Abstract

Variable crease origami that exhibits crease topological morphing allows a given crease pattern to be folded into multiple shapes, greatly extending the reconfigurability of origami structures. However, it is a challenge to enable the thick-panel forms of such crease patterns to bifurcate uniquely and reliably into desired modes. Here, thick-panel theory combined with cuts is applied to a stacked origami tube with multiple bifurcation paths. The thick-panel form corresponding to the stacked origami tube is constructed, which can bifurcate exactly between two desired modes without falling into other bifurcation paths. Then, kinematic analysis is carried out, and the results reveal that the thick-panel origami tube is kinematically equivalent to its zero-thickness form with one degree-of-freedom (DOF). In addition, a reconfigurable physical prototype of the thick-panel origami tube is produced, which achieves reliable bifurcation control through a single actuator. Such thick-panel origami tubes with controllable reconfigurability have great potential engineering applications in the fields of morphing systems such as mechanical metamaterials, morphing wings, and deployable structures.

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References

1.
Lang
,
R. J.
,
2017
,
Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami
,
CRC Press
,
Boca Raton, FL
.
2.
Wang
,
K.
, and
Chen
,
Y.
,
2011
, “
Folding a Patterned Cylinder by Rigid Origami
,”
Origami
,
5
, pp.
265
276
.
3.
Fang
,
H.
,
Li
,
S.
,
Ji
,
H.
, and
Wang
,
K. W.
,
2016
, “
Uncovering the Deformation Mechanisms of Origami Metamaterials by Introducing Generic Degree-Four Vertices
,”
Phys. Rev. E
,
94
(
4
), p.
043002
.
4.
Waitukaitis
,
S.
, and
Van Hecke
,
M.
,
2016
, “
Origami Building Blocks: Generic and Special Four-Vertices
,”
Phys. Rev. E
,
93
(
2
), p.
023003
.
5.
Zimmermann
,
L.
, and
Stanković
,
T.
,
2020
, “
Rigid and Flat Foldability of a Degree-Four Vertex in Origami
,”
ASME J. Mech. Rob.
,
12
(
1
), p.
011004
.
6.
Miura
,
K.
,
1985
, “
Method of Packaging and Deployment of Large Membranes in Space
,”
Inst. Space Astronaut. Sci. Rep.
,
618
, pp.
1
9
.
7.
Wu
,
S.
,
Ze
,
Q.
,
Dai
,
J.
,
Udipi
,
N.
,
Paulino
,
G. H.
, and
Zhao
,
R.
,
2021
, “
Stretchable Origami Robotic Arm With Omnidirectional Bending and Twisting
,”
Proc. Natl. Acad. Sci.
,
118
(
36
), p.
e2110023118
.
8.
Overvelde
,
J. T.
,
De Jong
,
T. A.
,
Shevchenko
,
Y.
,
Becerra
,
S. A.
,
Whitesides
,
G. M.
,
Weaver
,
J. C.
,
Hoberman
,
C.
, and
Bertoldi
,
K.
,
2016
, “
A Three-Dimensional Actuated Origami-Inspired Transformable Metamaterial With Multiple Degrees of Freedom
,”
Nat. Commun.
,
7
(
1
), pp.
1
8
.
9.
Bolanos
,
D.
,
Ynchausti
,
C.
,
Brown
,
N.
,
Pruett
,
H.
,
Hunter
,
J.
,
Clark
,
B.
,
Bateman
,
T.
,
Howell
,
L. L.
, and
Magleby
,
S. P.
,
2022
, “
Considering Thickness-Accommodation, Nesting, Grounding and Deployment in Design of Miura-Ori Based Space Arrays
,”
Mech. Mach. Theory
,
174
, p.
104904
.
10.
Chen
,
Y.
,
Peng
,
R.
, and
You
,
Z.
,
2015
, “
Origami of Thick Panels
,”
Science
,
349
(
6246
), pp.
396
400
.
11.
Meloni
,
M.
,
Cai
,
J.
,
Zhang
,
Q.
,
Sang-Hoon Lee
,
D.
,
Li
,
M.
,
Ma
,
R.
,
Parashkevov
,
T. E.
, and
Feng
,
J.
,
2021
, “
Engineering Origami: A Comprehensive Review of Recent Applications, Design Methods, and Tools
,”
Adv. Sci.
,
8
(
13
), p.
2000636
.
12.
Peng
,
R.
,
Ma
,
J.
, and
Chen
,
Y.
,
2018
, “
The Effect of Mountain-Valley Folds on the Rigid Foldability of Double Corrugated Pattern
,”
Mech. Mach. Theory
,
128
, pp.
461
474
.
13.
Tachi
,
T.
, and
Hull
,
T. C.
,
2017
, “
Self-Foldability of Rigid Origami
,”
ASME J. Mech. Rob.
,
9
(
2
), p.
021008
.
14.
Filipov
,
E. T.
,
Tachi
,
T.
, and
Paulino
,
G. H.
,
2015
, “
Origami Tubes Assembled Into Stiff, yet Reconfigurable Structures and Metamaterials
,”
Proc. Natl. Acad. Sci.
,
112
(
40
), pp.
12321
12326
.
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
.
16.
Wang
,
R.
,
Song
,
Y.
, and
Dai
,
J. S.
,
2021
, “
Reconfigurability of the Origami-Inspired Integrated 8r Kinematotropic Metamorphic Mechanism and Its Evolved 6r and 4r Mechanisms
,”
Mech. Mach. Theory
,
161
, p.
104245
.
17.
Pratapa
,
P. P.
,
Liu
,
K.
, and
Paulino
,
G. H.
,
2019
, “
Geometric Mechanics of Origami Patterns Exhibiting Poisson's Ratio Switch by Breaking Mountain and Valley Assignment
,”
Phys. Rev. Lett.
,
122
(
15
), p.
155501
.
18.
Pratapa
,
P. P.
,
Liu
,
K.
,
Vasudevan
,
S. P.
, and
Paulino
,
G. H.
,
2021
, “
Reprogrammable Kinematic Branches in Tessellated Origami Structures
,”
ASME J. Mech. Rob.
,
13
(
3
), p.
031004
.
19.
Lyu
,
S.
,
Qin
,
B.
,
Deng
,
H.
, and
Ding
,
X.
,
2021
, “
Origami-Based Cellular Mechanical Metamaterials With Tunable Poisson's Ratio: Construction and Analysis
,”
Int. J. Mech. Sci.
,
212
, p.
106791
.
20.
Yasuda
,
H.
,
Gopalarethinam
,
B.
,
Kunimine
,
T.
,
Tachi
,
T.
, and
Yang
,
J.
,
2019
, “
Origami-Based Cellular Structures With In Situ Transition Between Collapsible and Load-Bearing Configurations
,”
Adv. Eng. Mater.
,
21
(
12
), p.
1900562
.
21.
Overvelde
,
J. T.
,
Weaver
,
J. C.
,
Hoberman
,
C.
, and
Bertoldi
,
K.
,
2017
, “
Rational Design of Reconfigurable Prismatic Architected Materials
,”
Nature
,
541
(
7637
), pp.
347
352
.
22.
Suh
,
J.-E.
,
Miyazawa
,
Y.
,
Yang
,
J.
, and
Han
,
J.-H.
,
2022
, “
Self-Reconfiguring and Stiffening Origami Tube
,”
Adv. Eng. Mater.
,
24
(
5
), p.
2101202
.
23.
Treml
,
B.
,
Gillman
,
A.
,
Buskohl
,
P.
, and
Vaia
,
R.
,
2018
, “
Origami Mechanologic
,”
Proc. Natl. Acad. Sci.
,
115
(
27
), pp.
6916
6921
.
24.
Liu
,
Z.
,
Fang
,
H.
,
Xu
,
J.
, and
Wang
,
K.-W.
,
2023
, “
Discriminative Transition Sequences of Origami Metamaterials for Mechanologic
,”
Adv. Intell. Syst.
,
5
(
1
), p.
2200146
.
25.
Yamaguchi
,
K.
,
Yasuda
,
H.
,
Tsujikawa
,
K.
,
Kunimine
,
T.
, and
Yang
,
J.
,
2022
, “
Graph-Theoretic Estimation of Reconfigurability in Origami-Based Metamaterials
,”
Mater. Des.
,
213
, p.
110343
.
26.
Liu
,
B.
,
Liao
,
Y.
,
Yang
,
Y.
,
Yang
,
C.
,
Tian
,
Y.
, and
Yin
,
H.
,
2023
, “
Design and Analysis of Reconfigurable and Deployable Thin-Walled Architectural Equipment Inspired by Mirror-Miura Origami Patterns
,”
Eng. Struct.
,
286
, p.
116059
.
27.
Liu
,
C.
, and
Felton
,
S. M.
,
2018
, “
Transformation Dynamics in Origami
,”
Phys. Rev. Lett.
,
121
(
25
), p.
254101
.
28.
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
.
29.
Liu
,
Z.
,
Fang
,
H.
,
Xu
,
J.
, and
Wang
,
K.
,
2021
, “
A Novel Origami Mechanical Metamaterial Based on Miura-Variant Designs: Exceptional Multistability and Shape Reconfigurability
,”
Smart Mater. Struct.
,
30
(
8
), p.
085029
.
30.
Tao
,
J.
, and
Li
,
S.
,
2022
, “
Asymmetric Multi-Stability From Relaxing the Rigid-Folding Conditions in a Stacked Miura-Ori Cellular Solid
,”
Thin-Walled Struct.
,
179
, p.
109685
.
31.
Chen
,
Y.
,
Feng
,
H.
,
Ma
,
J.
,
Peng
,
R.
, and
You
,
Z.
,
2016
, “
Symmetric Waterbomb Origami
,”
Proc. R. Soc. A
,
472
(
2190
), p.
20150846
.
32.
Wang
,
C.
,
Li
,
J.
, and
Zhang
,
D.
,
2023
, “
Motion Singularity Analysis of the Thick-Panel Kirigami
,”
Mech. Mach. Theory
,
180
, p.
105162
.
33.
Dai
,
J. S.
, and
Rees Jones
,
J.
,
1999
, “
Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds
,”
ASME J. Mech. Des.
,
121
(
3
), pp.
375
382
.
34.
Chen
,
Y.
,
Lv
,
W.
,
Li
,
J.
, and
You
,
Z.
,
2017
, “
An Extended Family of Rigidly Foldable Origami Tubes
,”
ASME J. Mech. Rob.
,
9
(
2
), p.
021002
.
35.
Tachi
,
T.
,
2009
, “
One-DOF Cylindrical Deployable Structures With Rigid Quadrilateral Panels
,”
Proceedings of the International Association for Shell and Spatial Structures, Editorial Universitat Politècnica de València
,
València, Spain
,
Sept. 28–Oct.2
, pp.
2295
2305
.
36.
Lv
,
W.
,
Chen
,
Y.
, and
Zhang
,
J.
,
2023
, “
Thick-Panel Origami Tubes With Hexagonal Cross-Sections
,”
ASME J. Mech. Rob.
,
15
(
5
), pp.
051012
.
37.
Zhang
,
X.
, and
Chen
,
Y.
,
2019
, “
Vertex-Splitting on a Diamond Origami Pattern
,”
ASME J. Mech. Rob.
,
11
(
3
), pp.
031014
.
38.
Wang
,
C.
,
Zhang
,
D.
,
Li
,
J.
, and
You
,
Z.
,
2022
, “
Kirigami-Inspired Thick-Panel Deployable Structures
,”
Int. J. Solids Struct.
,
251
, p.
111752
.
39.
Hunt
,
K. H.
, and
Hunt
,
K. H.
,
1978
,
Kinematic Geometry of Mechanisms
,
Oxford University Press
,
New York
.
40.
Feng
,
H.
,
Chen
,
Y.
,
Dai
,
J. S.
, and
Gogu
,
G.
,
2017
, “
Kinematic Study of the General Plane-Symmetric Bricard Linkage and Its Bifurcation Variations
,”
Mech. Mach. Theory
,
116
, pp.
89
104
.
41.
Liu
,
B.
,
Liang
,
H.
,
Han
,
Z.-H.
, and
Yang
,
G.
,
2022
, “
Surrogate-Based Aerodynamic Shape Optimization of a Morphing Wing Considering a Wide Mach-Number Range
,”
Aerosp. Sci. Technol.
,
124
, pp.
107557
.
42.
Denavit
,
J.
, and
Hartenberg
,
R. S.
,
1955
, “
A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices
,”
ASME J. Appl. Mech.
,
22
(
2
), pp.
215
221
.
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