## 2 Materials and Methods  
### Materials and Experimental Setup  
Figure 1 shows the experimental setup for the implementation of the proposed two-point bending test. Consequently, a total of sixteen two-point bending tests were carried out on the six strain gauges used as force sensors. The tests were carried out utilizing an INSTRON 4467 universal testing machine, which has a cell load of 10 N and a precision of 0.0025 N. Through the control panel and the software IX of the INSTRON, the geometric parameters and the characteristics of each test were defined. Furthermore, the reference values for force and displacement were established. All of the tests were performed at a constant speed of 1 mm/min, with a total displacement of the loading nose of 2 mm, which is in agreement with the ASAE Standard method S368.2 [21]. Simultaneously, the instrumental signal (indicated in Section 2.2) was recorded as a result of the data acquisition system, the devices developed, and the proposed strain gauge. In this sense, to subject the strain gauge to pure bending, each sensor was embedded within the sensing area employing two 3 mm thick printed circuit boards (PCB). Thus, these points are mentioned in Table 1, while the PCB plates were fitted to a 10-mm-thick acrylic plate (base of the materials testing machine) through an aluminum device as shown in Figure 1a,c. In this study, six strain gauges (from G1 to G6 as shown in Figure 1a,c) used as force sensors were assessed. The strain gauges employed were simple, uniaxial, miniature strain gauges fabricated with copper-nickel alloy and completely coated with polyamide [22]. Their average geometric dimensions were 2.56 mm wide, 6.0 mm long and 0.06 mm thick, and their sensing area was 1.6 mm wide and 2.0 mm long, with a nominal resistance of 120\(\Omega\). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Sensor Dimensions**} & \multicolumn{4}{c}{**Trial Characteristics**} \\ \hline
**Sensor** & **b (mm)** & **e (mm)** & **Lo (mm)** & **Lo/e** & **x\({}_{\mathbf{o}}\) (mm)** & **Rep** & **x\({}_{\mathbf{o}}\)/e** & **x\({}_{\mathbf{o}}\)/Lo** & **k (mm)** & **T (\({}^{\circ}\)C)** \\ \hline G1 & 2.54 & 0.060 & 2.27 & 37.8 & 1.22 & 5 & 20.3 & 0.54 & 0.30 & 27.9 \(\pm\) 0.4 \\ \hline G2 & 2.58 & 0.055 & 3.25 & 59.1 & 2.30 & 2 & 41.8 & 0.71 & 0.60 & 26.4 \(\pm\) 1.0 \\ \hline G3 & 2.54 & 0.050 & 2.30 & 46.0 & 1.35 & 2 & 27.0 & 0.59 & 0.35 & 26.4 \(\pm\) 0.6 \\ \hline G4 & 2.58 & 0.065 & 2.53 & 38.9 & 1.68 & 2 & 25.8 & 0.66 & 0.69 & 26.6 \(\pm\) 0.4 \\ \hline G5 & 2.54 & 0.065 & 2.46 & 37.8 & 1.51 & 2 & 23.2 & 0.61 & 0.44 & 26.5 \(\pm\) 0.4 \\ \hline G6 & 2.52 & 0.065 & 1.88 & 28.9 & 1.00 & 3 & 15.4 & 0.53 & \(-\)0.05 & 19.2 \(\pm\) 2.6 \\ \hline Average & 2.55 & 0.060 & 2.45 & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimensions of the strain gauge sensors and characteristics of the bending tests. Figure 1: Proposed two-point bending test: (**a**) INSTRON and experimental setup for implementing the bending test (loading nose width 1.0 \(\pm\) 0.05 mm), (**b**) scheme of the bending test and data recording, (**c**) details of the strain gauge embedment. Table 1 shows the geometric dimensions and mechanical characteristics of the strain gauges used in the bending tests. Width (b), thickness (e), and the beam span (L\({}_{0}\)) were measured using a micrometer with a precision of 0.01 mm. The position of the loading nose concerning the embedent (x\({}_{\text{o}}\)) and the location of the embedent concerning the central axis of the sensing area (k) were measured using a Vernier caliper with a precision of 0.05 mm and verified using a photographic sample with a precision of 0.01 mm. The number of repetitions (R) was reduced to two due to the low coefficient of variation obtained for the G1 sensor, for which five repetitions were carried out.