## 2 Materials and Methods
### Pinch Data Acquisition System
\[\text{Force}=-0.9447+0.02371\times\text{Voltage}+0.3632\times\text{Position}, \tag{1}\]  
In performing the hysteresis test to the customized pinch force load cell, dynamic loading (0-50 N) and unloading (from 50 to 0 N) were applied at the contact point 11.5 mm, which is approximately  
Figure 4: Stress analysis of the pincer object where an external force is applied at the free end. Figure 3: Pinch force load cell. at the midpoint of the pinching length. Figure A1 (Appendix A) shows the loading and unloading curves of voltage and force measurements recorded from the pinch force load cell and INSTRON(r) 3366 machine, respectively. The solid line is the force-voltage relationship for dynamic loading, while the dotted line is the force-voltage relationship for dynamic unloading. The hysteresis is defined as the difference in voltage offset between loading and unloading lines at the midpoint on the force axis. The following formula gives the percentage of hysteresis:  
\[\text{Hysteresis}=100\%\times(V_{mu}-V_{ml})/(V_{max}-V_{min})=0.287\%. \tag{2}\]  
where \(V_{mu}\) (892.46 mV) is the voltage value on the unloading line in Figure A1 at midpoint force \(F_{m}\) (23.86 N), \(V_{ml}\) (898.1 mV) is the voltage value on the loading line at \(F_{m}\), \(V_{max}\) (1960.86 mV) is the maximum voltage value on the loading line, and \(V_{min}\) (0 mV) is the minimum voltage value on the unloading line. The hysteresis of 0.287% can be considered negligible [52]. Furthermore, it is much lower than the hysteresis of thin-film pressure sensors (5%) [53]. Similar hysteresis tests were performed at the other contact points resulting in similarly negligible hysteresis. Figure 3.0 Calibration setup of the pinch force load cell. Figure 3.1 _Cont._  
In performing the repeatability test, a dynamic loading (0-50 N) was applied three times at the contact point 11.5 mm. The Coefficient of Variation (CV) was used to calculate the repeatability. CV is given by the ratio between standard deviation and mean values of three repeated voltage measurements at each force point ranging from F\({}_{\text{min}}\) (2.28 N) to F\({}_{\text{max}}\) (50 N). Then, all CVs are averaged to provide a single CV [49; 54]. The \"Cfvar\" function in SPSS Statistics(r) V21 was used to calculate the CV. The CV value of \(1.43\pm 0.447\%\) was obtained which indicates high repeatability [55]. In addition, it is smaller than the CV value of thin-film pressure sensors (\(2.1\pm 2.3\%\)) [49]. In replacing the manual gentle pull by the therapist, a linear electric system was used. The linear actuator system consists of a linear electric actuator, AC servo motor, AC servo driver, and Arduino(r) Due. To run the linear electric actuator, an AC servo motor (SM0602--400 Watt) was coupled in-line to the drive cap of the linear electric actuator. The output analog signal of Arduino(r) Due controls the AC servo motor through the AC servo driver (M2 DV-3D02R). The linear actuator system can exert automatic pulling force ranging from 0 to 63.25 N with a resolution of 0.5 N.  
A pulling force is produced when the volunteer pinches the pincer object and then resists the automatic pull generated by the linear actuator system. An off-the-shelf pulling force load cell (STA-1-50 Aluminium S Type Tension) is located between the pincer object and the linear electric actuator to measure the pulling force. The voltage-force relationship of the pulling force load cell was established by the manufacturer, as shown in Figure 3.2 The pulling force load cell has 0.03% accuracy, 0.01% repeatability, 0.05 N resolution, and R\({}^{2}\) = 1 linearity. Figure 3.3 (**a**) Force–voltage curves at five contact points; and (**b**) estimated plane of force as a function of voltage and position. Figure 3.4 Voltage–force relationship for pulling force load cell. In detecting the slip onset, the LVDT displacement sensor was used. The LVDT sensor and linear electric actuator were clamped together such that they move in parallel.