# A Low-Cost IoT-Based Bidirectional Torque Measurement System with Strain Gauge Technology
## 4 Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Applied Torque** & **Indicated** & **Standard Deviation** & **2 \(\times\) Standard** \\
**[N\(\cdot\)m]** & **Torque** & **[N\(\cdot\)m]** & **Deviation** \\ \hline
50 & 49.88658495 & 0.112584012 & 0.225168025 \\
45 & 45.64236065 & 0.155528737 & 0.311057475 \\
40 & 38.48384461 & 0.832847645 & 1.66569529 \\
35 & 34.59844455 & 0.889128071 & 1.778256143 \\
30 & 29.54496305 & 1.061565722 & 2.123131444 \\
25 & 27.42266205 & 1.782940305 & 3.565880609 \\
20 & 21.39366942 & 1.174873253 & 2.349746505 \\
15 & 13.15642551 & 0.133933479 & 0.267866959 \\
10 & 8.926782281 & 0.166290230 & 0.332580460 \\
5 & 5.188683855 & 0.298111577 & 0.596223154 \\ \(-\)5 & \(-\)4.244757547 & 0.674121561 & 1.348243122 \\ \(-\)10 & \(-\)9.750358511 & 1.007054651 & 2.014109302 \\ \(-\)15 & \(-\)15.06403354 & 1.170535944 & 2.341071889 \\ \(-\)20 & \(-\)20.14973559 & 1.215338251 & 2.430676502 \\ \(-\)25 & \(-\)25.07085006 & 1.196657446 & 2.393314893 \\ \(-\)30 & \(-\)29.96374104 & 1.143910161 & 2.287820322 \\ \(-\)35 & \(-\)34.94836928 & 1.037376598 & 2.074753196 \\ \(-\)40 & \(-\)40.00695376 & 0.845718874 & 1.691437749 \\ \(-\)45 & \(-\)44.9693359 & 0.583960687 & 1.167921373 \\ \(-\)50 & \(-\)49.9673941 & 0.328666241 & 0.657332481 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical analysis of calibration results. Figure 5: Calibration curve showing applied torque vs. indicated torque using fifth-order polynomial regression. The cost-accuracy analysis presented in Table 5 shows a markedly nonlinear relationship across the seven benchmarked designs. The Proposed Sensor (ID 1) sets the lowest cost at EUR 27 while achieving \(\pm\)2.5 N\(\cdot\)m (\(\approx\)5%FS) over \(\pm\)50 N\(\cdot\)m, a level of precision adequate for many service-robot tasks. A modest step up to the Exoskeleton Sensor (ID 2) halves the error to \(\pm\)2%FS across the same span, yielding the most favorable cost-to-accuracy ratio. The three low-torque variants, 1 N\(\cdot\)m, 5 N\(\cdot\)m, and 20 N\(\cdot\)m Sensors (ID 3-5), remain below EUR 100 yet confine capacity to \(\leq\)20 N\(\cdot\)m. Their 1-2%FS performance rivals both cheaper and dearer units when normalized to full scale. The Walking Robot Sensor (ID 6) quadruples the ID 2 cost to USD 213, attaining similar \(\leq\)2%FS accuracy; its price premium largely reflects environmental sealing and multi-axis capability rather than metrological gain. The Optical Sensor (ID 7) commands the highest price (USD \(<\) 250) and delivers the tightest tolerance (\(\pm\)1.5% RMS) but only within \(\pm\)5 N\(\cdot\)m, illustrating diminishing returns beyond the EUR 100 threshold unless exceptional low-torque precision is required. The qualitative distinctions presented in Table 6 pivot on calibration lineage, enclosure strategy, and wireless autonomy. The Proposed Sensor (ID 1) combines a fifth-order polynomial fit with integrated radio, targeting controlled-environment deployments. ID 2 benchmarks against a commercial transducer, encloses electronics in a 3D printed shell, and offers NRF24L01 telemetry, balancing laboratory reliability with wearable portability. Variants ID 3-5 inherit the same ATI-based calibration but forego both enclosure and wireless capability, maximizing economy for benchtop use. ID 6 couples six-axis load cell calibration with ESP32 Wi-Fi/BLE inside an IP67 case, delivering the most field-ready architecture at higher material and assembly costs. ID 7 relies on optical scale-factor fitting within a rigid CNC-milled aluminum enclosure and omits wireless capability, prioritizing structural stability and optical cleanliness over mobility. Overall, enclosure robustness and communication freedom, rather than calibration sophistication alone, drive the major architectural divergences among contemporary low-cost torque sensors.