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Mathematical Model Construction of the Bionic Irregular Surface of Turtle Shell.

Sanling Fu1, Zijun Chen2, Tianhua Chen3

  • 1College of Physical Engineering, Henan University of Science and Technology, Luoyang, China, haust.edu.cn.

Applied Bionics and Biomechanics
|May 15, 2026
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Summary

Researchers mimicked the Brazilian turtle shell

Keywords:
bionicsreverse engineeringtransplanter floating plateturtle abdominal armor surface

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Area of Science:

  • Bionics and Biomimetics
  • Mechanical Engineering
  • Surface Morphology Analysis

Background:

  • Rice transplanters face challenges with mud and water resistance due to their floating plate design.
  • The irregular surface of a turtle shell offers potential solutions for improved hydrodynamics and reduced resistance.

Purpose of the Study:

  • To mathematically model the turtle plastron surface for bionic design applications.
  • To investigate the feasibility of applying turtle shell morphology to enhance rice transplanter floating plates.

Main Methods:

  • Acquired 3D point cloud data of a Brazilian turtle's plastron using a 7-axis measuring machine and Geomagic Studio.
  • Segmented, filtered, and performed polynomial fitting on the data using CATIA and MATLAB.
  • Evaluated model accuracy using sum of squared errors (SSE), root mean square error (RMSE), and coefficient of determination (R²).

Main Results:

  • Developed valid mathematical models of four distinct turtle plastron surfaces.
  • Achieved mean relative errors within the acceptable ±5% engineering tolerance for front, rear, and side models.
  • Successfully transformed biological surface morphology into a usable mathematical representation.

Conclusions:

  • The bionic application of turtle shell surface morphology provides a theoretical basis for designing improved rice transplanter floating plates.
  • Mathematical modeling of biological surfaces enables effective biomimetic engineering solutions.
  • This research offers a reference for developing more efficient agricultural machinery through bionic design principles.