## 5 Experimental Results and Discussion
### Experimental Results  
Some stochastic results for the experiments that might be of interest are listed in Tables 3-8. Tables 3-5 list the results for the measured output positions when \(v\) = 5, 15, and 25 mm/s, respectively, in which, the stochastic values (i.e., the mean values with their uncertainty ranges evaluated by using the three-standard-deviation-band approach [30]) of the initial stroke position \(S_{i}\) (i.e., the relatively initial position of the moving platen measured when \(x=-3.439\) mm), the final stroke position \(S_{f}\) (i.e., the relatively final position of the moving platen measured when \(x=51.566\) mm), the stroke \(S\) (i.e., the overall moving distance of the moving platen measured in one motion cycle), and the stroke error \(\Delta S\) (when the theoretical stroke is 45.003 mm referring to Figure 6) are presented. Tables 6-8 then list the results for the measured input forces when \(v\) = 5, 15, and 25 mm/s, respectively, in which, the stochastic values of the extreme and root-mean-square (RMS) values in the forward stroke (FS) \(F_{\text{F(max)}}\) and \(F_{\text{F(rms)}}\) (i.e., the maximum and RMS values of the input force in the FS), the extreme and RMS values in the backward stroke (BS) \(F_{\text{B(min)}}\) and \(F_{\text{B(rms)}}\) (i.e., the minimum and RMS values of the input force in the BS), and also the measured input forces at the toggle position (when \(x=51.566\) mm in the FS) \(F_ \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Term**} & \multicolumn{4}{c}{**Stochastic result (N)**} \\ \cline{2-5}  & \(\Delta r_{\text{g}}\) = 0.00 mm & \(\Delta r_{\text{g}}\) = 0.25 mm & \(\Delta r_{\text{g}}\) = 0.50 mm & \(\Delta r_{\text{g}}\) = 0.75 mm \\ \hline Extreme value in FS \(F_{\text{F(max)}}\) & 66.032 \(\pm\) 17.772 & 48.819 \(\pm\) 14.692 & 108.367 \(\pm\) 12.236 & 269.966 \(\pm\) 36.694 \\ RMS value in FS \(F_{\text{F(rms)}}\) & 23.045 \(\pm\) 3.054 & 19.025 \(\pm\) 1.516 & 40.357 \(\pm\) 6.898 & 117.941 \(\pm\) 17.599 \\ Extreme value in BS \(F_{B\text{(min)}}\) & \(-\)147.437 \(\pm\) 25.544 & \(-\)54.892 \(\pm\) 6.975 & \(-\)84.609 \(\pm\) 10.057 & \(-\)246.336 \(\pm\) 22.966 \\ RMS value in BS \(F_{B\text{(rms)}}\) & 59.982 \(\pm\) 5.610 & 28.155 \(\pm\) 2.013 & 33.094 \(\pm\) 2.694 & 104.091 \(\pm\) 10.206 \\ Value at toggle position \(F_{\text{TP}}\) & 2.877 \(\pm\) 3.386 & 28.690 \(\pm\) 9.473 & 106.655 \(\pm\) 11.971 & 223.383 \(\pm\) 27.948 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Stochastic results for the measured input forces when \(v\) = 5 mm/s. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Term**} & \multicolumn{4}{c}{**Stochastic result (N)**} \\ \cline{2-5}  & \(\Delta r_{\text{g}}\) = 0.00 mm & \(\Delta r_{\text{g}}\) = 0.25 mm & \(\Delta r_{\text{g}}\) = 0.50 mm & \(\Delta r_{\text{g}}\) = 0.75 mm \\ \hline Extreme value in FS \(F_{\text{F(max)}}\) & 113.887 \(\pm\) 9.546 & 75.209 \(\pm\) 4.825 & 149.142 \(\pm\) 12.193 & 300.124 \(\pm\) 23.999 \\ RMS value in FS \(F_{\text{F(rms)}}\) & 24.850 \(\pm\) 1.917 & 28.582 \(\pm\) 2.044 & 60.052 \(\pm\) 5.255 & 135.961 \(\pm\) 12.514 \\ Extreme value in BS \(F_{B\text{(min)}}\) & \(-\)52.013 \(\pm\) 3.904 & \(-\)76.086 \(\pm\) 6.657 & \(-\)117.523 \(\pm\) 14.073 & \(-\)292.028 \(\pm\) 21.391 \\ RMS value in BS \(F_{B\text{(rms)}}\) & 27.452 \(\pm\) 1.097 & 32.503 \(\pm\) 2.859 & 48.496 \(\pm\) 4.294 & 131.139 \(\pm\) 10.510 \\ Value at toggle position \(F_{\text{TP}}\) & 0.878 \(\pm\) 4.076 & 18.186 \(\pm\) 5.898 & 145.657 \(\pm\) 11.635 & 266.727 \(\pm\) 23.079 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Stochastic results for the measured output positions when \(v\) = 15 mm/s.