## 3 Results  
Performing an examination of the energy-consumption characteristic points \(E\) as a function of the wheel clamping force \(F_{d}\) (Table 1) showed that there is a clear curvilinear relationship between the wheel clamping force \(F_{d}\) and the energy \(E\) required to drive the wheel of the wheelchair coupled to the roller (Figure 7 S). The characteristics for this roller were approximated using a geometric function (2), with a coefficient of determination R\({}^{2}\) = 0.9965 and an Akaike Information Criterion Corrected (AICC) value of \(-47.454\). This was the third smallest result of all tested function models with a row of no more than 2. The confidence band of the selected mathematical model was represented by confidence intervals for the parameters \(a\) (3) and \(b\) (4), determined at a confidence level of \(p\) = 0.05  
\[E(F_{d})=a\cdot F_{d}^{b\cdot F_{d}}=3.110\cdot F_{d}^{0.0030\cdot F_{d}} \tag{2}\]  
\[a\;\epsilon(3.009;3.211) \tag{3}\]  
\[b\;\epsilon(0.0029;0.0031) \tag{4}\]  
Figure 7: Diagram of mathematical models of characteristics \(E(F_{d})\) for rigid roller S and flexible rollers E, where characteristic points marked as s are measurement points for rigid roller, E8 are measurement points for flexible roller containing 8 spokes, E10 are measurement points for flexible roller containing 10 spokes, E12 are measurement points for a flexible roller containing 12 spokes, E14 are measurement points for a flexible roller containing 14 spokes, E16 are measurement points for a flexible roller containing 16 spokes, and E18 are measurement points for a flexible roller containing 18 spokes. In the case of flexible rollers, an increased scatter of the measured characteristic points was found (Appendix A Tables A1-A6), which indicates the influence of the number of ribs on the energy-consumption characteristic \(E(F_{d})\). To evaluate whether the use of a flexible roller reduces the energy consumption required to drive a wheelchair wheel, a common mathematical model was developed for all variants of the number of ribs in flexible rollers (Figure 7E) (5). Using this simplification, it was assumed that the mathematical function represents a flexible roller with an average number of ribs equal to 13, calculated as the mean across all tested variants. The geometric function used had a coefficient of determination \(R^{2}\) = 0.9396 and an Akaike Information Criterion Corrected (AICC) value of \(-37.569\), which was the third smallest score among all tested function models with an order no greater than 2. The confidence band of the selected mathematical model is presented by confidence intervals of the parameters a (6) and b (7) determined for a confidence level of \(p\) = 0.05. \[E(F_{d})=a\cdot F_{d}^{b\cdot F_{d}}=2.855\cdot F_{d}^{0.0030\cdot F_{d}} \tag{5}\]  
\[a\;\epsilon\langle 2.589;3.121\rangle \tag{6}\]  
\[b\;\epsilon\langle 0.0027;0.0033\rangle \tag{7}\]  
Analyzing the results obtained, it was found that the main trend of the energy-consumption characteristics of the flexible roller \(E(F_{d})\) is below those of the rigid roller. This finding is supported by the derived mathematical function model for the entire set of points measured during the flexible roller test (Figure 7E). Based on the measured characteristics, it is shown that the use of flexible rollers results in a reduction in the energy required to drive the wheel coupled to the roller of the reverse lock module. For the clamping force \(F_{d}\) = 10 N, this reduction is 8%, while for \(F_{d}\) = 100 N, it increases to 13%. The positive effect of using flexible elements in reducing the negative impact of variable force forcing is confirmed by studies of flexible wheelsets in locomotives [29]. A linear relationship was also identified between the clamping force of the reversing lock module roller \(F_{d}\) and the percentage reduction in energy consumption \(\Delta E_{S-E}\) between the rigid and flexible rollers (Figure 8).