We study the kinematics of leaf-out origami and explore its potential usage as multitransformable structures without the necessity of deforming the origami's facets or modifying its crease patterns. Specifically, by changing folding/unfolding schemes, we obtain various geometrical configurations of the leaf-out origami based on the same structure. We model the folding/unfolding motions of the leaf-out origami by introducing linear torsion springs along the crease lines, and we calculate the potential energy during the shape transformation. As a result, we find that the leaf-out structure exhibits distinctive values of potential energy depending on its folded stage, and it can take multiple paths of potential energy during the transformation process. We also observe that the leaf-out structure can show bistability, enabling negative stiffness and snap-through mechanisms. These unique features can be exploited to use the leaf-out origami for engineering applications, such as space structures and architectures.

References

References
1.
Kobayashi
,
H.
,
Kresling
,
B.
, and
Vincent
,
J. F. V.
,
1998
, “
The Geometry of Unfolding Tree Leaves
,”
Proc. R. Soc. B
,
265
(
1391
), pp.
147
154
.
2.
De Focatiis
,
D. S. A.
, and
Guest
,
S. D.
,
2002
, “
Deployable Membranes Designed From Folding Tree Leaves
,”
Philos. Trans. R. Soc., A
,
360
(
1791
), pp.
227
238
.
3.
Mahadevan
,
L.
, and
Rica
,
S.
,
2005
, “
Self-Organized Origami
,”
Science
,
307
(
5716
), p.
1740
.
4.
Cai
,
J.
,
Deng
,
X.
,
Xu
,
Y.
, and
Feng
,
J.
,
2015
, “
Geometry and Motion Analysis of Origami-Based Deployable Shelter Structures
,”
J. Struct. Eng.
,
141
(
10
), p.
06015001
.
5.
Kuribayashi
,
K.
,
Tsuchiya
,
K.
,
You
,
Z.
,
Tomus
,
D.
,
Umemoto
,
M.
,
Ito
,
T.
, and
Sasaki
,
M.
,
2006
, “
Self-Deployable Origami Stent Grafts as a Biomedical Application of Ni-Rich TiNi Shape Memory Alloy Foil
,”
Mater. Sci. Eng.: A
,
419
(
1–2
), pp.
131
137
.
6.
Tsuda
,
Y.
,
Mori
,
O.
,
Funase
,
R.
,
Sawada
,
H.
,
Yamamoto
,
T.
,
Saiki
,
T.
,
Endo
,
T.
, and
Kawaguchi
,
J.
,
2011
, “
Flight Status of IKAROS Deep Space Solar Sail Demonstrator
,”
Acta Astronaut.
,
69
(
9–10
), pp.
833
840
.
7.
Schenk
,
M.
, and
Guest
,
S. D.
,
2013
, “
Geometry of Miura-Folded Metamaterials
,”
Proc. Natl. Acad. Sci. U.S.A.
,
110
(
9
), pp.
3276
3281
.
8.
Zirbel
,
S. A.
,
Lang
,
R. J.
,
Thomson
,
M. W.
,
Sigel
,
D. A.
,
Walkemeyer
,
P. E.
,
Trease
,
B. P.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2013
, “
Accommodating Thickness in Origami-Based Deployable Arrays
,”
ASME J. Mech. Des.
,
135
(
11
), p.
111005
.
9.
Ahmed
,
S.
,
Ounaies
,
Z.
, and
Frecker
,
M.
,
2014
, “
Investigating the Performance and Properties of Dielectric Elastomer Actuators as a Potential Means to Actuate Origami Structures
,”
Smart Mater. Struct.
,
23
(
9
), p.
094003
.
10.
Felton
,
S.
,
Tolley
,
M.
,
Demaine
,
E.
,
Rus
,
D.
, and
Wood
,
R.
,
2014
, “
A Method for Building Self-Folding Machines
,”
Science
,
345
(
6197
), pp.
644
646
.
11.
Saito
,
K.
,
Tsukahara
,
A.
, and
Okabe
,
Y.
,
2014
, “
New Deployable Structures Based on an Elastic Origami Model
,”
ASME J. Mech. Des.
,
137
(
2
), p.
021402
.
12.
Hanna
,
B. H.
,
Lund
,
J. M.
,
Lang
,
R. J.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2014
, “
Waterbomb Base: A Symmetric Single-Vertex Bistable Origami Mechanism
,”
Smart Mater. Struct.
,
23
(
9
), p.
094009
.
13.
Waitukaitis
,
S.
,
Menaut
,
R.
,
Chen
,
B. G.-g.
, and
van Hecke
,
M.
,
2015
, “
Origami Multistability: From Single Vertices to Metasheets
,”
Phys. Rev. Lett.
,
114
(
5
), p.
055503
.
14.
Hawkes
,
E.
,
An
,
B.
,
Benbernou
,
N. M.
,
Tanaka
,
H.
,
Kim
,
S.
,
Demaine
,
E. D.
,
Rus
,
D.
, and
Wood
,
R. J.
,
2010
, “
Programmable Matter by Folding
,”
Proc. Natl. Acad. Sci. U.S.A.
,
107
(
28
), pp.
12441
12445
.
15.
Yasuda
,
H.
, and
Yang
,
J.
,
2015
, “
Reentrant Origami-Based Metamaterials With Negative Poisson's Ratio and Bistability
,”
Phys. Rev. Lett.
,
114
(
18
), p.
185502
.
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