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Research Papers

Single Degree-of-Freedom Rigidly Foldable Cut Origami Flashers

[+] Author and Article Information
Robert J. Lang

Lang Origami,
Alamo, CA 94507
e-mail: robert@langorigami.com

Spencer Magleby

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: magleby@byu.edu

Larry Howell

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: lhowell@byu.edu

Manuscript received June 29, 2015; final manuscript received October 18, 2015; published online March 7, 2016. Assoc. Editor: Mary Frecker.

J. Mechanisms Robotics 8(3), 031005 (Mar 07, 2016) (15 pages) Paper No: JMR-15-1166; doi: 10.1115/1.4032102 History: Received June 29, 2015; Revised October 18, 2015

We present the design for a family of deployable structures based on the origami flasher, which are rigidly foldable, i.e., foldable with revolute joints at the creases and planar rigid faces. By appropriate choice of sector angles and introduction of a cut, a single degree-of-freedom (DOF) mechanism is obtained. These structures may be used to realize highly compact deployable mechanisms.

Copyright © 2016 by ASME
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References

Figures

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Fig. 1

Scheel's wind-up membrane. Left: nearly open. Right: starting to close. From Ref. [12].

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Fig. 2

The Palmer–Shafer origami flasher. Left: nearly fully deployed. Right: stowed. From Ref. [1].

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Fig. 3

A polyhedral flasher with fourfold rotational symmetry. Top row: an ideal polyhedral flasher (left: crease pattern and right: folded form). Middle row: the same structure, modified to spread the layers to accommodate nonzero thickness. Bottom row: the same structure, but with additional reverse folds added to reduce the height. Note that the crease patterns and folded forms are shown at different scales; the diameter of the folded form is approximately the diameter of the central polygon of the crease pattern in each case.

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Fig. 4

The four distinct types of fold in a flasher. Here, we use the origami convention of drawing mountain folds as solid lines, valleys as dashed, with different tones for the four families of fold.

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Fig. 5

A degree-4 vertex. Left: crease pattern. Right: folded form.

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Fig. 6

A simplified flasher, containing only diagonal, bend, and central polygon folds. Left: the full crease pattern. Right: a close-up, with labeled sector angles.

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Fig. 7

Cut lines on the simple flasher. We cut out the central polygon and cut in from the edges along a diagonal fold.

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Fig. 8

Vertex and angle indexing in the simple flasher

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Fig. 9

A single-DOF flasher for various values of γbend. From upper left to lower right: γbend=0deg,3deg,5deg,10deg,20deg,30deg,40deg,65deg, and 87deg. Note that the scale varies from one subfigure to the next.

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Fig. 10

A view from the top of the flasher of Fig. 9 for γbend=80deg, showing collisions with the inner layers

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Fig. 11

A top view of the flasher with m = 4, n = 3, ϵ=3deg, δ=43.5deg, and γbend=87deg. Lines A and B indicate possible alternate cut lines.

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Fig. 12

Crease pattern with the addition of a pair of reverse folds along one of the diagonals

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Fig. 13

A portion of the crease pattern of a reverse-folded flasher, with reverse folds emanating from each of the diagonal vertices

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Fig. 14

A single-DOF reverse-folded flasher for various values of γbend. From upper left to lower right: γbend=0deg,3deg,5deg,10deg,20deg,30deg,40deg,65deg,    and87deg.

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Fig. 15

A view from the top of the flasher of Fig. 14 for γbend=80deg, showing collisions with the inner layers

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Fig. 16

A rigidly foldable flasher for various values of γbend. From upper left to lower right: γbend=0deg,3deg,5deg,10deg,20deg,30deg,40deg,65deg, and 87deg.

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Fig. 17

A rigidly foldable flasher near the endpoints of the motion. Left: γbend=1deg. Right: γbend=85deg (different scale).

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Fig. 18

A rigidly foldable hexagonal flasher near the endpoints of the motion. Left: γbend=0.5deg. Right: γbend=56deg (different scale).

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Fig. 19

A flasher with reverse folds only along the {s0,j,k} and {r0,j,k} lines with fivefold rotational symmetry. Top left: crease pattern. Top right: top view of the folded form. Bottom left: perspective view of the flasher with equally spaced cut planes. Bottom right: side view of same.

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Fig. 20

A constant-height flasher for m = 6, nr = 9, ε=3deg, and h = 4.8. Left: crease pattern. Right: folded form. In this flasher, the cut runs along the {s0,0,k} chain of creases.

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Fig. 21

A wood veneer laminate fabricated constant-height flasher for m = 6, nr = 9, ε=3deg, and h = 4.8. Top left: stowed state, top view. Top right: stowed state, side view. Bottom left: partially folded. Bottom right: deployed.

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Fig. 22

Schematic of a degree-4 vertex. (a) The vertex embedded in a unit sphere. Dashed lines are valley folds, and dotted lines are mountain folds. (b) The trace of the vertex on the Gaussian sphere. Since γ3 is a mountain fold, its sign is negative.

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