# Flexible Shear and Normal Force Sensor Using only One Layer of Polyvinylidene Fluoride Film
## 4 Result and Discussion
Since the processed value was independent to the speed of the applied force and was only proportional to the magnitude, this value allowed us to directly obtain the magnitude of the force applied to the sensor. Figure 6 shows the processed value integrated from the sensor output in Figure 6. The peak value of the processed value was proportional to the force applied to the sensor regardless of the speed. When a shear force was applied in the \(+x\) direction, the P1 sensor generated a positive value, whereas the P3 sensor generated a negative value (Figure 6a). When a normal force was applied in the \(-z\) direction, the P1 and P3 sensors generated negative values (Figure 6b). According to these results, we were able to determine whether the direction of the force applied to the sensor was in the \(x\) direction or the \(z\) direction only on the basis of the polarity of the processed value of the P1 and P3 sensors. That is, if \(I_{1}\times I_{3}\ <0\), then a shear force was applied; otherwise, if \(I_{1}\times I_{3}\ >0\), then a normal force was applied. Figure 5: Output voltages of a sensor module when (**a**) a shear stress of 75.67 kPa and (**b**) a normal stress of 96.17 kPa were applied. The red arrows indicate the direction of the applied force. Furthermore, we were able to also estimate the magnitude of the applied force through the peak value of the processed value. Specifically, to study the sensitivity of the applied force through the sensor, we conducted an additional series of experiments using the sensor by applying different shear and normal pressures in the range 45-86 kPa and 100-260 kPa, respectively. The results are plotted as processed value versus pressure in Figure 7a,b. The absolute value of the processed value increased linearly as the applied pressure increased, and the linear fittings were overlapped with these results to compare the sensitivity of each sensor. When a shear force was applied on the sensor, the slopes of the fitting line of the P1, P2, and P3 sensors were 0.910, 0.198, and \(-\)0.390, respectively. At this point, it can be seen that the sensors located on the leg of the trapezoid bump (P1 and P3) were relatively more sensitive than the sensor located on the upper base of the trapezoid bump (P2). When a normal force was applied, the slopes of the fitting line were \(-\)0.194, \(-\)0.119, and \(-\)0.135, respectively. Because of the different sensitivities of the sensors, we could utilize the P1 and P3 sensors to detect the shear force with their signals, which were particularly sensitive to shear force, and we used the remaining sensor (P2) for the normal force. In particular, the force applied to the sensor could be decomposed into \(F_{z}\) in the normal direction and \(F_{x}\) in the shear direction. We expressed \(F_{x}\) as a function of \(I_{x}\), which was defined only by the signals of the P1 and P3 sensors, as follows:  
\[I_{x}=\frac{I_{1}-I_{3}}{2} \tag{2}\]  
where \(I_{1}\) and \(I_{3}\) are the processed values of the P1 and P3 sensors, respectively. Moreover, we expressed \(F_{z}\) as a function of \(I_{z}\), which was defined as follows:  
\[I_{z}=I_{2} \tag{3}\]  
where \(I_{2}\) is the processed value of the P2 sensor. According to these definitions, \(I_{x}\) and \(I_{z}\) are plotted in Figure 7c,d, respectively. We observed that \(I_{x}\) was mainly affected by a change in the corresponding shear force component \(F_{x}\) and had linearity with respect to the shear force (Figure 7c) and that \(I_{z}\) also had the same tendency as that of \(F_{z}\) (Figure 7d). At this time, the value of \(I_{z}\) was comparable to that of \(I_{x}\) when the shear force was applied (Figure 7c), whereas the absolute value of \(I_{x}\) was very small compared to \(I_{z}\) when the normal force was applied (Figure 7d). Therein, the value of \(I_{z}\) had considerable magnitude since it was impossible in reality that only the shear force is applied.