## 3 Additional Observation
Therefore, if there was a need for a direct tabular comparison of the basic geometric parameters of the original wheel (which would constitute the first row of the table) with the parameters of the recreated wheel (which would constitute the third row of the table), one more middle row of the table should be added with the values of the parameters of the recreated wheel converted thanks to _EIG_, bringing this wheel to a common module with the original wheel. Table 3 explains this. The situation is different from a technological perspective if the wheel being recreated is to be manufactured using hobbing processing. Previously, two Greek scientists, [PERSON] and [PERSON] [22,23], showed that, in such a case, the filet changes slightly, thus causing a change in the thickness of the tooth at the base. This, in turn, directly affects the bending strength of the tooth. However, the question must be answered: to what extent can the module be changed in relation to the nominal tested gear so that the reconstructed geometry makes mathematical sense and has practical usefulness in terms of the values of alternative geometric parameters? Such a study will be necessary due to geometric and technological limitations in converting a given set of geometric parameters into an alternative set. Figure 3 shows two graphs for an example of a spur gear with straight teeth and parameters: \(z=18\), \(m=5\), \(x=0\), \(y=1\), \(c^{*}=0.2\), \(\alpha=20^{\circ}\). It is clearly visible from Figure 3a that, for module 4.70 (i.e., \(\Delta m=0.30\) mm), a wheel geometry is achieved, which is impossible from the design point of view (for example, due to the negative whole depth factor \(y=-3.604\)). This variant is close to the left asymptote of the graph, for which \(\alpha=0^{\circ}\). However, on the right side, where the graph has no limits on the argument domain, theoretically, the value of the module can be increased indefinitely. However, this graph is not coupled with the limit value of the shift factor at which tooth undercutting occurs at the base. The graph presented in Figure 3b is an alternative version of the graph in Figure 3a, with the parameter on the vertical axis changed from the profile angle to the profile shift factor. The same conclusions can be drawn from it, but it additionally shows the shape of the function of the pres \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(m\) & \(\alpha\) & \(y\) & \(x\) & \(c^{*}\) & \(p_{b}\) [mm] & \(d_{x}\) [mm] & \(s_{x}\) [mm] \\ \hline
1.98 & 18.344\({}^{\circ}\) & 1.028 & \(-0.0876\) & 0.200 & & \\
1.97 & 17.445\({}^{\circ}\) & 1.034 & \(+0.0507\) & 0.165 & & \\
1.96 & 16.490\({}^{\circ}\) & 1.032 & \(+0.1981\) & 0.180 & & \\
1.95 & 15.466\({}^{\circ}\) & 1.020 & \(+0.3576\) & 0.216 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Alternative sets of geometric parameters of the same gear (example data). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \(m\) & \(\alpha\) & \(y\) & \(x\) & \(c^{*}\) \\ \hline The recreated gear & 1.97 & 17.538\({}^{\circ}\) & 1.0339 & \(+0.0509\) & 0.1658 \\ The identical gear (_EIG_) & 1.98 & 18.432\({}^{\circ}\) & 1.0278 & \(-0.0874\) & 0.1666 \\ The nominal gear & 1.98 & 18.344\({}^{\circ}\) & 1.0280 & \(-0.0876\) & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the recreated wheel with the original wheel (example data). the future, it is planned to create three-dimensional design maps to enable more effective recognition of the relationships between all three parameters: \(m\), \(x\), and \(\alpha\). With reference to the previous conclusion, each set of geometric parameters of the gear wheel has its alternative version in an infinite number, but nevertheless within a range limited by the value of the limit shift factor and of the limit whole depth factor. This requires further research in the future. However, during reverse engineering, the authors do not expect to obtain a recreated modulus value that differs significantly from the nominal value.