# Design and Calibration of a Tri-Directional Contact Force Measurement System
## 6 Discussion of Results  
Results of the calibration procedure showed the expected linear behavior of the force sensors that measured the applied axial forces with reasonable accuracy but it also showed coupling error in the unloaded sensor branches due to the mechanical coupling. Apart from the transmission of mechanical coupling, the error can also be attributed to the slight inaccuracy in positioning of the sensors during the assembly. Nevertheless, for necked collar links, the coupling error was observed to be slightly less as compared to the locknut collar links due to its geometry with slender section that allowed bending and acted as hinge. Repeatability test indicated that the disassembling and reassembling process affects the calibration matrix, which means that for accurate measurement, the calibration of the force measurement system will have to be performed once it is installed on the experimental test rig and will have to be repeated if the sensors are disassembled and reassembled. Results of the simultaneous loading test yet again proved the existence of the coupling between the three branches. Coupling errors were found to be substantial after examining the force measured by each force sensor for each load case. However, it was observed once more that the coupling error for the necked collar link was less than that for the locknut collar. Alternatively, the decoupling matrix was used to compute the decoupled applied forces that considerably reduced the error percentage and were checked to be within 2% of the actual values. The decoupling method was marginally more effective for measurement system with necked collar links as compared with locknut collar links because of the relatively less coupling error in the first place. The dynamic loading experiment demonstrated the ability of the measurement system to measure the dynamic forces. Generally, the three force sensors independently displayed good dynamic characteristics with fast response and with no delay. However, operating in the tripod configuration, dynamic errors were observed that can also be attributed to the mechanical coupling and to the slight misalignment during the assembly and during the loading of the third sensor. The decoupling method was effective in computing the decoupled forces from the measured dynamic forces irrespective of their amount. The mean absolute errors evaluated for the decoupled forces were fairly less as compared to the mean absolute errors calculated with the forces measured directly during the dynamic loading experiment. However, the performance of the tri-directional force measurement system was adversely affected when the excitation frequency was above the first natural frequency of the system. This factor limited the range of excitation frequency at which the force measurement system could be dynamically tested. Nevertheless, this is not a general threshold frequency of the force measurement system and it depends on the structure where the force measurement system is mounted. The study demonstrated that the proposed force measurement system was able to measure dynamic forces with good accuracy for excitation frequency less than the first natural frequency of the system. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{3}{c}{**Applied Forces (N)**} & \multicolumn{6}{c}{**Mean Absolute Error (N)**} \\ \hline
**Freq** & **Amp** & **Static** & \multicolumn{3}{c}{**Measured Force Outputs**} & \multicolumn{3}{c}{**Decoupled Applied Forces**} \\ \hline
**Hz** & \(F_{\mathbf{x}}\), \(F_{\mathbf{y}}\) & \(F_{\mathbf{z}}\) & \(F_{1}\) & \(F_{2}\) & \(F_{3}\) & \(\widetilde{F}_{\mathbf{x}}\) & \(\widetilde{F}_{\mathbf{y}}\) & \(\widetilde{F}_{\mathbf{z}}\) \\ \hline
100 & 6.5 & 7.8 & 0.2218 & 0.4966 & 0.3642 & 0.1630 & 0.2269 & 0.1403 \\
100 & 12 & 17.8 & 0.5290 & 1.1998 & 0.7268 & 0.3244 & 0.1880 & 0.1732 \\
100 & 17.5 & 27.8 & 0.6686 & 2.0222 & 0.9254 & 0.0986 & 0.1161 & 0.0371 \\
100 & 31.5 & 47.3 & 1.3155 & 3.2154 & 1.5284 & 0.3416 & 0.2689 & 0.0475 \\ \hline \hline \end{tabular}
\end{table}