Research Papers

Designing Rigidly Foldable Horns Using Bricard's Octahedron

[+] Author and Article Information
Tomohiro Tachi

Department of General Systems Studies,
Graduate School of Arts and Sciences,
The University of Tokyo,
3-8-1 Komaba, Meguro-Ku,
Tokyo 153-8902, Japan
e-mail: tachi@idea.c.u-tokyo.ac.jp

Manuscript received July 1, 2015; final manuscript received September 21, 2015; published online March 7, 2016. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(3), 031008 (Mar 07, 2016) (6 pages) Paper No: JMR-15-1171; doi: 10.1115/1.4031717 History: Received July 01, 2015; Revised September 21, 2015

This paper proposes a design method to obtain a family of rigidly foldable structures with one degree-of-freedom (DOF). The mechanism of flat-foldable degree-four cones and mutually compatible cones sharing a boundary is interpreted as the mechanism of Bricard's flexible octahedra. By sequentially concatenating compatible cones, one can design horn-shaped rigid-origami mechanisms. This paper presents a method to inversely obtain rigidly foldable horns that follow given space curves. The resulting rigidly foldable horns can be used as building blocks for a transformable cellular structure and attachments to existing rigidly foldable structures.

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Fig. 1

Three types of Bricard's octahedra. Type 1: Two-fold rotationally symmetric. Type 2: Mirror symmetric. Type 3: Bidirectionally flat-foldable. Two of eight triangle facets are removed for visualization.

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Fig. 2

The folding modes (a) and (b) of (i) the bidirectionally flat-foldable vertex (top) and (ii) the developable flat-foldable vertex (bottom). Note that in case (i-b) we cannot avoid self-intersection.

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Fig. 3

In the limit α = β→0, the cone of case (i) approaches a cylinder. In this case the ratio of panel widths is α:β.

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Fig. 4

Connected cones. OABCDO′ represents a transformable Bricard's octahedron.

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Fig. 5

Crease pattern of connected cones

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Fig. 6

Constructing the unfolded pattern of connected cones

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Fig. 7

Generating an origami surface from a polygonal curve

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Fig. 8

Generating a horn from a flat-foldable origami surface

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Fig. 9

A zig-zag horn from a polygonal curve

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Fig. 10

Folding motion of a curved horn. The leftmost configuration is the completely “unfolded” state, and the rightmost configuration is the limit of folding without collision. Global collision occurs if we continue to fold further. Notice that the torsion of the curve increases as the structure is folded.

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Fig. 11

Crease pattern of a curved horn. Right piece is overlayed on top of left piece, and sewn together to form a horn.

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Fig. 12

A variation of a crinkle that can substitute a fold line

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Fig. 13

The crease curve of a generalized Miura-ori mechanism match the concatenated cones

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Fig. 14

Proof of existence of point D



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