## 3 Design of the Accepted Solution
Hence, the torque of the electromotor on the output shaft is given by the following formulation:  
\[P_{v}=M_{h}\cdot\omega=109.22\cdot 2.932=320.23\;W. \tag{34}\]  
Considering the total drivetrain efficiency \(\eta_{c}\), the total power of the electromotor is:  
\[P_{m}=\frac{P_{v}}{\eta_{c}}=\frac{320.23}{0.98\cdot 0.65\cdot 0.99}=507.79\;W. \tag{35}\]  
The input parameters for Equations (12)-(27) are listed in Table 4, where:  
\(f_{p1}\)--coefficient of friction of the upper trolley wheels;  
\(f_{p2}\)--coefficient of friction of the bottom trolley wheels;  
\(r_{p1}\)--radius of the pinion of the upper guidance;  
\(r_{p2}\)--radius of the pinion of the bottom guidance;  
\(e_{a1}\)--forward moving distance of the upper guidance wheels;  
\(e_{b1}\)--forward moving distance of the bottom guidance wheels;  
\(e_{b2}\)--forward moving distance of the side guiding rollers of the bottom guidance;  
\(\eta_{1}\)--gearbox efficiency;  
\(\eta_{2}\)--bearing efficiency;  
\(\eta_{3}\)--efficiency of the gear rack and the pinion;  
\(m_{1}\)--weight of the platform;  
\(m_{2}\)--weight of the load;  
\(n_{m}\)--nominal rpm under the load;  
\(g\)--gravitational acceleration;  
\(\alpha\)--slope angle;  
\(v\)--operational speed of the platform;  
\(i\)--gear ratio;  
\(m\)--module of the gear rack and the pinion;  
\(z\)--number of pinion teeth;  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(f_{p1}\) & 0.05 & \(n_{m}\) & 46.666 \(\mathrm{s}^{-1}\) \\ \(f_{p2}\) & 0.05 & \(g\) & 9.81 \(\mathrm{m}\cdot\mathrm{s}^{-2}\) \\ \(r_{p1}\) & 0.0075 \(\mathrm{m}\) & \(\alpha\) & max. 47\(  
\(M_{BR}\)**--friction moment of the bearing; \(R\)**--outer radius of the annulus area of the bearing; \(r\)**--inner radius of the annulus area of the bearing; \(d\)**--reference diameter of the pinion; \(\omega\)**--angular velocity of the pinion. Table 5 contains the moments of resistance forces and the corresponding powers of the platform electromotor, which are determined for all calculated loads. The designations mean the following:  
\(M_{a1}\)**--friction moment of the upper trolley wheels; \(M_{a2}\)**--friction moment of an axial pin of the upper trolley; \(M_{b1}\)**--friction moment of the bottom trolley wheels; \(M_{b2}\)**--friction moment of the side guiding rollers of the bottom platform guidance; \(M_{5}\)**--resistance moment due to the track inclination; \(P_{v}\)**--electromotor power without mechanical losses; \(P_{m}\)**--electromotor power including mechanical losses. Using the described calculation, we detected that the electromotor with the power of \(P_{m}\) = 500 W and with the torque overload coefficient of \(\xi\) = 3.3 is the sufficient solution for the created platform. The dependence of resistance moments and the electromotor power on the load is shown in Figure 10. It indicates values of the electromotor power needed for overcoming resistance moments resulting from the load. Figure 11 depicts the dependence of the electromotor power on the slope angle at constant loads, namely at 225 kg, 300 kg and 375 kg. We can see that the proposed electromotor is a suitable drivetrain for the designed platform (Figure 1) for the real slope angle of \(\alpha=30^{\circ}\) (Figure 3).