High-Resolution Displacement Measurement Using a Lever Accelerometer Combination

IUT JOURNAL OF ENGINEERING AND TECHNOLOGY (JET), Special issue (IUT-ICCET), June 2025 1st International Conference on Core Engineering & Technology (IUT-ICCET 2024) Journal homepage: https://jet.iutoic-dhaka.edu/ High-Resolution Displacement Measurement Using a Lever Accelerometer Combination 1MD SHAH WALI ULLAH*, 1 SHAKIB ARAFAT TAPU, 1 REDOYAN JOYAB HIRA and 1 MUKTA CHAKMA 1Department of Mechanical Engineering, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh. *E-mail of the corresponding Author: [email protected] ABSTRACT Measuring small linear displacement with high resolution is a challenge that has been dealt with using numerous complex methods. This study focuses on developing an experimental system that leverages a mechanical amplification mechanism converting diminutive deflections into larger ones which are easily detectable with the help of available electro-mechanical components and to produce digital readouts. This amplification is achieved by a lever-like mechanism. Lever transforms and amplifies the linear displacement into angular displacement, which is then picked up by the accelerometer. The change in gravitational acceleration in one of the axes of the accelerometer can be calibrated to measure the linear displacement. Such a mechanism provides users the possibility to adjust resolution and range as needed. The aforementioned mechanism has been tested in a data acquisition system with proper calibration by precisely detecting and measuring the movement of a shaft with a high resolution maintaining great accuracy. Moreover, the use of off the-shelf components can reduce the cost significantly over more conventional approaches.. KEYWORDS: Lever Mechanism, Linear Displacement, Data Acquisition. NOMENCLATURE l distance of the shaft from the pivot [mm] d displacement of the shaft [mm] θ angular rotation [°] 1. INTRODUCTION In the modern world, accurate methods for measuring displacement with great precision are a critical requirement. Even minor advancements in precision affects the vast majority of engineering and scientific applications including fields like control engineering, micro-manufacturing and robotics. A wide variety of traditional displacement measurement techniques, such as Linear Variable Differential Transformers (LVDTs) [1] or laser interferometry [2] are already in use but those often face limitations in terms of cost and operational complexity. To address these challenges, this experimental research paper presents a novel approach that uses a mechanical lever system and a high-sensitivity accelerometer along with a micro controller in order to achieve high-resolution displacement measurement which would be affordable on a global scale. The research was conducted experimentally as a part of data acquisition project to measure torque in a Torsion meter [3].In this system, with the application of torque, the twisting of the specimen was converted into linear displacement of a IUT JOURNAL OF ENGINEERING AND TECHNOLOGY (JET), Special issue (IUT-ICCET), June 2025 13 needle-like shaft attached to the setup. The total displacement of the shaft from the beginning to the failure of the test specimen due to the application of torque was only 6mm which was too small for effective calibration. So, a seesaw-like mechanism of particular dimension and height was designed to convert the 6mm linear deflection to a larger static acceleration of gravity, making it easier to measure with ADXL 345 [4]. This method enhances the resolution of the accelerometer by amplifying small displacements through a mechanical lever system. Thus, this amplification facilitates the precision and responsiveness of ADXL 345 while mitigating noise and drift, making it suitable for applications where traditional methods might fail or be cost-prohibitive. This paper discusses the foundation of the lever-accelerometer measurement system with minimal cost, presents the design and experimental validation, and explores its potential applications in various industries. This research was conducted experimentally and the results demonstrate the system’s capability to measure displacements with higher precision and accuracy, offering a versatile and cost-effective alternative to all the conventional methods practically. 2. LITERATURE REVIEW Accelerometers are used for measuring the spatial position of a device using the double integration of the acceleration like Park et al. (2013) [5]. But typically, this method is very erroneous. To reduce the error Ferrero R et al. (2019) [6], (2016) [7] used Kalman filter with great effect. Further work has been done to introduce a better method of fitting polynomial extremum with a better correction effect to eliminate the trend term error caused by the DC component by Niu et al. (2019) [8]. Other works based on this double integration method include fault detection using vibration transducers by Katalin et al. (2014) [9]. The main limitations in double integration method are noise amplification, effects of vibration and external disturbances, high computational cost, initial conditions and cumulative errors. Cumulative errors mainly arise because the integration process compounds inaccuracies in accelerometer data over time, namely in the form of sensor noise, bias drift and sampling rate errors. Very small fluctuations in initial accelerometer data also gets amplified when it’s integrated twice. Variation in sampling rate can also distort the final output. For small displacement this cumulative error is more significant. Niu et al. [8] measured displacement using the double integral method with their developed polynomial fitting algorithm in the range between 12.47 m to 12.76 m with an error ranging from 1.79% to 0.53%. Hoang et al. [10] measured displacement from 0 cm to 200 cm range with a maximum error of approximately 0.4%. Ferrero et al. [6] showed that error in double integral method range from 79.5% to 67.5% when displacement is measured in the range of 10 cm to 30 cm. Introduction of Kalman Filter significantly reduced the error to 16.7% to 10.7% in the same range. Pang et al. [11] showed that use of Kalman filter results in a position error of 17.66 m per mg per square min. However, the lever accelerometer combination eliminates the need for double integration. Rather a simple linear fit is enough to provide displacement data with very high accuracy. This newer method bypasses the need for integration altogether, thus error multiplication is considerably less. 3. METHODOLOGY: This study utilizes a lever-accelerometer mechanism to measure the vertical displacement of a machine shaft. The dimensions of the lever were thus made specific for the shaft in question. All structural parts were 3D printed and as for the accelerometer, ADXL 345 was selected for its compact shape and repeatability. To calibrate the setup, readings were taken from accelerometer for every 0.05mm displacement of the shaft. The mentioned displacement was measured by a Mitutoyo Height Gauge [12].The linear movement was translated into an angular displacement of required magnification and then a linear fit was applied to the acquired data for taking measurement. Arduino Mega 2560 [13] was used as the micro controller for this operation. A ST3375 LCD [14] was used to show output values. General flowchart of the operation is visualized in figure 1. IUT JOURNAL OF ENGINEERING AND TECHNOLOGY (JET), Special issue (IUT-ICCET), June 2025 14 Figure 1: Flowchart of the operation 3.1. Design In this specific case, the design parameters of the lever were adjusted according to the free space below the shaft whose movement needed to be measured. The accelerometer was mounted on one end while the shaft head was placed at the other end. The downward displacement of the shaft resulted in angular rotation about the pivot. Although the displacement might be very small, the angular amplification resulted in a large rotation about the X-axis of the accelerometer. Although there is a translatory motion, only the rotational motion is detected by the accelerometer. 3.2. Sensitivity control The degree of angular rotation can be easily controlled just by placing the position of the needle-like shaft further away from or closer to the pivoting point. In this study, the shaft was placed at 6mm, 8mm, and 10mm further from the pivot as shown in Figure 2. The resulting angular rotations are shown belowtanθ = d l For l = 6 mm and d = 4.8 mm, tanθ = 4.8 6 ⇒ θ = 38.65° For l = 8 mm and d = 4.8 mm, tanθ = 4.8 8 ⇒ θ = 30.96° For l = 10 mm and d = 4.8 mm, tanθ = 4.8 10 ⇒ θ = 25.64° IUT JOURNAL OF ENGINEERING AND TECHNOLOGY (JET), Special issue (IUT-ICCET), June 2025 15 (a) l = 6 mm (b) l = 8mm (c) l = 10 mm Figure 2: Schematic diagram for the shaft position from the pivot and corresponding angular rotation. IUT JOURNAL OF ENGINEERING AND TECHNOLOGY (JET), Special issue (IUT-ICCET), June 2025 16 Figure 3: Picture of experimental setup IUT JOURNAL OF ENGINEERING AND TECHNOLOGY (JET), Special issue (IUT-ICCET), June 2025 17 Figure 4: Variation of ADXL reading with the change of vertical displacement of the shaft. Table 1. Accelerometer to Arduino Mapping ADXL 345 pin Corresponding Arduino pin SDA SDA SCL SCL Vcc 5V GND GND IUT JOURNAL OF ENGINEERING AND TECHNOLOGY (JET), Special issue (IUT-ICCET), June 2025 18 Table 2. ST3375 to Arduino Mapping ST3375 display pin Corresponding Arduino pin LED 3.3v SCK 52 SDA 51 A0 9 Reset 8 CS 53 GND GND VCC 5v IUT JOURNAL OF ENGINEERING AND TECHNOLOGY (JET), Special issue (IUT-ICCET), June 2025 19 Figure 5: Best fit curves for the displacement-ADXL output. 3.3. Interfacing with Arduino ADXL 345 was interfaced with Arduino via I2C protocol [15] . A serial clock pin (SCL) of the Arduino Controller board pulses at a regular interval, and a serial data pin (SDA) over which data is transmitted between Arduino and accelerometer. The accelerometer is supplied with 5V from the Arduino board directly. A ST3375 LCD was also interfaced with Arduino so that the output values can be displayed. Table 1 indicates the pinout references between ADXL 345 and Arduino and Table 2 tells the same between ST3375 LCD and Arduino. Figure 3 shows the final setup. 3.4. Taking data for calibration and finding characteristics equation X-axis readings of ADXL 345 were taken from the Arduino serial monitor for 0.05mm of displacement. These readings indicate the change in gravitational acceleration due to rotation. Firstly, with l = 6mm, five ADXL values were taken for every displacement value. Sufficient time was allowed to stabilize the readout from the ADXL. A plot of the averaged ADXL value against the displacement of the shaft was done and is shown in Figure 4. The initial ADXL reading (at 0mm) was subtracted from all the outputs to eliminate dependency on initial starting angle. A best-fit line was determined through regression analysis, shown in Figure 5, which was then used as the characteristic equation for the setup. Finally, the Arduino was programmed to show output in millimeters corresponding to the angular displacement which was sensed by the accelerometer. The ADXL 345 output is fairly linear, so when the characteristic equation is known, the program is written such that the initial angle of the lever with the horizontal axis doesn’t need to be perfectly zero. Basically, any starting angle is considered as the starting point(0mm) from which the measurement is initiated. The same process was repeated for l = 8mm and l = 10mm to observe the change in sensitivity and how the error in measurement varies. All the data were taken within the prescribed operating condition of the ADXL 345 and external factors like high airflow were eliminated by conducting the experiment in a closed room. 4. RESULTS AND DISCUSSION After calibration, the setup was tested by measuring the vertical displacement of the same shaft. The result shows acceptable accuracy for the shaft placement at 6mm from the pivot. However, the accuracy IUT JOURNAL OF ENGINEERING AND TECHNOLOGY (JET), Special issue (IUT-ICCET), June 2025 20 decreases, and uncertainty increases significantly as the shaft was placed at 8mm and 10mm from the pivot. To visualize the result, a scatter plot consisting of height gauge measurement in X-axis and mode of the outputs taken from the setup in Y-axis was plotted. Absolute deviation of outputs from the mode at each point was multiplied by 10 and shown using the error bar in Figure 6. The multiplication was conducted to enhance visualization because the true deviation is too small to be distinguished easily. 4.1. Error analysis One inherent source of error in this setup is the height gauge used during calibration process. The height gauge in question is Mitutoyo digital height gauge 192-611 with the accuracy of ±0.05mm with quantizing error of ±1. As the height gauge is very widely used, the analysis is limited to comparing measured outputs to the height gauge output only. The accelerometer has a sensitivity of ±2G to ±16G. As this sensitivity will automatically introduce errors while getting output data, calculating the final output accuracy of the setup will include all the intermediate errors. To analyze the repeatability of the setup, the displacement output placing the shaft at 6mm from the pivot(l = 6mm) was taken 5 times for a range of linear displacement of the shaft (0.05mm-4.8mm) with 0.05mm increment for each step. Then for each step, the standard deviation was calculated. The average standard deviation and maximum standard deviation for the whole range of output were then calculated to represent the repeatability. To measure accuracy, the maximum difference between the output result and the actual displacement (from the height gauge) for each step was calculated and averaged out. These steps were then repeated for l = 8mm and l = 10mm. The best results were obtained when the shaft was placed 6mm from the pivot. All the findings are presented in Table 3.