Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Multistable inflatable origami structures at the metre scale

Abstract

From stadium covers to solar sails, we rely on deployability for the design of large-scale structures that can quickly compress to a fraction of their size1,2,3,4. Historically, two main strategies have been used to design deployable systems. The first and most frequently used approach involves mechanisms comprising interconnected bar elements, which can synchronously expand and retract5,6,7, occasionally locking in place through bistable elements8,9. The second strategy makes use of inflatable membranes that morph into target shapes by means of a single pressure input10,11,12. Neither strategy, however, can be readily used to provide an enclosed domain that is able to lock in place after deployment: the integration of a protective covering in linkage-based constructions is challenging and pneumatic systems require a constant applied pressure to keep their expanded shape13,14,15. Here we draw inspiration from origami—the Japanese art of paper folding—to design rigid-walled deployable structures that are multistable and inflatable. Guided by geometric analyses and experiments, we create a library of bistable origami shapes that can be deployed through a single fluidic pressure input. We then combine these units to build functional structures at the metre scale, such as arches and emergency shelters, providing a direct route for building large-scale inflatable systems that lock in place after deployment and offer a robust enclosure through their stiff faces.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Triangular facets as building blocks for large-scale inflatable and bistable origami structures.
Fig. 2: Bistable and inflatable origami shapes.
Fig. 3: Metre-scale inflatable archway.
Fig. 4: Metre-scale inflatable shelter.

Data availability

The datasets generated or analysed during the current study are available from the corresponding author on reasonable request.

Code availability

The code generated during the current study is available from the corresponding author on reasonable request.

References

  1. 1.

    Pellegrino, S. Deployable Structures in Engineering (Springer-Verlag, 2014).

  2. 2.

    You, Z. & Pellegrino, S. Foldable bar structures. Int. J. Solids Struct. 34, 1825–1847 (1997).

    Article  Google Scholar 

  3. 3.

    Liu, Y., Du, H., Liu, L. & Leng, J. Shape memory polymers and their composites in aerospace applications: a review. Smart Mater. Struct. 23, 023001 (2014).

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Puig, L., Barton, A. & Rando, N. A review on large deployable structures for astrophysics missions. Acta Astron. 67, 12–26 (2010).

    Article  Google Scholar 

  5. 5.

    Zhao, J.-S., Chu, F. & Feng, Z.-J. The mechanism theory and application of deployable structures based on SLE. Mech. Mach. Theory, 44, 324–335 (2009).

    Article  Google Scholar 

  6. 6.

    Mira, L. A., Thrall, A. P. & De Temmerman, N. Deployable scissor arch for transitional shelters. Autom. Constr. 43, 123–131 (2014).

    Article  Google Scholar 

  7. 7.

    Thrall, A. P., Adriaenssens, S., Paya-Zaforteza, I. & Zoli, T. P. Linkage-based movable bridges: design methodology and three novel forms. Eng. Struct. 37, 214–223 (2012).

    Article  Google Scholar 

  8. 8.

    Arnouts, L. I. W., Massart, T. J., De Temmerman, N. & Berke, P. Structural optimisation of a bistable deployable scissor module. In Proc. IASS Annual Symposium 2019—Structural Membranes 2019 (eds Lázaro, C. et al.) (2019).

  9. 9.

    García-Mora, C. J. & Sánchez-Sánchez, J. Geometric method to design bistable and non—bistable deployable structures of straight scissors based on the convergence surface. Mech. Mach. Theory 146, 103720 (2020).

    Article  Google Scholar 

  10. 10.

    Cadogan, D., Stein, J. & Grahne, M. Inflatable composite habitat structures for lunar and Mars exploration. Acta Astron. 44, 399–406 (1999).

    Article  Google Scholar 

  11. 11.

    Block, J., Straubel, M. & Wiedemann, M. Ultralight deployable booms for solar sails and other large gossamer structures in space. Acta Astron. 68, 984–992 (2011).

    CAS  Article  Google Scholar 

  12. 12.

    Sifert, E., Reyssat, E., Bico, J. & Roman, B. Programming stiff inflatable shells from planar patterned fabrics. Soft Matter 16, 7898–7903 (2020).

    ADS  Article  Google Scholar 

  13. 13.

    Siéfert, E., Reyssat, E., Bico, J. & Roman, B. Bio-inspired pneumatic shape-morphing elastomers. Nat. Mater. 18, 16692–16696 (2019).

    Article  Google Scholar 

  14. 14.

    Usevitch, N. S. et al. An untethered isoperimetric soft robot. Sci. Robot. 5, eaaz0492 (2020).

    Article  Google Scholar 

  15. 15.

    Skouras, M. et al. Designing inflatable structures. ACM Trans. Graph. 33, 63 (2014).

    Article  Google Scholar 

  16. 16.

    Rus, D. & Tolley, M. T. Design, fabrication and control of origami robots. Nat. Rev. Mater. 3, 101–112 (2018).

    ADS  Article  Google Scholar 

  17. 17.

    Onal, C. D., Wood, R. J. & Rus, D. An origami-inspired approach to worm robots. IEEE ASME Trans. Mechatron. 18, 430–438 (2013).

    Article  Google Scholar 

  18. 18.

    Onal, C. D., Tolley, M. T., Wood, R. J. & Rus, D. Origami-inspired printed robots. IEEE ASME Trans. Mechatron. 20, 2214–2221 (2015).

    Article  Google Scholar 

  19. 19.

    Li, S. et al. A vacuum-driven origami “magic-ball” soft gripper. In 2019 International Conference on Robotics and Automation (ICRA) 7401–7408 (IEEE, 2019).

  20. 20.

    Miskin, M. Z. et al. Graphene-based bimorphs for micron-sized, autonomous origami machines. Proc. Natl Acad. Sci. USA 115, 466–470 (2018).

    ADS  CAS  Article  Google Scholar 

  21. 21.

    Silverberg, J. L. et al. Using origami design principles to fold reprogrammable mechanical metamaterials. Science 345, 647–650 (2014).

    ADS  CAS  Article  Google Scholar 

  22. 22.

    Dudte, L. H., Vouga, E., Tachi, T. & Mahadevan, L. Programming curvature using origami tessellations. Nat. Mater. 15, 583–588 (2016).

    ADS  CAS  Article  Google Scholar 

  23. 23.

    Filipov, E. T., Tachi, T. & Paulino, G. H. Origami tubes assembled into stiff, yet reconfigurable structures and metamaterials. Proc. Natl Acad. Sci. USA 112, 12321–12326 (2015).

    ADS  CAS  Article  Google Scholar 

  24. 24.

    Overvelde, J. T. B., Weaver, J. C., Hoberman, C. & Bertoldi, K. Rational design of reconfigurable prismatic architected materials. Nature 541, 347–352 (2017).

    ADS  CAS  Article  Google Scholar 

  25. 25.

    Iniguez-Rabago, A., Li, Y. & Overvelde, J. T. B. Exploring multistability in prismatic metamaterials through local actuation. Nat. Commun. 10, 5577 (2019).

    ADS  CAS  Article  Google Scholar 

  26. 26.

    Seymour, K. et al. Origami-based deployable ballistic barrier. In Proc. 7th International Meeting on Origami in Science Mathematics and Education 763–778 (2018).

  27. 27.

    Del Grosso, A. & Basso, P. Adaptive building skin structures. Smart Mater. Struct. 19, 124011 (2010).

    ADS  Article  Google Scholar 

  28. 28.

    Tachi, T. in Origami 5 (eds Wang-Iverson, P. et al.) Ch. 20 (CRC Press, 2011).

  29. 29.

    Zirbel, S. A. et al. Accommodating thickness in origami-based deployable arrays. J. Mech. Des. 135, 111005 (2013).

    Article  Google Scholar 

  30. 30.

    You, Z. & Cole, N. Self-locking bi-stable deployable booms. In 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference AIAA 2006-1685 (ARC, 2006); https://arc.aiaa.org/doi/abs/10.2514/6.2006-1685.

  31. 31.

    Lang., R. J. A computational algorithm for origami design. In Proc. 12th Annual ACM Symposium on Computational Geometry 98–105 (1996); https://ci.nii.ac.jp/naid/80009084712/en/.

  32. 32.

    Demaine, E. D. & Mitchell, J. S. B. Reaching folded states of a rectangular piece of paper. In Proc. 13th Canadian Conference on Computational Geometry (CCCG 2001) 73–75 (2001).

  33. 33.

    Demaine, E. D. & Tachi, T. Origamizer: a practical algorithm for folding any polyhedron. In Proc. 33rd International Symposium on Computational Geometry (SoCG 2017) 34:1–34:15 (2017).

    MATH  Google Scholar 

  34. 34.

    Martinez, R. V., Fish, C. R., Chen, X. & Whitesides, G. M. Elastomeric origami: programmable paper-elastomer composites as pneumatic actuators. Adv. Funct. Mater. 22, 1376–1384 (2012).

    CAS  Article  Google Scholar 

  35. 35.

    Li, S., Vogt, D. M., Rus, D. & Wood, R. J. Fluid-driven origami-inspired artificial muscles. Proc. Natl Acad. Sci. USA 114, 13132–13137 (2017).

    ADS  CAS  Article  Google Scholar 

  36. 36.

    Kim, W. et al. Bioinspired dual-morphing stretchable origami. Sci. Robot. 4, eaay3493 (2019).

    Article  Google Scholar 

  37. 37.

    Kamrava, S., Mousanezhad, D., Ebrahimi, H., Ghosh, R. & Vaziri, A. Origami-based cellular metamaterial with auxetic, bistable, and self-locking properties. Sci. Rep. 7, 46046 (2017).

    ADS  CAS  Article  Google Scholar 

  38. 38.

    Hanna, B., Lund, J., Lang, R., Magleby, S. & Howell, L. Waterbomb base: a symmetric single-vertex bistable origami mechanism. Smart Mater. Struct. 23, 094009 (2014).

    ADS  Article  Google Scholar 

  39. 39.

    Cai, J., Deng, X., Ya, Z., Jian, F. & Tu, Y. Bistable behavior of the cylindrical origami structure with Kresling pattern. J. Mech. Des. 137, 061406 (2015).

    Article  Google Scholar 

  40. 40.

    Silverberg, J. L. et al. Origami structures with a critical transition to bistability arising from hidden degrees of freedom. Nat. Mater. 14, 389–393 (2015).

    ADS  CAS  Article  Google Scholar 

  41. 41.

    Waitukaitis, S., Menaut, R., Gin-ge Chen, B. & van Hecke, M. Origami multistability: from single vertices to metasheets. Phys. Rev. Lett. 114, 055503 (2015).

    ADS  Article  Google Scholar 

  42. 42.

    Yasuda, H. & Yang, J. Reentrant origami-based metamaterials with negative Poisson’s ratio and bistability. Phys. Rev. Lett. 114, 185502 (2015).

    ADS  CAS  Article  Google Scholar 

  43. 43.

    Reid, A., Lechenault, F., Rica, S. & Adda-Bedia, M. Geometry and design of origami bellows with tunable response. Phys. Rev. E 95, 013002 (2017).

    ADS  Article  Google Scholar 

  44. 44.

    Faber, J. A., Arrieta, A. F. & Studart, A. R. Bioinspired spring origami. Science 359, 1386–1391 (2018).

    ADS  CAS  Article  Google Scholar 

  45. 45.

    Dolciani, M. P., Donnelly, A. J. & Jurgensen, R. C. Modern Geometry, Structure and Method (Houghton Mifflin, 1963).

  46. 46.

    Connelly, R. The rigidity of polyhedral surfaces. Math. Mag. 52, 275–283 (1979).

    MathSciNet  Article  Google Scholar 

  47. 47.

    Connelly, R., Sabitov, I. & Walz, A. The bellows conjecture. Contrib. Algebr. Geom. 38, 1–10 (1997).

    MathSciNet  MATH  Google Scholar 

  48. 48.

    Mackenzie, D. Polyhedra can bend but not breathe. Science 279, 1637–1637 (1998).

    CAS  Article  Google Scholar 

  49. 49.

    Chen, Y., Feng, H., Ma, J., Peng, R. & You, Z. Symmetric waterbomb origami. Proc. R. Soc. A 472, 20150846 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  50. 50.

    Paulino, G. H. & Liu. K. Nonlinear mechanics of non-rigid origami: an efficient computational approach. Proc. R. Soc. A 473, 20170348 (2017).

Download references

Acknowledgements

We thank E. Demaine, J. Ku, T. Tachi and Yunfang Yang for insightful discussions; S. Lindner-Liaw, M. Bhattacharya and M. Starkey for assistance in the fabrication of the centimetre-scale and large-scale structures; and A. E. Forte for his valuable comments and suggestions on the manuscript. This research was supported by NSF through the Harvard University Materials Research Science and Engineering Center grant number DMR-1420570 and DMREF grant number DMR-1922321, as well as the Fund for Scientific Research-Flanders (FWO).

Author information

Affiliations

Authors

Contributions

D.M., B.G., C.H. and K.B. proposed and developed the research idea. D.M. conducted the numerical calculations. D.M., B.G. and C.J.G.-M. designed and fabricated the centimetre-scale and metre-scale structures. D.M. performed the experiments. D.M., B.G. and K.B. wrote the paper. K.B. supervised the research.

Corresponding authors

Correspondence to Chuck Hoberman or Katia Bertoldi.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Larry Howell, Glaucio Paulino and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This file contains Supplementary Information, including Supplementary Figures 1-30 and additional references.

Supplementary Video 1

Fabrication of centimetre-scale structures. To realize centimetre-scale structures, we use two different methods based on cardboard and 3D-printed faces. In the first method, we assemble laser-cut cardboard facets with double-sided adhesive tape to form the hinges. In the second approach, we connect 3D-printed faces with flexible laser-cut sheets to form the hinges and coat the structures with a thin layer of silicone rubber to create an airtight cavity.

Supplementary Video 2

Inflatable and bistable origami shapes. In an attempt to design inflatable origami structures with flat and expanded stable configurations, we create a library of shapes realized by assembling two different triangles.

Supplementary Video 3

Multistable inflatable origami structures at the metre-scale. By combining our library of bistable origami shapes, we build metre-scale structures that (i) transform from a compact shape to an expanded one; (ii) deploy and retract through a single pressure input; (iii) harness multistability to lock in place after deployment; and (iv) provide a robust enclosure through their stiff faces.

Supplementary Video 4

Fabrication of the metre-scale shelter. The metre-scale shelter is fabricated out of 8 ft × 4 ft, 4-mm-thick, corrugated plastic sheets. We use a digital cutting system to cut the different parts of the shelter and pattern the hinges by scoring the sheets to reduce the thickness locally. To create an inflatable cavity, we connect the cut parts with adhesive tape.

Peer Review File

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Melancon, D., Gorissen, B., García-Mora, C.J. et al. Multistable inflatable origami structures at the metre scale. Nature 592, 545–550 (2021). https://doi.org/10.1038/s41586-021-03407-4

Download citation

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing