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Large-displacement symmetrical foldable cones
1Advanced Structures Group, Department of Engineering, University of Cambridge, CB2 1PZ, United Kingdom.
Physical Review. E
|December 24, 2021
Summary
Researchers determined the equilibrium shape of foldable cones (f-cones) using geometry. This nonrigid origami model simplifies calculations while retaining accuracy for moderate displacements.
Area of Science:
- Origami mechanics
- Geometric modeling
- Nonrigid structures
Background:
- Foldable cones (f-cones) are examples of nonrigid origami with curved faces.
- Understanding their equilibrium shape is crucial for applications in deployable structures and robotics.
Purpose of the Study:
- To determine the exact equilibrium shape of a symmetrical f-cone using only geometrical considerations.
- To develop a simplified analytical method for predicting f-cone shapes.
Main Methods:
- Treating the f-cone as intersecting cones with equal fold angles.
- Utilizing the spherical image of the vertex and Gauss's mapping for moderate displacements.
- Deriving closed-form expressions for shape parameters.
Main Results:
- The exact equilibrium shape of a symmetrical f-cone was determined through geometrical analysis.
- A simplified analytical method was developed, reducing computational effort compared to direct linearization.
- Closed-form expressions for shape parameters were obtained, accurately representing variations.
Conclusions:
- Geometrical considerations alone are sufficient to determine the exact equilibrium shape of symmetrical f-cones.
- The proposed analytical method offers a computationally efficient alternative to existing frameworks.
- The findings provide a valuable framework for understanding and designing nonrigid origami structures.
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