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Journal of Mechanical Design | Volume 137 | Issue 9 | research-article
Research Papers: Design Automation

Regular Folding Pattern for Deployable Nonaxisymmetric Tubes1

[+] Author and Article Information
Sachiko Ishida

Assistant Professor
Mem. ASME
Department of Mechanical Engineering,
Meiji University,
1-1-1, Higashimita, Kawasaki,
Kanagawa 2148571, Japan
e-mail: sishida@meiji.ac.jp

Taketoshi Nojima

Meiji Institute for Advanced Study
of Mathematical Sciences,
Meiji University,
4-21-1, Nakano,
Tokyo 1648525, Japan
e-mail: taketoshinojima@gmail.com

Ichiro Hagiwara

Professor
Fellow ASME
Meiji Institute for Advanced Study
of Mathematical Sciences,
Meiji University,
4-21-1, Nakano,
Tokyo 1648525, Japan
e-mail: ihagi@meiji.ac.jp

2Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 22, 2014; final manuscript received July 10, 2015; published online July 28, 2015. Assoc. Editor: Kazuhiro Saitou.

J. Mech. Des 137(9), 091402 (Jul 28, 2015) (9 pages) Paper No: MD-14-1630; doi: 10.1115/1.4031070 History: Received September 22, 2014
Article
References
Figures
Tables

This paper presents two techniques for modeling the folding patterns of deployable nonaxisymmetric tubes using regular arrangement of the fold lines and three different fundamental folding designs, namely, Miura folding, bellows folding, and torsional buckling-based folding. The first modeling technique involves the cutting and removal of unnecessary parts from the original folding pattern of the corresponding straight cylinder, and the second technique involves the design of additional fold lines for folding the unnecessary parts into the tube without being cut. The applicability and constraints of each folding design and modeling technique are discussed and summarized.
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References

1
Freeland, R. E. , Bilyeu, G. D. , Veal, G. R. , and Mikulas, M. M. , 1998, “Inflatable Deployable Space Structures Technology Summary,” 49th International Astronautical Congress, Melbourne, Australia, Sept. 28–Oct. 2, Paper No. IAF-98-I.5.01.
2
Guest, S. D. , and Pellegrino, S. , 1996, “A New Concept for Solid Surface Deployable Antennas,” Acta Astronaut., 38(2), pp. 103–113. [CrossRef]
3
Johnson, L. , Young, R. M. , and Montgomery, E. E., IV , 2007, “Recent Advances in Solar Sail Propulsion Systems at NASA,” Acta Astronaut., 61(1–6), pp. 376–382. [CrossRef]
4
Tsuda, Y. , Mori, O. , Funase, R. , Sawada, H. , Yamamoto, T. , Saiki, T. , Endo, T. , and Kawaguchi, J. , 2011, “Flight Status of IKAROS Deep Space Solar Demonstration,” Acta Astronaut., 69(9), pp. 833–840. [CrossRef]
5
Zhao, X. , Hu, Y. , and Hagiwara, I. , 2011, “Shape Optimization to Improve Energy Absorption Ability of Cylindrical Thin-Walled Origami Structure,” J. Comput. Sci. Technol., 5(3), pp. 148–162. [CrossRef]
6
Ma, J. , and You, Z. , 2013, “A Novel Origami Crash Box With Varying Profiles,” ASME Paper No. DETC2013-13495.
7
Miura, K. , 2013, “Foldable Plate Structures and Applications,” Bull. Soc. Automot. Technol. Jpn., 67(5), pp. 52–58 (in Japanese).
8
Kuribayashi, K. , Tsuchiya, K. , You, Z. , Tomus, D. , Umemoto, M. , Ito, T. , and Sasaki, M. , 2006, “Self-Deployable Origami Stent Grafts as a Biomedical Application of Ni-Rich TiNi Shape Memory Alloy Foil,” Mater. Sci. Eng., A, 419(1–2), pp. 131–137. [CrossRef]
9
Guest, S. D. , and Pellegrino, S. , 1994, “The Folding of Triangulated Cylinders, Part I—Geometric Considerations,” ASME J. Appl. Mech., 61(4), pp. 773–777. [CrossRef]
10
Nojima, T. , 2001, “Structure With Folding Lines, Folding Line Forming Mold, and Folding Line Forming Method,” Patent No. WO 2001081821 A9.
11
Nojima, T. , 2002, “Modelling of Folding Patterns in Flat Membranes and Cylinders by Origami,” Int. J. Jpn. Soc. Mech. Eng., 45(1), pp. 364–370.
12
Hunt, G. W. , and Ario, I. , 2005, “Twist Bucking and the Foldable Cylinder: An Exercise in Origami,” Int. J. Non-Linear Mech., 40(6), pp. 833–843. [CrossRef]
13
Fujimoto, S. , and Nishiwaki, M. , 1982, Souzousuru Origami Asobi Heno Shoutai, Asahi Culture Center, Osaka, Japan (in Japanese).
14
Zhao, S. , Gu, L. , and Froemming, S. R. , 2012, “Performance of Self-Expanding Nitinol Stent in a Curved Artery: Impact of Stent Length and Deployment Orientation,” ASME J. Biomech. Eng., 134(7), p. 071007. [CrossRef]
15
Miura, K. , 1985, “Method of Packaging and Deployment of Large Membranes in Space,” The Institute of Space and Astronautical Science, Sagamihara, Japan, Report No. 618.

Figures

Grahic Jump Location
Fig. 1

Folding patterns for foldable cylinders: (a) Miura folding, (b) bellows folding, and (c) torsional buckling-based folding

+Folding patterns for foldable cylinders: (a) Miura folding, (b) bellows folding, and (c) torsional buckling-based folding
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Folding patterns for foldable cylinders: (a) Miura folding, (b) bellows folding, and (c) torsional buckling-based folding
Grahic Jump Location
Fig. 2

Polyhedral approximation of torus and developed unit pattern (m = 6)

+Polyhedral approximation of torus and developed unit pattern (m = 6)
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Polyhedral approximation of torus and developed unit pattern (m = 6)
Grahic Jump Location
Fig. 3

Unit patterns for constructing deployable torus: (a) by Miura folding (m = 12), (b) by bellows folding (m = 4), and (c) by torsional buckling-based folding (m = 6)

+Unit patterns for constructing deployable torus: (a) by Miura folding (m = 12), (b) by bellows folding (m = 4), and (c) by torsional buckling-based folding (m = 6)
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Unit patterns for constructing deployable torus: (a) by Miura folding (m = 12), (b) by bellows folding (m = 4), and (c) by torsional buckling-based folding (m = 6)
Grahic Jump Location
Fig. 4

Developed patterns with joint part for connecting two different tubes, and physical model: (a) pattern of torus with joint part obtained by Miura folding, (b) straight cylinder for connection to torus, (c) physical model of two tori connected by cylinder in (1) folded state, (2) expansion state, and (3) expanded state, and (d) strip folding of pattern

+Developed patterns with joint part for connecting two different tubes, and physical model: (a) pattern of torus with joint part obtained by Miura folding, (b) straight cylinder for connection to torus, (c) physical model of two tori connected by cylinder in (1) folded state, (2) expansion state, and (3) expanded state, and (d) strip folding of pattern
View Large  |  Save Figure  |  Download Slide (.ppt)
Developed patterns with joint part for connecting two different tubes, and physical model: (a) pattern of torus with joint part obtained by Miura folding, (b) straight cylinder for connection to torus, (c) physical model of two tori connected by cylinder in (1) folded state, (2) expansion state, and (3) expanded state, and (d) strip folding of pattern
Grahic Jump Location
Fig. 5

Deployable pattern of twisting tube, and physical model: (a) pattern with positions of unnecessary parts shifted, (b) physical model of twisted tube in (1) folded state, (2) expansion state, and (3) expanded state, and (c) aerial view of expanded state

+Deployable pattern of twisting tube, and physical model: (a) pattern with positions of unnecessary parts shifted, (b) physical model of twisted tube in (1) folded state, (2) expansion state, and (3) expanded state, and (c) aerial view of expanded state
View Large  |  Save Figure  |  Download Slide (.ppt)
Deployable pattern of twisting tube, and physical model: (a) pattern with positions of unnecessary parts shifted, (b) physical model of twisted tube in (1) folded state, (2) expansion state, and (3) expanded state, and (c) aerial view of expanded state
Grahic Jump Location
Fig. 6

Physical model of torus: (a) bellows folding pattern, (b) construction by folding pattern, and (c) strip folding of pattern

+Physical model of torus: (a) bellows folding pattern, (b) construction by folding pattern, and (c) strip folding of pattern
View Large  |  Save Figure  |  Download Slide (.ppt)
Physical model of torus: (a) bellows folding pattern, (b) construction by folding pattern, and (c) strip folding of pattern
Grahic Jump Location
Fig. 7

Physical model of torus: (a) torsional buckling-based pattern, (b) construction using folding pattern, and (c) strip folding of pattern

+Physical model of torus: (a) torsional buckling-based pattern, (b) construction using folding pattern, and (c) strip folding of pattern
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Physical model of torus: (a) torsional buckling-based pattern, (b) construction using folding pattern, and (c) strip folding of pattern
Grahic Jump Location
Fig. 8

Construction of nonaxisymmetric tube using Archimedean spiral: (a) Archimedean spiral (plane view), (b) discrete Archimedean spiral (plane view), and (c) polyhedral Archimedean tube (aerial view)

+Construction of nonaxisymmetric tube using Archimedean spiral: (a) Archimedean spiral (plane view), (b) discrete Archimedean spiral (plane view), and (c) polyhedral Archimedean tube (aerial view)
View Large  |  Save Figure  |  Download Slide (.ppt)
Construction of nonaxisymmetric tube using Archimedean spiral: (a) Archimedean spiral (plane view), (b) discrete Archimedean spiral (plane view), and (c) polyhedral Archimedean tube (aerial view)
Grahic Jump Location
Fig. 9

Flat-foldable nonaxisymmetric tube produced from Archimedean spiral: (a) pattern of nonaxisymmetric tube and (b) physical model in (1) folded state, (2) expansion state, and (3) expanded state

+Flat-foldable nonaxisymmetric tube produced from Archimedean spiral: (a) pattern of nonaxisymmetric tube and (b) physical model in (1) folded state, (2) expansion state, and (3) expanded state
View Large  |  Save Figure  |  Download Slide (.ppt)
Flat-foldable nonaxisymmetric tube produced from Archimedean spiral: (a) pattern of nonaxisymmetric tube and (b) physical model in (1) folded state, (2) expansion state, and (3) expanded state
Grahic Jump Location
Fig. 10

Flat-foldable toroidal tube: (a) pattern of flat-foldable torus with additional fold lines on subparts (in red) and (b) pattern when (1) folded, (2) subparts are folded to form torus, and (3) fully inflated to form straight cylinder

+Flat-foldable toroidal tube: (a) pattern of flat-foldable torus with additional fold lines on subparts (in red) and (b) pattern when (1) folded, (2) subparts are folded to form torus, and (3) fully inflated to form straight cylinder
View Large  |  Save Figure  |  Download Slide (.ppt)
Flat-foldable toroidal tube: (a) pattern of flat-foldable torus with additional fold lines on subparts (in red) and (b) pattern when (1) folded, (2) subparts are folded to form torus, and (3) fully inflated to form straight cylinder
Grahic Jump Location
Fig. 11

Flat-foldable toroidal tube: (a) pattern of flat-foldable torus with additional fold lines on subparts (in red) and (b) pattern when (1) folded, (2) subparts are folded to form torus, and (3) fully inflated to form straight cylinder

+Flat-foldable toroidal tube: (a) pattern of flat-foldable torus with additional fold lines on subparts (in red) and (b) pattern when (1) folded, (2) subparts are folded to form torus, and (3) fully inflated to form straight cylinder
View Large  |  Save Figure  |  Download Slide (.ppt)
Flat-foldable toroidal tube: (a) pattern of flat-foldable torus with additional fold lines on subparts (in red) and (b) pattern when (1) folded, (2) subparts are folded to form torus, and (3) fully inflated to form straight cylinder

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