## 5 Experimental Results and Discussion
### Experimental Results
\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 8: Stochastic results for the measured input forces when \(v\) = 25 mm/s. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Term**} & \multicolumn{4}{c}{**Stochastic result (mm)**} \\ \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 Initial stroke position \(S_{i}\) & \(-\)0.074 \(\pm\) 0.028 & \(-\)0.017 \(\pm\) 0.020 & \(-\)0.104 \(\pm\) 0.017 & \(-\)0.129 \(\pm\) 0.017 \\ Final stroke position \(S_{f}\) & 45.378 \(\pm\) 0.017 & 45.403 \(\pm\) 0.012 & 45.460 \(\pm\) 0.003 & 45.425 \(\pm\) 0.006 \\ Stroke \(S\) & 45.452 \(\pm\) 0.037 & 45.420 \(\pm\) 0.016 & 45.564 \(\pm\) 0.017 & 45.555 \(\pm\) 0.014 \\ Stroke error \(\Delta S\) & 0.448 \(\pm\) 0.037 & 0.417 \(\pm\) 0.016 & 0.561 \(\pm\) 0.017 & 0.551 \(\pm\) 0.014 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Stochastic results for the measured output positions when \(v\) = 15 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 \(F_{\text{F(max)}}\) & 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 \(\pm\) 25.54 From the stochastic results listed in Tables 3-5, it can be observed that the mean values of the initial and final stroke positions, \(S_{i}\) and \(S_{f}\), all slightly deviated from their theoretical values 0.000 and 45.003 mm, respectively. For all of the three input speeds, the positional deviations for the mean values of \(S_{i}\) ranged between \(-0.011\) and \(-0.180\) mm, and those for  
Figure 16: The averaged input force curves obtained when \(v=25\) mm/s. Figure 14: The averaged input force curves obtained when \(v=5\) mm/s. Figure 15: The averaged input force curves obtained when \(v=15\) mm/s. the mean values of \(S_{f}\) ranged between 0.269 and 0.466 mm; while the mean values of the resultant stroke errors, \(\Delta S\), ranged between 0.383 and 0.561 mm. The varying trends of the positional deviations were not quite proportional to the increased magnitudes of \(\Delta\)\(\pi_{8}\) and \(v\). Such positional uncertainties should be mainly caused by clearances in revolute joints of the constructed mechanism, since such clearances caused by sliding fits [29] could not be completely eliminated and would result in a similar effect of \"backlash\" when producing reciprocating motions. However, the varying trends of the resultant stroke errors were approximately proportional to the increased magnitudes of \(\Delta\)\(\pi_{8}\) and \(v\).