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One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...

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Related Experiment Video

Updated: Jul 16, 2026

Simulation of a Scaled Assembly Process with Collaboration of a Robotic Arm and Monitoring through a Vision System for Quality Control

Simulation of a Scaled Assembly Process with Collaboration of a Robotic Arm and Monitoring through a Vision System for Quality Control

Published on: August 29, 2025

Subpixel Edge Localization via Ruled-Sigmoid Surfaces and Its Application for Precision Analysis of Cycloidal Gear

Jing Zhang¹, Po Du¹, Wenzhen Zhao¹

¹School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China.

Sensors (Basel, Switzerland)

|July 15, 2026

Summary

A new machine vision system offers efficient cycloidal gear inspection. This method achieves high accuracy (within 10 μm deviation) and reduces inspection time to 13 seconds.

Keywords:

cycloidal gear edge localization sigmoid subpixel visual measurement

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Area of Science:

Mechanical Engineering
Metrology
Computer Vision

Background:

Traditional cycloidal gear inspection methods face limitations in efficiency and data dimensionality.
Accurate measurement of cycloidal gear profiles is crucial for assessing machining quality.

Purpose of the Study:

To develop a comprehensive machine vision-based inspection method for cycloidal gears.
To improve the efficiency and accuracy of cycloidal gear metrology.

Main Methods:

Established a high-precision vision platform utilizing a Sigmoid surface-based edge detection algorithm for sub-pixel localization.
Implemented logarithmic transformation and light intensity compensation to correct saturation errors.
Calibrated pixel equivalents and compensation coefficients using standard metrology tools.
Reconstructed sub-pixel tooth profiles in a physical coordinate system via multi-coordinate transformation.

Main Results:

Achieved point-to-point deviation within 10 μm compared to coordinate measuring machines (CMM).
Demonstrated a repeat positioning accuracy of 0.8 μm.
Reduced the full inspection cycle time for cycloidal gears to 13 seconds.
Identified inherent tooth profile deviations ranging from 24 μm to 37 μm.

Conclusions:

The proposed machine vision system significantly enhances inspection efficiency and accuracy for cycloidal gears.
The hybrid analytical method allows simultaneous evaluation of critical geometric tolerances.
This method overcomes the limitations of traditional single-dimensional inspection techniques.