## 3 Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\mathbf{F_{d}}\) [N] & & \(\mathbf{E}\) [J] & \\ \hline
**avg** & \(\pm\) & **avg** & \(\pm\) \\ \hline
12.70 & 1.01 & 3.49 & 0.06 \\
29.05 & 1.26 & 4.22 & 0.05 \\
28.48 & 1.24 & 4.12 & 0.07 \\
37.25 & 1.28 & 4.76 & 0.07 \\
39.93 & 1.28 & 4.95 & 0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the points of the energy intensity characteristic \(E\) of the rigid roller as a function of the clamping force \(F_{d}\), determined on the basis of the measurement sample n = 5 and the confidence level \(p\) = 0.05. Figure 8: Plot of reduction in energy demand when using flexible rollers \(\Delta E_{S-E}\) as a function of roller clamping force \(F_{d}\). The determined linear relationship of energy reduction was written with the mathematical function (8):  
\[\Delta E_{5-E}=(0.0005\cdot F_{d}+0.0777)\cdot 100\% \tag{8}\]  
In the case of reducing the propulsion energy required when using flexible rollers, the number of ribs in the roller used had a significant effect. Based on the measured characteristic points (Appendix A, Tables A1-A6), a mathematical function model was determined for each roller variant (Figure 9). The determined characteristics are described by a common model of the mathematical function (9), while the parameters of the model depend on the number of ribs present in the roller with geometric dimensions according to Figure 5. The ranges of variation for the parameters and the model fit evaluation indices for the different rib number variants are presented in Table 2.  
\[E(F_{d})=a\cdot F_{d}^{b\cdot F_{d}} \tag{9}\]  
All the determined characteristics of flexible rollers after exceeding the clamping force \(F_{d}=50\) N are below those of a rigid roller. This indicates that flexible rollers reduce the energy demand associated with driving the wheel coupled frictionally to the roller of the reversing lock module. Only rollers E16 and E18 result in higher energy consumption for a clamping force \(F_{d}\) below 50 N. This phenomenon is attributed to the stiffening of the flexible rollers caused by the large number of ribs, which results in negligible deformation under low clamping forces. Figure 9: Diagrams of mathematical models of characteristics \(E(F_{d})\) for rollers: S—rigid, E8—flexible with 8 ribs, E10—flexible with 10 ribs, E12—flexible with 12 ribs, E14—flexible with 14 ribs, E16—flexible with 16 ribs, E18—flexible with 18 ribs. The analysis of the change in energy intensity was carried out for a procedure that did not take into account the number of ribs in the flexible roller (from 8 to 18 ribs) (Figure 10). This involved taking measurements for all roller variants and deriving an averaged model for a flexible roller with an average number of ribs equal to 13. This approach allowed checking only the effect of the direction of rotation of the wheelchair wheel on the energy intensity of the wheelchair wheel-flexible roller system of the reversing lock module. On the basis of the performed measurements of the characteristic points for each variant, an averaged model of the mathematical function describing the energy intensity of the tested (\(E_{DH}\) and \(E_{DS}\)) system during driving in the DH direction (10) and the DS direction was derived. (11). For the function describing the DH direction, a coefficient of determination \(R^{2}\) = 0.857 and an Akaike Information Criterion Corrected (AICC) value of \(-\)16.53 were obtained, which represented the second smallest result among all tested function models with an order not greater than 2. Conversely, for the function describing the DS direction, a coefficient of determination \(R^{2}\) = 0.917 and an AICC value of \(-\)28.76 were obtained, making it the smallest result among all tested function models with an order not greater than 2.