The is a method of folding a flat surface such as a sheet of paper into a smaller area. The fold is named for its inventor,
Japanese
astrophysicist Kōryō Miura.
The
crease patterns of the Miura fold form a
tessellation of the surface by
parallelograms. In one direction, the creases lie along straight lines, with each parallelogram forming the
mirror reflection of its neighbor across each crease. In the other direction, the creases zigzag, and each parallelogram is the
translation of its neighbor across the crease. Each of the zigzag paths of creases consists solely of
mountain fold
A mountain is an elevated portion of the Earth's crust, generally with steep sides that show significant exposed bedrock. Although definitions vary, a mountain may differ from a plateau in having a limited summit area, and is usually higher th ...
s or of
valley fold
A valley is an elongated low area often running between Hill, hills or Mountain, mountains, which will typically contain a river or stream running from one end to the other. Most valleys are formed by erosion of the land surface by rivers ...
s, with mountains alternating with valleys from one zigzag path to the next. Each of the straight paths of creases alternates between mountain and valley folds.
[. Reproduced in ''British Origami'', 1981, and online at the British Origami Society web site.]
The Miura fold is related to the
Kresling fold, the
Yoshimura fold
In mathematics, the Schwarz lantern is a polyhedral approximation to a cylinder, used as a pathological example of the difficulty of defining the area of a smooth (curved) surface as the limit of the areas of polyhedra. It is formed by stac ...
and the Hexagonal fold, and can be framed as a generalization of these folds.
The Miura fold is a form of
rigid origami, meaning that the fold can be carried out by a continuous motion in which, at each step, each parallelogram is completely flat. This property allows it to be used to fold surfaces made of rigid materials, making it distinct from the
Kresling fold and
Yoshimura fold
In mathematics, the Schwarz lantern is a polyhedral approximation to a cylinder, used as a pathological example of the difficulty of defining the area of a smooth (curved) surface as the limit of the areas of polyhedra. It is formed by stac ...
which cannot be rigidly folded and require panel
deformations to compress to a compact state.
For instance, large
solar panel arrays for space satellites in the
Japanese space program have been Miura folded before launch and then spread out in space.
A folded Miura fold can be packed into a compact shape, its thickness reflecting only the thickness of the folded material. Folded material can be unpacked in one motion by pulling on its opposite ends, and likewise folded by pushing the two ends together. In the solar array application, this property reduces the number of
motors required to unfold this shape, reducing weight and complexity.
Applications
The 1996
Space Flyer Unit deployed the 2D Array from a Miura folded configuration.
The inflatable membrane structure of the SPROUT satellite is carried into space in the Miura-folded state, and then deployed using inflatable tubes themselves carried into space in the Octagon-folded state.
Other potential applications of this fold include surgical devices such as
stents and flat-foldable furniture.
Researchers at the
University of Fribourg used the Miura fold to stack
hydrogel
A hydrogel is a crosslinked hydrophilic polymer that does not dissolve in water. They are highly absorbent yet maintain well defined structures. These properties underpin several applications, especially in the biomedical area. Many hydrogels ar ...
films, generating electricity similarly to
electric eel
The electric eels are a genus, ''Electrophorus'', of neotropical freshwater fish from South America in the family Gymnotidae. They are known for their ability to stun their prey by generating electricity, delivering shocks at up to 860 volts ...
s. The Miura fold is used to cause many parts of the stack to contact each other simultaneously.
References
External links
Origami science
Paper folding
Japanese inventions
{{Mathematics of paper folding