x}\) and the reaction torque \(M_{R}\). The torque \(M_{h}\) is in the equilibrium with the torque due to the force \(F_{t}\) on the radius of the pitch circle of the pinion. Thus, the force \(F_{t}\) loads the shaft by torsion and by bending. Figure 12 represents the static strength analysis in two planes, namely in the \(y\)-\(z\) plane (Figure 12a) and in the \(x\)-\(z\) plane (Figure 12b). Substituting particular values into Equations (36)-(45) we obtain the maximal value of the bending stress of \(\sigma_{o1}=144.3\) MPa. Similar equations are also valid for Figure 12b. The analytical calculation gives the maximal value of the bending stress of \(\sigma_{o2}=139.5\) MPa and the maximal value of the torsion stress of \(\tau_{k}=41.4\) MPa. The resulting bending stress in two perpendicular planes is determined by the following equation:  
Figure 11:2  
When we substitute values to the Equation (45), the resulting value of the bending stress is \(\sigma_{o}=200.7\) MPa. The calculation of the reduced stress according to the von-Misses theory is:  
Figure 11:3  
Numerical calculations of the reduced stress in the analysed shaft were performed using the Inventor Nastran software package (Autodesk Inc., San Rafael, CA, USA), which is based on the finite element method [32; 33; 34; 35]. The results are shown in Figures 13 and 14. Both analyses reached very similar results. The material of the shaft with the pinion is steel marked 42 CrMo4.