## 3 Results and Discussion  
Figure 3a illustrates the printed strain-gauge pattern on the PET substrate. The pattern was 7.76 mm in width and 13 mm in length. Seven samples were prepared for each topographical condition. The initial resistances of the printed strain-gauge patterns after sintering are depicted in Figure 3b. The resistance steadily decreased as the number of stacked layers or the width increased. The mean and standard deviation (SD) values of the resistance for each topographical condition are summarized in Table 1. The maximum percentage coefficient of variability, calculated as SD/mean \(\times\) 100 (%CV), was 3.8% for the seven-droplet pattern. The minimum %CV was 1.6% for the two-droplet pattern. All %CV values were less than 5%, demonstrating the excellent reliability of the experimental dataset. In addition, normality was verified in the Anderson-Darling test for all datasets, as presented in Table 1 (\(p\) > 0.05). Figure 2: (**a**) Three-dimensional printer. (**b**) Three-dimensionally printed pillars with various arc-shaped cross sections. Figure 4 shows the cross-sectional profiles of the printed strain-gauge patterns. Figure 4a indicates that the thickness of the printed pattern was proportional to the number of stacked layers, and that the evenness of the pattern deteriorated for the five-layer pattern. It is assumed that the amount of evaporation was greater in the edge area of the deposited ink than in the central area, and that the resulting unbalanced evaporation forced the solute to move to the side area, producing a so-called coffee-ring effect [20,21]. The thickness of the coffee-ring stain superposed in the following printed layers. The peaks for single-, three- and five-layer patterns were 0.11934 \(\upmu\)m, 0.32591 \(\upmu\)m and 1.0 \(\upmu\)m, respectively. Figure 4b illustrates the cross-sectional profiles of the printed strain-gauge patterns as a function of the numbers of droplets. The widths of the two-, four- and seven-droplet patterns with a fixed drop spacing of 30 \(\upmu\)m were 144.87 \(\upmu\)m, 176.19 \(\upmu\)m and 264.29 \(\upmu\)m, respectively. The width was not much smaller for two droplets than for four droplets, because the droplet could spread on the hydrophilic substrate to result in a compressed \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Topography**} & \multicolumn{1}{c}{**Mean (\(\Omega\))**} & \multicolumn{1}{c}{**SD (\(\Omega\))**} & \multicolumn{1}{c}{**\%CV**} & \multicolumn{1}{c}{\(p\)**} \\ \hline Stacked & Five layers & 111.04 & 3.08 & 2.8 & 0.136 \\ layers & Three layers & 273.23 & 8.21 & 3.0 & 0.639 \\  & Single layer & 774.00 & 18.36 & 2.4 & 0.069 \\ \hline Width & Seven & 410.87 & 15.52 & 3.8 & 0.304 \\  & droplets & 580.41 & 11.39 & 2.0 & 0.477 \\  & Two droplets & 927.78 & 15.02 & 1.6 & 0.687 \\ \hline \hline \end{tabular} SD, standard deviation; \%CV, percentage coefficient of variability.  
\end{table} 
Table 1: Statistical evaluation of measured resistances of the printed strain-gauge patterns. Figure 4: Cross-sectional profiles of printed strain-gauge patterns as a function of (**a**) the number of stacked layers and (**b**) the width. Figure 3: (**a**) Design of the printed strain gauge. (**b**) Resistance variations of the printed strain gauges. Blue and orange bars are for stacked layers and different widths, respectively. Data are mean and standard deviation values. The influence of the topography of the printed serpentine pattern on the sensitivity was investigated. The stacked-layer specimens were subjected to tensile stress in a bending test. The strains calculated using Equation (2) varied from 0.625% to 2.5%. It was observed that the gauge factor increased from 2.471 to 3.098 as more layers were stacked, as shown in Figure 7. It was particularly interesting that the gauge factor also increased with the number of droplets, corresponding to an increased width. The gauge factor varied from 2.047 for two droplets to 2.589 for seven droplets, as shown in Figure 8.