## 3 Design of the Accepted Solution
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**X = +0.1 m** & **225 kg** & **300 kg** & **375 kg** & **X = \(-\)0.1 m** & **225 kg** & **300 kg** & **375 kg** \\ \hline \(R_{az}\) (N) & 2786.39 & 3483.74 & 4171.09 & \(R_{az}\) (N) & 2786.39 & 3483.74 & 4181.09 \\ \(R_{bz}\) (N) & 2786.39 & 3483.74 & 4181.09 & \(R_{bz}\) (N) & 2786.39 & 3483.74 & 4181.09 \\ \(R_{bt}\) (N) & 2719.17 & 3257.26 & 3795.35 & \(R_{bt}\) (N) & 2719.17 & 3257.26 & 3795.35 \\ \(R_{an}\) (N) & \(-\)307.81 & \(-\)437.54 & \(-\)567.27 & \(R_{an}\) (N) & 708.42 & 917.43 & 1126.44 \\ \(R_{bm}\) (N) & 2843.47 & 3474.98 & 4106.5 & \(R_{bm}\) (N) & 1827.24 & 2120.01 & 2412.78 \\ \(\sum\lvert R_{an}\rvert+\lvert R_{bn}\rvert\) (N) & 3151.28 & 3912.52 & 4673.77 & \(\sum R_{an}+R_{bm}\) (N) & 2535.66 & 3037.44 & 3539.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculated values of reaction effects considering the geometry of the device and values of loads. Furthermore, these results are used for the calculation of resistance forces, which arise during the platform operation on the track. Because of the rolling of guiding wheels of the trolleys (Figure 7), rolling resistance arises. This rolling resistance occurs between wheels and pins. Movement of the platform causes elastic deformation of the track as well as the platform wheels. This elastic deformation results in resistance moment arising. As we can see in Figure 7, the upper trolley transmits the reactions \(R_{az}\) and \(R_{an}\). Four guiding wheels are mounted on the trolley, however they do not ensure the transmitting of the force \(R_{az}\), therefore, it is assumed, that a sliding force between the guiding wheels and the spacer rings side surfaces will arise. On the contrary, the force \(R_{an}\) causes rolling resistance and pin friction during the operation. The total resistance of the guiding wheel is given by the following formulations:  
\[M_{a1}=R_{an}\cdot(e_{a1}+r_{\alpha 1}\cdot f_{\alpha 1}), \tag{12}\]  
\[M_{a1}=\frac{(G_{1}+G_{2})\cdot\sin\alpha\cdot 32-G_{2}\cdot x}{t}\cdot(e_{a1}+r _{\alpha 1}\cdot f_{\alpha 1}). \tag{13}\]  
The friction resistance moment of the spacer ring is calculated as follows:  
\[M_{a2}=f_{k}\cdot\int\limits_{L}^{R}x\cdot dR_{az}. \tag{14}\]  
Figure 6: Dependence of values of the reaction forces \(R_{an}\), \(R_{bn}\) and \(R_{sum}\) on the platform geometry (position of the centre of gravity \(G_{2}\)). Figure 7: Transmission of reaction forces on the upper trolley of the platform. The area (Figure 8), on which the force \(R_{az}\) acts, is determined:  
\[S=\pi\cdot\Big{(}R^{2}-r^{2}\Big{)}. \tag{15}\]  
The value of the pressure acting on the spacer ring is calculated:  
\[p=\frac{R_{az}}{S}=\frac{R_{az}}{\pi\cdot(R^{2}-r^{2})}. \tag{16}\]  
Substituting the Equations (20) and (21) into the Equation (18) we obtain:  
\[M_{a2}=f_{k}\cdot\int\limits_{r}^{R}x\cdot\frac{R_{az}}{\pi\cdot(R^{2}-r^{2})} \cdot dA, \tag{17}\]  
where the elementary surface \(dA\) is shown in Figure 8 and it is given by the formulation:  
\[dA=2\cdot\pi\cdot x\cdot dxM. \tag{18}\]  
By application of the Equation (16) into the Equation (14) we obtain:  
\[M_{a1}=R_{an}\cdot(e_{a1}+r_{\alpha 1}\cdot f_{\alpha 1}), \tag{12}\]0  
\[M_{a1}=R_{an}\cdot(e_{a1}+r_{\alpha 1}\cdot f_{\alpha 1}), \tag{12}\]1  
\[M_{a1}=R_{an}\cdot(e_{a1}+r_{\alpha 1}\cdot f_{\alpha 1}), \tag{12}\]2  
As we can see in Figure 9, the bottom trolley transmits the force reactions \(R_{bm}\), \(R_{bz}\) and \(R_{bt}\). The first reaction \(R_{bm}\) is transmitted by means of guiding wheels, which are mounted on rolling bearings. \[M_{a1}=R_{an}\cdot(e_{a1}+r_{\alpha 1}\cdot f_{\alpha 1}), \tag{12}\]3 (**a**) The elementary area and integration boundaries for determining the resistance moment; (**b**) the reduction in the slope resistance to the output shaft of the platform drivetrain. The force \(R_{bz}\) is transmitted to the platform mechanism by means of side rollers, which are mounted on steel pins.