0
Technical Briefs

Geometric Analysis of a Foldable Barrel Vault With Origami

[+] Author and Article Information
Jianguo Cai

Lecturer Key Laboratory of
C & PC Structures of Ministry of Education,
National Prestress Engineering Research Center,
Southeast University,
Nanjing 210096, China
e-mail: j.cai@seu.edu.cn

Yixiang Xu

Lecturer Department of Civil Engineering,
Strathclyde University,
Glasgow G12 8QQ, UK
e-mail: yixiang.xu@strath.ac.uk

Jian Feng

Professor
Key Laboratory of C & PC Structures
of Ministry of Education,
National Prestress Engineering Research Center,
Southeast University,
Nanjing 210096, China
e-mail: fengjian@seu.edu.cn

1Corresponding author.

Contributed by the Design Innovation and Devices of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 8, 2012; final manuscript received August 14, 2013; published online September 24, 2013. Assoc. Editor: Alexander Slocum.

J. Mech. Des 135(11), 114501 (Sep 24, 2013) (6 pages) Paper No: MD-12-1552; doi: 10.1115/1.4025369 History: Received November 08, 2012; Revised August 14, 2013

This paper investigates the geometry of a foldable barrel vault with modified Miura-ori patterns, which displays a curvature during the motion. The principal of spherical trigonometry was used to obtain the relationship of the inclined angles between adjacent folded papers of Miura-ori. Then, the radius, span, rise, and longitudinal length of the foldable barrel vault in all configurations throughout the motion are determined. The results show that the radius of curvature grows exponentially and the span increases during deployment. Furthermore, the rise increases first, followed by a decrease with increasing deployment angle.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Topics: Geometry
Your Session has timed out. Please sign back in to continue.

References

Jensen, F. V., 2004, “Concepts for Retractable Roof Structures,” Ph.D. thesis, University of Cambridge, Cambridge, UK.
De Temmerman, N., 2007, “Design and Analysis of Deployable Bar Structures for Mobile Architectural Applications,” Ph.D. thesis, Vrije Universiteit Brussel, Brussels, Belgium.
De Temmerman, N., Mollaert, M., Van Mele, T., and De Laet, L., 2007, “Design and Analysis of a Foldable Mobile Shelter System,” Int. J. Space Struct., 22(3), pp. 161–168. [CrossRef]
Miura, K., 1980, “Method of Packaging and Deployment of Large Membrane in Space,” Proceedings of the 31st Congress of International Astronautical Federation, Tokyo, Japan, pp. 1–10.
Dureisseix, D., 2012, “An Overview of Mechanisms and Patterns With Origami,” Int. J. Space Struct., 27(1), pp. 1–14. [CrossRef]
De Focatiis, D. S. A., and Guest, S. D., 2002, “Deployable Membranes Designed From Folding Tree Leaves,” Phil. Trans. R. Soc. Lond. A., 360(1791), pp. 227–238 [CrossRef].
Tachi, T., 2010, “Geometric Considerations for the Design of Rigid Origami Structures,” Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2010, Nov. 8–12, Shanghai, China.
Gioia, F., Dureisseix, D., Motro, R., and Maurin, B., 2012, “Design and Analysis of a Foldable/Unfoldable Corrugated Architectural Curved Envelop,” ASME J. Mech. Des., 134(3), p. 031003. [CrossRef]
Wu, W., and You, Z., 2010, “Modelling Rigid Origami With Quaternions and Dual Quaternions,” Phil. Trans. R. Soc. Lond. A., 466(2119), pp. 2155–2174. [CrossRef]
Schenk, M., and Guest, S. D., 2009, “Folded Textured Sheets,” Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2009, Alberto Domingo and Carlos Lazaro, eds. Sep. 28–Oct. 2, Universidad Politecnica de Valencia, Valencia, Spain.
Piekarski, M., 2000, “Constructional Solutions for Two-Way-Fold-Deployable Space Trusses,” IUTAM-IASS Symposium on Deployable Structures: Theory and Applications, pp. 301–310.
Elsayed, E. A., and Basily, B. B., 2004, “A Continuous Folding Process for Sheet Materials,” Int. J. Mater. Prod. Technol., 21(1/2/3), pp. 217–238. [CrossRef]
Basily, B. B., and Elsayed, E. A., 2004, “Dynamic Axial Crushing of Multi-Layer Core Structures of Folded Chevron Patterns,” J. Mater. Prod. Technol., 21(1/2/3), pp.169–185. [CrossRef]
Kling, D. H., 2007, “Folding Method and Apparatus,” U.S. Patent Application 20,070,273,077.
Schenk, M., Allwood, J. M., and Guest, S. D., 2011, “Cold Gas-Pressure Folding of Miura-Ori Sheets,” Proceedings of International Conference on Technology of Plasticity (ICTP 2011), Sept. 25–30, Aachen, Germany.
Chew Min, C., and Suzuki, H., 2008, “Geometrical Properties of Paper Spring,” Manufacturing Systems and Technologies for the New Frontier, pp. 159–162.
Miura, K., 1966, “The Theory of Paper Sculpture,” Bull Junior Coll. Art, 4, pp. 61–66.
Huffman, D., 1976, “Curvature and Creases: A Primer on Paper,” IEEE Trans. Comput., C-25(10), pp. 1010–1019. [CrossRef]
Hull, T., 2006, Project Origami, A K Peter/CRC Press, Wellesley, MA.
Tachi, T., 2009, “Generalization of Rigid Foldable Quadrilateral Mesh Origami,” Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2009, Alberto Domingo and Carlos Lazaro, eds. Sep. 28–Oct. 2, Universidad Politecnica de Valencia, Valencia, Spain.
Clough-Smith, J. H., 1978, An Introduction to Spherical Trigonometry, Brown, Son & Ferguson, Glasgow, UK.

Figures

Grahic Jump Location
Fig. 1

Modified modules of Miura-ori

Grahic Jump Location
Fig. 2

Foldable structure with modified modules of Miura-ori

Grahic Jump Location
Fig. 3

3D figures of the folded barrel vault during the motion

Grahic Jump Location
Fig. 4

The analytical model of Miura-ori elements

Grahic Jump Location
Fig. 5

Spherical triangles of Miura-ori elements

Grahic Jump Location
Fig. 6

Foldable barrel vault with two modified Miura-ori modules

Grahic Jump Location
Fig. 7

Turned Miura-ori module

Grahic Jump Location
Fig. 8

The foldable barrel vault during the motion

Grahic Jump Location
Fig. 9

The model for the span and rise

Grahic Jump Location
Fig. 10

The model for the longitudinal length

Grahic Jump Location
Fig. 11

R/l against the deployment angle ψ

Grahic Jump Location
Fig. 12

S/l against the deployment angle ψ

Grahic Jump Location
Fig. 13

H/l against the deployment angle ψ

Grahic Jump Location
Fig. 14

d/b against the deployment angle ψ

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In