# A Low-Cost IoT-Based Bidirectional Torque Measurement System with Strain Gauge Technology
## 1 Introduction  
Torque measurement plays a pivotal role in automotive engineering, machine diagnostics, and industrial process control, enabling engineers to optimize performance, ensure safety, and implement predictive maintenance strategies [1, 2, 3, 4]. In automotive drivetrains, for example, real-time torque data can reveal inefficiencies, mechanical failures, or abnormal operating conditions before they escalate into costly repairs or hazardous situations. The system specifically targets the absence of low-cost, bidirectionally calibrated torque sensors for drivetrain shafts in small laboratories and resource-constrained factories, where high-cost commercial solutions remain prohibitive. The key innovation lies in the systematic integration of commercially available components with robust bidirectional calibration methodology and wireless data transmission, specifically designed for rotating shaft applications. The mounting methodology for rotating shafts and the comprehensive polynomial calibration approach for both clockwise and counterclockwise torque measurement represent the primary technical contributions. The development of this torque sensor system addresses the need for affordable, bidirectional torque measurement in automotivedrivetrains. While commercial sensors provide high accuracy, their cost and proprietary calibration protocols limit accessibility for research and small-scale industrial applications. This work introduces an alternative Internet of Things (IoT)-enabled platform that integrates low-cost components (e.g., 24-bit signal amplifier HX711, ESP8266) with robust polynomial calibration, enabling real-time monitoring at under EUR 30. All electronic subassemblies were acquired as off-the-shelf components from Chinese marketplace resellers, a procurement route that ensured rapid availability and kept costs low. The system's design prioritizes ease of assembly and adaptability, making it suitable for evaluating drivetrain performance in resource-constrained environments. If validated, such sensors could extend to permanent vehicle integration, supporting traction control and predictive maintenance systems akin to tire pressure monitoring solutions. Unlike many commercial torque transducers that replace a section of the drivetrain with a proprietary shaft and flange set, the proposed sensor is bonded directly to the existing shaft and therefore requires no cutting, machining, or bespoke adapters. This drop-in installation greatly simplifies retrofitting and preserves the dynamic balance of the drivetrain. Despite these advances, practical challenges remain. Calibration procedures must rigorously address nonlinearity, hysteresis, and the need for traceability to reference standards. The presence of additional torque components due to mechanical couplings or installation effects can introduce systematic errors that must be compensated, either through detailed physical modeling or data-driven approaches such as neural networks. Robust calibration protocols, utilizing dedicated calibration devices and cross-validation against reference instruments, are essential for ensuring the reliability and reproducibility of torque measurements in real-world environments. Principal error contributors include gauge-mounting misalignment, mounting-induced bending moments, thermo-elastic drift, and humidity-induced adhesive creep; these factors are mitigated through symmetry verification, real-time temperature correction, and conformal coating. Dynamic uncertainties arising from shaft vibration and parasitic bending add \(\leq\)1% FS at 1 kHz, but finite-element compensation and anti-alias filtering limit the residual error to \(<\)0.3% FS [5; 6; 7; 8]. Furthermore, most published solutions focus solely on unidirectional torque measurement and often lack comprehensive calibration and error analysis, limiting their applicability in scenarios involving reversible or oscillatory loads.