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Centroid of a Body: Problem Solving

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The centroid of a body is a crucial concept in engineering and physics. Finding the centroid of a body can help determine its stability, its balance point, and even its design. In this context, consider a thin wire bent in the form of a quarter circular arc. Polar coordinates are used to calculate the centroid. The wire is first divided into small differential elements of a length equal to the radius multiplied by the differential angle.
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Related Experiment Video

Updated: Jan 9, 2026

Three-Dimensional Finger Motion Tracking during Needling: A Solution for the Kinematic Analysis of Acupuncture Manipulation

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High-Precision Centroid Measurement Method Based on 3D Scanning and Hooke's Law.

Xin He¹, Zhen Li², Xin Pan²

¹Engineering Training Center, Tianjin University of Technology and Education, Tianjin 300222, China.

Sensors (Basel, Switzerland)

|December 11, 2025

Summary

A new method combines 3D scanning and Hooke's law sensing to precisely determine object centroids. This approach overcomes limitations of traditional methods, offering improved accuracy for engineering and manufacturing applications.

Keywords:

3D scanning Hooke’s law centroid measurement multi-point weighing method

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Last Updated: Jan 9, 2026

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Area of Science:

Metrology
Mechanical Engineering
Aerospace Engineering

Background:

Accurate centroid determination is vital for quality control in aerospace and manufacturing.
Traditional methods like multi-point weighing suffer from range limitations, alignment errors, and lateral force interference, reducing precision.

Purpose of the Study:

To develop a novel measurement framework for precise centroid determination.
To overcome the limitations of existing centroid measurement techniques.

Main Methods:

Synergizing high-precision 3D scanning with Hooke's law-based mechanical sensing.
Utilizing non-contact 3D scanning for geometric compatibility and eliminating mechanical positioning dependencies.
Integrating linear spring-based force transduction and active anti-tilt compensation with 3D scanning and motor leveling.

Main Results:

Experimental validation showed sub-millimeter accuracy compared to multi-point weighing.
Measured centroid deviations were 0.01 mm (X-axis), 0.06 mm (Y-axis), and 0.03 mm (Z-axis).
Achieved a composite spatial precision of 0.07 mm.

Conclusions:

The proposed methodology offers enhanced operational capabilities for centroid measurement systems.
Provides new theoretical insights and a robust approach for measuring complex parts and systems.