# A Low-Cost IoT-Based Bidirectional Torque Measurement System with Strain Gauge Technology
## 3 Materials and Methods  
The developed torque measurement system, depicted in Figure 1, consists of strain gauges R\({}_{\text{g1}}\), R\({}_{\text{g2}}\), R\({}_{\text{g3}}\), R\({}_{\text{g4}}\) positioned at \(\pm\)45\({}^{\circ}\) angles relative to the shaft axis, forming two pairs on opposite sides; a signal conditioning module specifically designed for strain gauge/loadcell applications; a microcontroller; a DC-DC converter; and a rechargeable battery. The strain gauge configuration maximizes sensitivity to torsional strain while compensating for temperature and bending effects [26]. The torque measurement approach is based on the application of strain gauges to a rotating shaft, following procedures described by [PERSON] et al. and [PERSON] et al. [27; 28]. For multi-axis measurement considerations, design principles from [PERSON] et al. are referenced [29]. The core of the measurement system consists of four BF350\(-\)3 HA\(-\)E foil strain gauges (1,2), an HX711 precision load cell amplifier (3), a Wemos D1 Minii ESP8266 microcontroller (4), a 400 mAh lithium polymer (Li\(-\)Po) battery (6), and a DC-DC step-down converter (5) as illustrated in Figure 2[30]. All components, made in China, were chosen based on cost, availability, and compatibility with open-source development platforms. The BF350-3 HA-E strain gauges are widely used for force and deformation measurements. Their small size and high sensitivity make them suitable for mounting on rotating shafts. Each BF350-3 HA\(-\)E strain gauge consists of two sensitive elements arranged at \(\pm\)45 degrees relative to the longitudinal axis. The HX711 is a conditioning signal module that includes a voltage regulator, a programmable gain voltage amplifier, a 24\(-\)bit analog\(-\)to\(-\)digital converter (ADC), and a serial data transmission peripheral. It is designed for load cells, weigh scales, and industrial control applications. It provides the necessary amplification and digitization of the strain gauge output. The Wemos D1 Minii ESP8266 is a compact, Wi-Fi-enabled microcontroller that supports Arduino programming. The 400 mAh Li-Po battery, regulated by a DC-DC converter, ensures stable operation for extended periods. The chosen shaft for torque measurement has a diameter of 10 mm and a length of 600 mm. The shaft surface was prepared by sanding and cleaning with isopropyl alcohol to ensure optimal adhesion of the strain gauges. Gauges were bonded to the shaft using a two-part epoxy adhesive, following the manufacturer's recommended procedure and the strain gauge application methods described by [PERSON] and [PERSON] et al. [26; 28]. After curing, the gauges were connected in a full Wheatstone bridge configuration using fine copper wire and solder, as depicted in Figure 2.  
Figure 1: Schematic of the strain gauge Wheatstone bridge configuration and signal flow. The completed bridge was tested for continuity and baseline resistance, and the output wires were routed through a flexible cable to the amplifier and microcontroller assembly. Data acquisition was performed using an Arduino-based system, which has been shown to be effective for both laboratory and field applications [17; 31]. For alignment and calibration procedures, methods from [PERSON] et al. were adapted [32; 33; 34]. Firmware for the ESP8266 was developed using the Arduino IDE. The code handled initialization, periodic reading of the HX711 output, and digital filtering. Calibration was performed using a certified dynamometric wrench, which applied known torque values to the shaft in increments of 5 N\(\cdot\)m, from 5 N\(\cdot\)m up to 50 N\(\cdot\)m. For each applied torque, multiple digital output readings from the HX711 were recorded. As shown in Figure 3, the half shaft (3), on which the torque sensor (2) is mounted, is rigidly clamped at one end (1). Using the certified torque wrench (4), a known torque is applied to the shaft. This setup enables precise calibration of the sensor output against reference torque values, ensuring accurate and repeatable measurement performance.