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Introduction to the Miura Fold

The Miura fold or Miura-ori is one of the most extensively used origami patterns in engineering applications and is named after Dr. Kōryō Miura who created it for deploying structures in space1, such as the solar panels on the Space Flyer Unit in 19952. The Miura fold exhibits properties of interest to engineering, such as a negative Poisson ratio, flat- and rigid-foldability, and actuation in a single degree of freedom3.

The Poisson ratio is a measure of the deformation of a material in the direction perpendicular to the loading. Most materials have a positive Poisson ratio, meaning they expand in another direction when compressed in one (or contract when stretched). For example, if you have a block of clay and press down on it, it will expand in the horizontal direction as it shrinks in the vertical. This is what makes the Miura fold interesting, as the negative Poisson ratio means it will expand in both the horizontal and vertical directions under compression. This kind of material is called ‘auxetic’ and occurs in nature, such as in numerous types of hardwood4.

Flat-foldability refers to the ability of a model to be pressed flat without wrinkles or additional creases5 while rigid-foldability means the model is created by folding about the crease lines without twisting or stretching6 (i.e., treating creases as hinges between flat plates), which makes the Miura fold a type of rigid origami. ‘Actuation in a single degree of freedom’ means the structure made with the Miura fold can move along one axis, such as deployed/undeployed for a solar panel array. These properties are useful in engineering because flat-foldability enables designs which can stow away in a small amount of space and fold back out without undesired deformations and rigid-foldability is easier to apply to engineering designs, which often work with rigid materials (although the Miura fold has also more recently been used in a crawling soft robot7).

The Miura fold is quite simple for such a versatile pattern, consisting of only the basic mountain and valley folds. I recommend this video tutorial for those who want to learn how to make this pattern.

References:

  1. “MIURA FOLDING: APPLYING ORIGAMI TO SPACE EXPLORATION.” International Journal of Pure and Applied Mathematics, vol. 79, no. 2, 2012, pp. 269–79. ijpam.eu, https://ijpam.eu/contents/2012-79-2/8/index.html.
  2. Institute of Space and Astronautical Science | JAXA. 25 Nov. 2005, https://web.archive.org/web/20051125174630/http://www.isas.jaxa.jp/e/enterp/missions/complate/sfu/2dsa.shtml.
  3. Turner, Nicholas, et al. “A Review of Origami Applications in Mechanical Engineering.” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 230, no. 14, Aug. 2016, pp. 2345–62. DOI.org (Crossref), https://doi.org/10.1177/0954406215597713.
  4. Marmier, Arnaud, et al. “Negative Poisson’s Ratio: A Ubiquitous Feature of Wood.” Materials Today Communications, vol. 35, June 2023, p. 105810. ScienceDirect, https://doi.org/10.1016/j.mtcomm.2023.105810.
  5. Schneider, Jonathan. “Flat-Foldability of Origami Crease Patterns.” (2004).
  6. Feng, Huijuan, et al. “Rigid Foldability and Mountain-Valley Crease Assignments of Square-Twist Origami Pattern.” Mechanism and Machine Theory, vol. 152, Oct. 2020, p. 103947. ScienceDirect, https://doi.org/10.1016/j.mechmachtheory.2020.103947.
  7. Yu, Meng, et al. “A Crawling Soft Robot Driven by Pneumatic Foldable Actuators Based on Miura-Ori.” Actuators, vol. 9, no. 2, June 2020, p. 26. www.mdpi.com, https://doi.org/10.3390/act9020026.