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Origami engineering

Nature Reviews Methods Primers volume 4, Article number: 40 (2024) Cite this article

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Abstract

Origami traces its origins to an ancient art form transforming flat thin surfaces into various complex, fabulous 3D objects. Nowadays, such transformation transcends art by offering a conceptual framework for non-destructive and scale-independent abstractions for engineering applications across diverse fields with potential impact in education, science and technology. For instance, a growing number of architected materials and structures are based on origami principles, leading to unique properties that are distinct from those previously found in either natural or engineered systems. To disseminate those concepts, this Primer provides a comprehensive overview of the major principles and elements in origami engineering, including theoretical fundamentals, simulation tools, manufacturing techniques and testing protocols that require non-standard set-ups. We highlight applications involving deployable structures, metamaterials, robotics, medical devices and programmable matter to achieve functions such as vibration control, mechanical computing and shape morphing. We identify challenges for the field, including finite rigidity, panel thickness accommodation, incompatibility with regular mechanical testing devices, manufacturing of non-developable patterns, sensitivity to imperfections and identifying the relevant physics at the scale of interest. We further envision the future of origami engineering aimed at next-generation multifunctional material and structural systems.

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Fig. 1: Origami overview.
Fig. 2: Origami experiments and manufacturing.
Fig. 3: Set-up designed for conducting compression and torsion experiments on the Kresling origami.
Fig. 4: Representation of the fusion of geometry, mathematics and art through origami tessellations.
Fig. 5: Mechanics of origami structures.
Fig. 6: Origami applications.

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Acknowledgements

D.M. acknowledges financial support from the European Union project ERC-CoG 2022-SFOAM-101086644. K.L. is supported by the National Key Research and Development Program of China (grant 2022YFB4701900) and the National Natural Science Foundation of China (grant 12372159). P.P.P. acknowledges support from the Indian Institute of Technology Madras through the seed grant and the Science & Engineering Research Board (SERB) of the Department of Science & Technology, Government of India (award SRG/2019/000999). Y.C. acknowledges the support of the National Natural Science Foundation of China (Projects 52320105005, 52035008) and the New Cornerstone Science Foundation through the XPLORER PRIZE (XPLORER-2020-1035). G.H.P. acknowledges financial support from the Natural Science Foundation (NSF) project 2323276. C.D. acknowledges the Army Research Office under Cooperative Agreement Number W911NF-22-2-0109.

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Author notes

  1. These authors contributed equally: Diego Misseroni, Phanisri P. Pratapa, Ke Liu.

Authors and Affiliations

  1. Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, Italy

    Diego Misseroni

  2. Department of Civil Engineering, Indian Institute of Technology Madras, Chennai, India

    Phanisri P. Pratapa

  3. Department of Advanced Manufacturing and Robotics, Peking University, Beijing, China

    Ke Liu

  4. Independent Researcher, Paris, France

    Biruta Kresling

  5. School of Mechanical Engineering, Tianjin University, Tianjin, China

    Yan Chen

  6. Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA, USA

    Chiara Daraio

  7. Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA

    Glaucio H. Paulino

  8. Princeton Materials Institute (PMI), Princeton University, Princeton, NJ, USA

    Glaucio H. Paulino

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Glossary

Bird’s feet condition

A single-vertex crease pattern can be rigidly folded if, and only if, it contains a bird’s foot, where a set of three creases of the same mountain/valley (M/V) assignment are separated sequentially by angles strictly between 0° and 180°, plus one additional crease of the opposite assignment.

Bloch wave reduction

A discrete Fourier transformation-based technique that enables efficient analysis of infinitely periodic lattice systems.

Colouring

The crease pattern of a flat-foldable origami structure (for example, crane) can be coloured such that no two neighbouring regions are assigned the same colour while using as few colours as possible.

Crease pattern

The pattern of creases left on the surface after an origami structure has been unfolded.

Creases

Marks left on the material surface after a fold has been unfolded.

Degree-four vertices

Vertices delimited by four creases or four panels. For example, parallelogram-based origami is composed of degree-four vertices.

Developable

Origami that can be unfolded into a flat sheet without overlapping or deformation of the panels.

Dihedral angle

The angle between adjacent panels, which describes the current configuration.

Elastic band gaps

The frequency range within which elastic wave propagation is prevented through the medium.

Extensions

Appendages on the panels that can be placed and glued onto the matching seats.

Flat-foldable

Origami that can be folded into a flattened state of zero volume.

Foldcore

A sandwich structure consisting of thin stiff facesheets and thick, low-density core made of an architected material (for example, origami).

Folding angles

The angles that are required for one panel of an adjacent pair to rotate until it meets the other panel in a consistent direction, which could be either the dihedral angle or its supplementary angle.

Kirigami

The Japanese art of cutting and folding thin sheets of materials (for example, paper) from flat into three-dimensional objects.

Linkages

Mechanisms built from stiff bars connected by freely rotating joints (rigid links).

Origami

The art of folding paper (or other surfaces) into three-dimensional shapes, usually from uncut squares or other continuous shapes.

Panels

The basic elements of an origami structure that occupy the area bounded by creases or borders of the surface.

Poisson’s ratio

The negative of the ratio of transverse strain to longitudinal strain in a material subject to uniaxial loading.

Right-hand thumb rule

A commonly used rule to determine direction of rotational quantities and associated vectors. Here, it is used to determine the direction or sign of the turning angles corresponding to an axis of rotation placed along the crease.

Rigid origami

Origami that can be folded while keeping all regions of the surface (for example, paper) flat and all crease lines straight.

Saint-Venant end effects

A small region near the point of load with non-uniform distribution of stress, where the effect of the exact form of the loading cannot be ignored.

Seats

Grooves made by material removal for precise placement of joints.

Tessellations

Coverings on a surface, using one or more patterns (tiles) with no overlaps and no gaps.

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Misseroni, D., Pratapa, P.P., Liu, K. et al. Origami engineering. Nat Rev Methods Primers 4, 40 (2024). https://doi.org/10.1038/s43586-024-00313-7

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