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Relative Motion Analysis using Rotating Axes - Acceleration

Relative Motion Analysis using Rotating Axes - Acceleration

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame. The absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame.
Time differentiation is...

Relative Motion Analysis - Acceleration

Relative Motion Analysis - Acceleration

A slider-crank mechanism converts rotational motion from the crank into linear motion of the slider or vice versa. This mechanism consists of three main parts: the crank, the connecting rod, and the slider. The movement of the slider-crank is an example of general plane motion as the fluctuating angle between the crank and the connecting rod. Consider a segment AB where point A is at the end of the slider and point B is on the diametrically opposite end to point A, on a crack. The variance in...

Relative Motion Analysis using Rotating Axes-Problem Solving

Relative Motion Analysis using Rotating Axes-Problem Solving

Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
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Relative Motion Analysis using Rotating Axes

Relative Motion Analysis using Rotating Axes

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it...

Absolute Motion Analysis- General Plane Motion

Absolute Motion Analysis- General Plane Motion

Visualize a drone, with its propellers spinning rapidly, hovering mid-air. The fascinating movements and operations of this drone can be comprehended by applying the principle of general plane motion.
As the drone's propellers rotate, an upward force is generated that counteracts the force of gravity, enabling the drone to lift off from the ground. This initial movement of the drone is along a straight path, representing a form of translational motion. In this phase, every point on the...

Relative Motion Analysis - Velocity

Relative Motion Analysis - Velocity

A stroke engine has a slider-crank mechanism that converts rotational motion from the crank into linear motion of the slider or vice versa. This mechanism consists of three main parts: the crank, the connecting rod, and the slider.
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Updated: Aug 19, 2025

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Virtual Axle Detector Based on Analysis of Bridge Acceleration Measurements by Fully Convolutional Network.

Steven Robert Lorenzen¹, Henrik Riedel¹, Maximilian Michael Rupp¹

¹Institute for Structural Mechanics and Design, Technical University of Darmstadt, 64287 Darmstadt, Germany.

Sensors (Basel, Switzerland)

|November 26, 2022

Summary

A new method uses accelerometers as Virtual Axle Detectors (VADs) for accurate vehicle axle detection on bridges. This approach achieves 95% detection accuracy, simplifying Bridge Weigh-In-Motion (BWIM) systems.

Keywords:

bridge weigh-in-motion continuous wavelet transformation field validation free-of-axle-detector fully convolutional networks machine learning moving load localisation nothing-on-road structural health monitoring

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Area of Science:

Civil Engineering
Structural Health Monitoring
Signal Processing

Background:

Accurate axle detection is crucial for Bridge Weigh-In-Motion (BWIM) systems.
Conventional methods often require specific bridge designs or dedicated sensors.
Arbitrary accelerometer placement offers a flexible alternative for data acquisition.

Purpose of the Study:

To develop a novel, bridge-type-independent method for axle detection using accelerometers.
To implement a simplified binary classification model for robust axle detection.
To establish Virtual Axle Detectors (VADs) without traditional axle detectors.

Main Methods:

Utilized accelerometers placed arbitrarily on a bridge structure.
Developed a Fully Convolutional Network (FCN) model for signal processing.
Processed acceleration signals as Continuous Wavelet Transforms (CWTs) for multi-scale analysis.

Main Results:

Achieved 95% axle detection accuracy on a steel trough railway bridge.
Correctly detected 128,599 out of 134,800 previously unseen axles.
90% of axles were detected with a maximum spatial error of 20 cm at speeds up to 56.3 m/s.

Conclusions:

The proposed method effectively uses accelerometers as Virtual Axle Detectors (VADs).
The FCN model demonstrates high accuracy and efficiency in real-world operating conditions.
This approach offers a versatile solution for axle detection in BWIM applications.