0
Research Papers

Mechanical Characteristics of Origami Mechanism Based on Thin Plate Bending Theory

[+] Author and Article Information
Yu Hongying

School of Mechatronics Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: mcadyhy@hit.edu.cn

Guo Zhen

School of Mechatronics Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: guozhen.vip@foxmail.com

Zhao Di

School of Mechatronics Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: zhaodilp1229@foxmail.com

Liu Peng

School of Mechatronics Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: liupengzd@foxmail.com

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received April 8, 2019; final manuscript received May 4, 2019; published online May 23, 2019. Assoc. Editor: Haleh Ardebili.

J. Appl. Mech 86(8), 081008 (May 23, 2019) (17 pages) Paper No: JAM-19-1170; doi: 10.1115/1.4043721 History: Received April 08, 2019; Accepted May 04, 2019

This paper introduces a method for calculating the deformation displacement of the origami mechanism. The bearing capacity of each face can be analyzed by the relationship between the stress and displacement, which can provide a reference for the origami design. The Miura origami mechanism unit is considered. First, the folding angle of each crease is solved based on the geometric characteristics. The deforming form of the creases is then analyzed, and the bending moment acting on the paper surface is solved. Based on the geometric characteristics and stress forms, the paper surface is modeled as a sheet. Based on the bending theory of a thin plate with small deflection, the complex external load forms are decomposed by Levy's method and the superposition principle, and the expression of the deflection curve during the folding process is obtained. According to the stress and bending moment equations, the relationship between the bending moment and displacement is obtained. Finally, through an application example, the maximum deflection of the paper surface is calculated by matlab, and the deflection diagram of the deformed paper surface is drawn, which verifies the expression of the deflection curve.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Gillman, A., Fuchi, K., and Buskohl, P. R., 2018, “Truss-Based Nonlinear Mechanical Analysis for Origami Structures Exhibiting Bifurcation and Limit Point Instabilities,” Int. J. Solids Struct., 147, pp. 80–93. [CrossRef]
Huffman, D. A., 1976, “Curvature and Creases: A Primer on Paper,” IEEE Trans. Comput., C-25(10), pp. 1010–1019. [CrossRef]
Miura, K., 1989, “A Note on Intrinsic Geometry of Origami,” Research of Pattern Formation, R. Takaki, ed., KTK Scientific Publishers, Tokyo, Japan, pp. 91–102.
Belcastro, S. M., and Hull, T. C., 2002, “Modelling the Folding of Paper Into Three Dimensions Using Affine Transformations,” Linear Algebra Appl., 348(1–3), pp. 273–282. [CrossRef]
Streinu, I., and Whiteley, W., 2004, Single-Vertex Origami and Spherical Expansive Motions (Lecture Notes in Computer Science), Springer-Verlag, Berlin, pp. 161–173.
Tachi, T., 2009, “Simulation of Rigid Origami,” Origami 4: Proceedings of the 4th International Meeting of Origami Mathematics, Science, and Education, Pasadena, CA, Sept., 2006, pp. 175–187.
Watanabe, N., and Kawaguchi, K. I., 2009, “The Method for Judging Rigid Foldability,” Origami 4: Proceedings of the 4th International Meeting of Origami Mathematics, Science, and Education, Pasadena, CA, Sept., 2006, pp. 165–174.
Wu, W., and You, Z., 2010, “Modelling Rigid Origami With Quaternions and Dual Quaternions,” Proc. Math. Phys. Eng. Sci., 466(2119), pp. 2155–2174. [CrossRef]
Chen, Y., and Feng, J., 2012, “Folding of a Type of Deployable Origami Structures,” Int. J. Struct. Stab. Dyn., 12(6), p. 1250054. [CrossRef]
Xi, Z., and Lien, J. M., 2014, “Folding Rigid Origami With Closure Constraints,” ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Volume 5B: 38th Mechanisms and Robotics Conference, Buffalo, NY, Aug. 17–20, ASME Paper No. DETC2014-35556, pp. V05BT08A052.
Abel, Z., Cantarella, J., Demaine, E. D., Eppstein, D., Hull, T. C., Ku, J. S., Lang, R. J., and Tachi, T., 2016, “Rigid Origami Vertices: Conditions and Forcing Sets,” Comput. Geom., 7(1), pp. 171–184.
Liu, S., Lv, W., Chen, Y., and Lu, G., 2016, “Deployable Prismatic Structures With Rigid Origami Patterns,” ASME J Mech. Robot., 8(3), p. 031002. [CrossRef]
Cai, J., Zhang, Y., Xu, Y., Zhou, Y., and Feng, J., 2016, “The Foldability of Cylindrical Foldable Structures Based on Rigid Origami,” ASME J Mech. Des., 138(3), p. 031401. [CrossRef]
Hernandez, E. A. P., Hartl, D. J., and Lagoudas, D. C., 2016, “Modeling and Analysis of Origami Structures With Smooth Folds,” Comput. Aided Des., 78, pp. 93–106. [CrossRef]
Schenk, M., and Guest, S. D., 2011, “Origami Folding: A Structural Engineering Approach,” Origami 5: Proceedings of the 5th International Meeting of Origami Mathematics, Science, and Education, Singapore, July 13–17, 2010, CRC Press, Boca Raton, FL, pp. 291–303.
Tachi, T., 2013, “Interactive Form-Finding of Elastic Origami,” Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium, Wroclaw, Poland, Sept. 23–27, 2013, pp. 23–27.
Hernandez, E. A. P., Hartl, D. J., Malak, R. J., and Lagoudas, D. C., 2014, “Origami-Inspired Active Structures: A Synthesis and Review,” Smart Mater. Struct., 23(9), p. 094001. [CrossRef]
Cai, J., Ren, Z., Ding, Y., Deng, X., Xu, Y., and Feng, J., 2017, “Deployment Simulation of Foldable Origami Membrane Structures,” Aerosp. Sci. Technol., 67, pp. 343–353. [CrossRef]
Hwang, H. D., and Yoon, S. H., 2015, “Constructing Developable Surfaces by Wrapping Cones and Cylinders,” Comput. Aided Des., 58, pp. 230–235. [CrossRef]
Zhu, L., Igarashi, T., and Mitani, J., 2013, “Soft Folding,” Comput. Graph. Forum, 32, pp. 167–176. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Sketch of the Miura origami unit: (a) schematic drawing and (b) model diagram

Grahic Jump Location
Fig. 2

Folding configuration of the Miura origami unit

Grahic Jump Location
Fig. 3

Section of creases before and after deformation: (a) section of creases before deformation and (b) section of creases after deformation

Grahic Jump Location
Fig. 4

Schematic diagram of a microsegment of the creases before and after deformation: (a) microindentation, (b) predeformation, and (c) postdeformation

Grahic Jump Location
Fig. 5

Geometric dimensions and coordinate systems of the paper surface P1

Grahic Jump Location
Fig. 6

Boundary supporting form of rectangular thin plate

Grahic Jump Location
Fig. 7

Internal force analysis diagram of a cell cube on P1

Grahic Jump Location
Fig. 8

Load distribution on P1

Grahic Jump Location
Fig. 9

Load distribution on the paper surface P2

Grahic Jump Location
Fig. 10

Variation diagram of the deflection w1: (a) three-dimensional view, (b) XY view, (c) XZ view, and (d) YZ view

Grahic Jump Location
Fig. 11

Variation diagram of the deflection w2: (a) three-dimensional view, (b) XY view, (c) XZ view, and (d) YZ view

Grahic Jump Location
Fig. 12

Folding configuration of the Miura origami unit in the Appendix: (a) triangle FGH, (b) triangle FGK, (c) triangle FKH, (d) triangle OGI, and (e) triangle EFL

Tables

Errata

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