Abstract

This paper applies the kirigami technique to a non-rigid foldable tubular origami to make a rigid foldable tubular design, i.e., a radially closable kirigami (RC-kiri). The laminar emergent torsional (LET) compliant joint is applied to surrogate the crease, which makes the design applicable in practical engineering applications. By incorporating a non-flat folding design, the folding angles of each crease are minimized, leading to a reduction in the strain exerted on engineering materials. The kinetostatic theoretical model is constructed using the principle of virtual work, and its results are compared with those obtained from a simulation model in finite element analysis (FEA). A 3D printed physical model is tested to obtain the relationship between forces and displacements. FEA and experimental results match with theoretical findings. This study builds a bridge between origami and kirigami and expands the application of LET joints to the fabrication of tubular kirigami.

References

1.
Sargent
,
B.
,
Butler
,
J.
,
Seymour
,
K.
,
Bailey
,
D.
,
Jensen
,
B.
,
Magleby
,
S.
, and
Howell
,
L.
,
2020
, “
An Origami-Based Medical Support System to Mitigate Flexible Shaft Buckling
,”
ASME J. Mech. Rob.
,
12
(
4
), p.
041005
.
2.
Paez
,
L.
,
Agarwal
,
G.
, and
Paik
,
J.
,
2016
, “
Design and Analysis of a Soft Pneumatic Actuator With Origami Shell Reinforcement
,”
Soft Rob.
,
3
(
3
), pp.
109
119
.
3.
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. U. S. A.
,
118
(
36
), p.
e2110023118
.
4.
Yao
,
S.
,
Zhu
,
H.
,
Liu
,
M.
,
Li
,
Z.
, and
Xu
,
P.
,
2020
, “
Energy Absorption of Origami Tubes With Polygonal Cross-Sections
,”
Thin-Walled Struct.
,
157
, p.
107013
.
5.
Zhai
,
Z.
,
Wang
,
Y.
, and
Jiang
,
H.
,
2018
, “
Origami-Inspired, on-Demand Deployable and Collapsible Mechanical Metamaterials With Tunable Stiffness
,”
Proc. Natl. Acad. Sci. U. S. A.
,
115
(
9
), pp.
2032
2037
.
6.
Ye
,
S.
,
Zhao
,
P.
,
Zhao
,
Y.
,
Kavousi
,
F.
,
Feng
,
H.
, and
Hao
,
G.
,
2022
, “
A Novel Radially Closable Tubular Origami Structure (RC-Ori) for Valves
,”
Actuators
,
11
(
9
).
7.
Miura
,
K.
, and
Tachi
,
T.
,
2010
, “
Synthesis of Rigid-Foldable Cylindrical Polyhedra
,”
Symmetry: Art and Science
,
Gmuend, Austria
,
Aug. 23–28
, pp.
1
4
.
8.
Bös
,
F.
,
Wardetzky
,
M.
,
Vouga
,
E.
, and
Gottesman
,
O.
,
2017
, “
On the Incompressibility of Cylindrical Origami Patterns
,”
ASME J. Mech. Des.
,
139
(
2
), p.
021404.
.
9.
Tachi
,
T.
, and
Miura
,
K.
,
2012
, “
Rigid-Foldable Cylinders and Cells
,”
J. Int. Assoc. Shell Spat. Struct.
,
53
, pp.
217
226
.
10.
Butler
,
J.
,
Morgan
,
J.
,
Pehrson
,
N.
,
Tolman
,
K.
,
Bateman
,
T.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2016
, “
Highly Compressible Origami Bellows for Harsh Environments
”.
11.
Melancon
,
D.
,
Forte
,
A. E.
,
Kamp
,
L. M.
,
Gorissen
,
B.
, and
Bertoldi
,
K.
,
2022
, “
Inflatable Origami: Multimodal Deformation via Multistability
,”
Adv. Funct. Mater.
,
32
(
35
), p.
2201891
.
12.
Pagano
,
A.
,
Yan
,
T.
,
Chien
,
B.
,
Wissa
,
A.
, and
Tawfick
,
S.
,
2017
, “
A Crawling Robot Driven by Multi-Stable Origami
,”
Smart Mater. Struct.
,
26
(
9
), p.
094007
.
13.
Jin
,
L.
,
Forte
,
A. E.
,
Deng
,
B.
,
Rafsanjani
,
A.
, and
Bertoldi
,
K.
,
2020
, “
Kirigami-Inspired Inflatables With Programmable Shapes
,”
Adv. Mater.
,
32
(
33
), p.
2001863
.
14.
Rafsanjani
,
A.
,
Jin
,
L.
,
Deng
,
B.
, and
Bertoldi
,
K.
,
2019
, “
Propagation of Pop Ups in Kirigami Shells
,”
Proc. Natl. Acad. Sci. U. S. A.
,
116
(
17
), pp.
8200
8205
.
15.
Delimont
,
I. L.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2015
, “
A Family of Dual-Segment Compliant Joints Suitable for Use as Surrogate Folds
,”
ASME J. Mech. Des.
,
137
(
9
), p.
092302
.
16.
Zhao
,
P.
,
Liu
,
J.
,
Wu
,
C.
,
Ye
,
S.
,
Yang
,
Q.
, and
Hao
,
G.
,
2023
, “
Deployment Analysis of Membranes With Creases Using a Nonlinear Torsion Spring Model
,”
Int. J. Mech. Sci.
,
255
, p.
108444
.
17.
Yang
,
M.
,
Grey
,
S. W.
,
Scarpa
,
F.
, and
Schenk
,
M.
,
2023
, “
Large Impact of Small Vertex Cuts on the Mechanics of Origami Bellows
,”
Extreme Mech. Lett.
,
60
, p.
101950
.
18.
Reid
,
A.
,
Lechenault
,
F.
,
Rica
,
S.
, and
Adda-Bedia
,
M.
,
2017
, “
Geometry and Design of Origami Bellows With Tunable Response
,”
Phys. Rev. E
,
95
(
1
), p.
013002
.
19.
Hwang
,
H.-Y.
,
2021
, “
Effects of Perforated Crease Line Design on Mechanical Behaviors of Origami Structures
,”
Int. J. Solids Struct.
,
230–231
, p.
111158
.
20.
Tachi
,
T.
,
2011
, “Rigid-Foldable Thick Origami,”
Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education
,
CRC Press
,
Boca Raton, FL
, pp.
253
264
.
21.
Lang
,
R. J.
,
Tolman
,
K. A.
,
Crampton
,
E. B.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2018
, “
A Review of Thickness-Accommodation Techniques in Origami-Inspired Engineering
,”
ASME Appl. Mech. Rev.
,
70
(
1
), p.
010805
.
22.
Pehrson
,
N. A.
,
Magleby
,
S. P.
,
Lang
,
R. J.
, and
Howell
,
L. L.
,
2016
, “
Introduction of Monolithic Origami With Thick-Sheet Materials
,”
Proc. IASS Annu. Symposia
,
2016
(
13
), pp.
1
10
.
23.
Lang
,
R. J.
,
Magleby
,
S.
, and
Howell
,
L.
,
2016
, “
Single Degree-of-Freedom Rigidly Foldable Cut Origami Flashers
,”
ASME J. Mech. Rob.
,
8
(
3
), p.
031005
.
24.
Butler
,
J.
,
Pehrson
,
N.
, and
Magleby
,
S.
,
2020
, “
Folding of Thick Origami Through Regionally Sandwiched Compliant Sheets
,”
ASME J. Mech. Rob.
,
12
(
1
), p.
011019
.
25.
Yu
,
J.
,
2015
, “
State-of-Art of Compliant Mechanisms and Their Applications
,”
Chin. J. Mech. Eng.
,
51
(
13
), p.
53
.
26.
Hao
,
G.
,
Yu
,
J.
, and
Li
,
H.
,
2016
, “
A Brief Review on Nonlinear Modeling Methods and Applications of Compliant Mechanisms
,”
Front. Mech. Eng.
,
11
(
2
), pp.
119
128
.
27.
Pehrson
,
N. A.
,
Bilancia
,
P.
,
Magleby
,
S.
, and
Howell
,
L.
,
2020
, “
Load–Displacement Characterization in Three Degrees-of-Freedom for General Lamina Emergent Torsion Arrays
,”
ASME J. Mech. Des.
,
142
(
9
), p.
093301
.
28.
Delimont
,
I. L.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2015
, “
Evaluating Compliant Hinge Geometries for Origami-Inspired Mechanisms
,”
ASME J. Mech. Rob.
,
7
(
1
), p.
011009
.
29.
Jacobsen
,
J. O.
,
Chen
,
G.
,
Howell
,
L. L.
, and
Magleby
,
S. P.
,
2009
, “
Lamina Emergent Torsional (LET) Joint
,”
Mech. Mach. Theory
,
44
(
11
), pp.
2098
2109
.
30.
Tao
,
J.
,
Khosravi
,
H.
,
Deshpande
,
V.
, and
Li
,
S.
,
2023
, “
Engineering by Cuts: How Kirigami Principle Enables Unique Mechanical Properties and Functionalities
,”
Adv. Sci.
,
10
(
1
), p.
2204733
.
31.
Sun
,
Y.
,
Ye
,
W.
,
Chen
,
Y.
,
Fan
,
W.
,
Feng
,
J.
, and
Sareh
,
P.
,
2021
, “
Geometric Design Classification of Kirigami-Inspired Metastructures and Metamaterials
,”
Structures
,
33
, pp.
3633
3643
.
32.
Morikawa
,
Y.
,
Yamagiwa
,
S.
,
Sawahata
,
H.
,
Numano
,
R.
,
Koida
,
K.
,
Ishida
,
M.
, and
Kawano
,
T.
,
2018
, “
Ultrastretchable Kirigami Bioprobes
,”
Adv. Healthc. Mater.
,
7
(
3
), p.
1701100
.
33.
Brooks
,
A. K.
,
Chakravarty
,
S.
,
Ali
,
M.
, and
Yadavalli
,
V. K.
,
2022
, “
Kirigami-Inspired Biodesign for Applications in Healthcare
,”
Adv. Mater.
,
34
(
18
), p.
2109550
.
34.
Park
,
J. J.
,
Won
,
P.
, and
Ko
,
S. H.
,
2019
, “
A Review on Hierarchical Origami and Kirigami Structure for Engineering Applications
,”
Int. J. Precis. Eng. Manuf.-Green Technol.
,
6
(
1
), pp.
147
161
.
35.
Iannucci
,
S.
, and
Li
,
S.
,
2020
, “
Pneumatic Extension Actuators With Kirigami Skins
,”
ASME 2020 Conference on Smart Materials, Adaptive Structures and Intelligent Systems
,
Online
,
Sept. 15
,
Vol. 84027, p. V001T08A001
.
36.
Babaee
,
S.
,
Shi
,
Y.
,
Abbasalizadeh
,
S.
,
Tamang
,
S.
,
Hess
,
K.
,
Collins
,
J. E.
,
Ishida
,
K.
, et al
,
2021
, “
Kirigami-Inspired Stents for Sustained Local Delivery of Therapeutics
,”
Nat. Mater.
,
20
(
8
), pp.
1085
1092
.
37.
Suh
,
J.-E.
,
Kim
,
T.-H.
, and
Han
,
J.-H.
,
2021
, “
New Approach to Folding a Thin-Walled Yoshimura Patterned Cylinder
,”
J. Spacecraft Rockets
,
58
(
2
), pp.
516
530
.
38.
Ye
,
S.
,
Zhao
,
P.
,
Li
,
S.
,
Kavousi
,
F.
, and
Hao
,
G.
,
2023
, “Modelling of a Tubular Kirigami (RC-Kiri) With Outside Lamina Emergent Torsional Joints,”
New Advances in Mechanisms, Transmissions and Applications
,
Springer Nature
,
Switzerland
, pp.
264
276
.
39.
Tachi
,
T.
,
2009
, “
Simulation of Rigid Origami
,”
Origami 4: Fourth Int. Meeting Origami Sci. Math. Educ.
,
4
.
40.
Bowen
,
L. A.
,
Baxter
,
W. L.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2014
, “
A Position Analysis of Coupled Spherical Mechanisms Found in Action Origami
,”
Mech. Mach. Theory
,
77
, pp.
13
24
.
41.
Hull
,
T.
,
2012
,
Project Origami: Activities for Exploring Mathematics
,
CRC Press
,
New York
.
42.
Chen
,
G.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2018
, “
Membrane-Enhanced Lamina Emergent Torsional Joints for Surrogate Folds
,”
ASME J. Mech. Des.
,
140
(
6
), p.
062303
.
43.
Young
,
W. C.
, and
Budynas
,
R. G.
,
2002
,
Formulas for Stress and Strain
, 7th ed.,
McGraw-Hill
,
New York
.
44.
Hao
,
G.
,
Li
,
H.
,
Nayak
,
A.
, and
Caro
,
S.
,
2018
, “
Design of a Compliant Gripper With Multimode Jaws
,”
ASME J. Mech. Rob.
,
10
(
3
), p.
031005
.
45.
Li
,
S.
,
Hao
,
G.
, and
Wright
,
W. M. D.
,
2021
, “
Design and Modelling of an Anti-Buckling Compliant Universal Joint With a Compact Configuration
,”
Mech. Mach. Theory
,
156
, p.
104162
.
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