https://orcid.org/0000-0002-9355-7515
Abstract
In recent decades, origami has transitioned from a traditional art form into a systematic field of scientific inquiry, characterized by attributes such as high foldability, lightweight frameworks, diverse deformation modes, and limited degrees-of-freedom. Despite the abundant literature on smart materials, actuation methods, design principles, and manufacturing techniques, comprehensive reviews focusing on the mechanical properties of origami-inspired structures are relatively rare and unsystematic. This review aims to fill this void by analyzing and summarizing the significant studies conducted on the mechanical properties of origami-inspired structures from 2013 to 2023. We begin with an overview that includes essential definitions of origami, classical origami patterns, and their associated tessellated or stacked structures. Following this, we delve into the principal dynamic modeling method for origami and conduct an in-depth analysis of the key mechanical properties of origami-inspired structures. These properties include tunable stiffness, bistability and multistability, metamechanical properties demonstrated by origami-based metamaterials, and bio-inspired mechanical properties. Finally, we conclude with a comprehensive summary that discusses the current challenges and future directions in the field of origami-inspired structures. Our review provides a thorough synthesis of both the mechanical properties and practical applications of origami-inspired structures, aiming to serve as a reference and stimulate further research.
References
1.
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
.10.1002/advs.2020006362.
Ai
, C.
, Chen
, Y.
, Xu
, L.
, Li
, H.
, Liu
, C.
, Shang
, F.
, Xia
, Q.
, and Zhang
, S.
, 2021
, “Current Development on Origami/Kirigami-Inspired Structure of Creased Patterns Toward Robotics
,” Adv. Eng. Mater.
, 23
(10
), p. 2100473
.10.1002/adem.2021004733.
Rus
, D.
, and Tolley
, M. T.
, 2018
, “Design, Fabrication and Control of Origami Robots
,” Nat. Rev. Mater.
, 3
(6
), pp. 101
–112
.10.1038/s41578-018-0009-84.
Peraza Hernandez
, E. A.
, Hartl
, D. J.
, and Lagoudas
, D. C.
, 2019
, Active Origami: Modeling, Design, and Applications
, Springer International Publishing
, Cham, Switzerland
.5.
Suh
, J.-E.
, and Han
, J.-H.
, 2023
, “An Origami-Based Adaptive Vibration Isolator With Yoshimura-Patterned Reconfigurable Module
,” J. Intell. Mater. Syst. Struct.
, 34
(18
), pp. 2157
–2171
.10.1177/1045389X2311645296.
Du
, Y.
, Keller
, T.
, Song
, C.
, Xiao
, Z.
, Wu
, L.
, and Xiong
, J.
, 2021
, “Design and Foldability of Miura-Based Cylindrical Origami Structures
,” Thin-Walled Struct.
, 159
, p. 107311
.10.1016/j.tws.2020.1073117.
Liu
, X.
, Tian
, Y.
, Chen
, F.
, Mu
, Y.
, Caratenuto
, A.
, Minus
, M. L.
, and Zheng
, Y.
, 2022
, “A Waterbomb Origami Tower for Convertible Photothermal Evaporation
,” J. Mater. Chem. A
, 10
(36
), pp. 18657
–18670
.10.1039/D2TA04365C8.
Wang
, S.
, Gao
, Y.
, Huang
, H.
, Li
, B.
, Guo
, H.
, and Liu
, R.
, 2022
, “Design of Deployable Curved-Surface Rigid Origami Flashers
,” Mech. Mach. Theory
, 167
, p. 104512
.10.1016/j.mechmachtheory.2021.1045129.
Kidambi
, N.
, and Wang
, K. W.
, 2020
, “Dynamics of Kresling Origami Deployment
,” Phys. Rev. E
, 101
(6
), p. 063003
.10.1103/PhysRevE.101.06300310.
Lang
, R. J.
, 2007
, “The Science of Origami
,” Phys. World
, 20
(2
), pp. 30
–31
.10.1088/2058-7058/20/2/3111.
Tachi
, T.
, 2010
, “Origamizing Polyhedral Surfaces
,” IEEE Trans. Visualization Comput. Graphics
, 16
(2
), pp. 298
–311
.10.1109/TVCG.2009.6712.
Chen
, Y.
, Fan
, L.
, Bai
, Y.
, Feng
, J.
, and Sareh
, P.
, 2020
, “Assigning Mountain-Valley Fold Lines of Flat-Foldable Origami Patterns Based on Graph Theory and Mixed-Integer Linear Programming
,” Comput. Struct.
, 239
, p. 106328
.10.1016/j.compstruc.2020.10632813.
Dudte
, L. H.
, Choi
, G. P. T.
, and Mahadevan
, L.
, 2021
, “An Additive Algorithm for Origami Design
,” Proc. Natl. Acad. Sci.
, 118
(21
), p. e2019241118
.10.1073/pnas.201924111814.
Cehula
, J.
, and Průša
, V.
, 2020
, “Computer Modelling of Origami-Like Structures Made of Light Activated Shape Memory Polymers
,” Int. J. Eng. Sci.
, 150
, p. 103235
.10.1016/j.ijengsci.2020.10323515.
Chen
, Q.
, Feng
, F.
, Lv
, P.
, and Duan
, H.
, 2022
, “Origami Spring-Inspired Shape Morphing for Flexible Robotics
,” Soft Rob.
, 9
(4
), pp. 798
–806
.10.1089/soro.2021.003016.
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
.10.1073/pnas.211002311817.
Yasuda
, H.
, Miyazawa
, Y.
, Charalampidis
, E. G.
, Chong
, C.
, Kevrekidis
, P. G.
, and Yang
, J.
, 2019
, “Origami-Based Impact Mitigation Via Rarefaction Solitary Wave Creation
,” Sci. Adv.
, 5
(5
), p. eaau2835
.10.1126/sciadv.aau283518.
Zhang
, Q.
, Wang
, X.
, Cai
, J.
, and Feng
, J.
, 2021
, “Motion Paths and Mechanical Behavior of Origami-Inspired Tunable Structures
,” Mater. Today Commun.
, 26
, p. 101872
.10.1016/j.mtcomm.2020.10187219.
Karagiozova
, D.
, Zhang
, J.
, Chen
, P.
, Lu
, G.
, and You
, Z.
, 2022
, “Response of Graded Miura-Ori Metamaterials to Quasi-Static and Dynamic In-Plane Compression
,” J. Aerosp. Eng.
, 35
(4
), p. 04022035
.10.1061/(ASCE)AS.1943-5525.000141620.
Kim
, W.
, Eom
, J.
, and Cho
, K.-J.
, 2022
, “A Dual-Origami Design That Enables the Quasisequential Deployment and Bending Motion of Soft Robots and Grippers
,” Adv. Intell. Syst.
, 4
(3
), p. 2100176
.10.1002/aisy.20210017621.
Liu
, C.
, Wohlever
, S. J.
, Ou
, M. B.
, Padir
, T.
, and Felton
, S. M.
, 2022
, “Shake and Take: Fast Transformation of an Origami Gripper
,” IEEE Trans. Rob.
, 38
(1
), pp. 491
–506
.10.1109/TRO.2021.307656322.
Li
, D.
, Fan
, D.
, Zhu
, R.
, Lei
, Q.
, Liao
, Y.
, Yang
, X.
, Pan
, Y.
, et al., 2023
, “Origami-Inspired Soft Twisting Actuator
,” Soft Rob.
, 10
(2
), pp. 395
–409
.10.1089/soro.2021.018523.
Jiao
, Z.
, Zhang
, C.
, Ruan
, J.
, Tang
, W.
, Lin
, Y.
, Zhu
, P.
, Wang
, J.
, Wang
, W.
, Yang
, H.
, and Zou
, J.
, 2021
, “Re-Foldable Origami-Inspired Bidirectional Twisting of Artificial Muscles Reproduces Biological Motion
,” Cell Rep. Phys. Sci.
, 2
(5
), p. 100407
.10.1016/j.xcrp.2021.10040724.
Lee
, K.
, Wang
, Y.
, and Zheng
, C.
, 2020
, “TWISTER Hand: Underactuated Robotic Gripper Inspired by Origami Twisted Tower
,” IEEE Trans. Rob.
, 36
(2
), pp. 488
–500
.10.1109/TRO.2019.295687025.
Dufour
, L.
, Owen
, K.
, Mintchev
, S.
, and Floreano
, D.
, 2016
, “A Drone With Insect-Inspired Folding Wings
,” Proceedings of the 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
, Daejeon, South Korea
, Oct. 9–14, pp. 1576
–1581
.10.1109/IROS.2016.775925526.
Johnson
, K.
, Arroyos
, V.
, Ferran
, A.
, Villanueva
, R.
, Yin
, D.
, Elberier
, T.
, Aliseda
, A.
, Fuller
, S.
, Iyer
, V.
, and Gollakota
, S.
, 2023
, “Solar-Powered Shape-Changing Origami Microfliers
,” Sci. Rob.
, 8
(82
), p. eadg4276
.10.1126/scirobotics.adg427627.
Phan
, H. V.
, and Park
, H. C.
, 2020
, “Mechanisms of Collision Recovery in Flying Beetles and Flapping-Wing Robots
,” Science
, 370
(6521
), pp. 1214
–1219
.10.1126/science.abd328528.
Sadeghi
, S.
, Allison
, S. R.
, Bestill
, B.
, and Li
, S.
, 2021
, “TMP Origami Jumping Mechanism With Nonlinear Stiffness
,” Smart Mater. Struct.
, 30
(6
), p. 065002
.10.1088/1361-665X/abf5b229.
Olan'g
, Q.
, Peng
, H.
, and Mao
, T.
, 2022
, “Characteristics of a Small Arbitrary Walking and Jumping Composite Soft Actuator With Origami Structure
,” Sens. Actuator A-Phys.
, 347
, p. 113904
.10.1016/j.sna.2022.11390430.
Göttler
, C.
, Elflein
, K.
, Siegwart
, R.
, and Sitti
, M.
, 2021
, “Spider Origami: Folding Principle of Jumping Spider Leg Joints for Bioinspired Fluidic Actuators
,” Adv. Sci.
, 8
(5
), p. 2003890
.10.1002/advs.20200389031.
Tang
, L.
, Li
, Y.
, and Li
, B.
, 2024
, “Moobot: A Miniature Origami Omnidirectional Jumping Robot With High Trajectory Accuracy
,” IEEE Trans. Ind. Electron.
, 71
(6
), pp. 6032
–6040
.10.1109/TIE.2023.329462932.
Kamrava
, S.
, Mousanezhad
, D.
, Felton
, S. M.
, and Vaziri
, A.
, 2018
, “Programmable Origami Strings
,” Adv. Mater. Technol.
, 3
(3
), p. 1700276
.10.1002/admt.20170027633.
Lu
, Q.
, Clark
, A. B.
, Shen
, M.
, and Rojas
, N.
, 2020
, “An Origami-Inspired Variable Friction Surface for Increasing the Dexterity of Robotic Grippers
,” IEEE Rob. Autom. Lett.
, 5
(2
), pp. 2538
–2545
.10.1109/LRA.2020.297283334.
Chen
, B.
, Shao
, Z.
, Xie
, Z.
, Liu
, J.
, Pan
, F.
, He
, L.
, Zhang
, L.
, et al., 2021
, “Soft Origami Gripper With Variable Effective Length
,” Adv. Intell. Syst.
, 3
(10
), p. 2000251
.10.1002/aisy.20200025135.
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
.10.1088/1361-665X/aa721e36.
Ze
, Q.
, Wu
, S.
, Nishikawa
, J.
, Dai
, J.
, Sun
, Y.
, Leanza
, S.
, Zemelka
, C.
, Novelino
, L. S.
, Paulino
, G. H.
, and Zhao
, R. R.
, 2022
, “Soft Robotic Origami Crawler
,” Sci. Adv.
, 8
(13
), p. eabm7834
.10.1126/sciadv.abm783437.
Jin
, T.
, Li
, L.
, Wang
, T.
, Wang
, G.
, Cai
, J.
, Tian
, Y.
, and Zhang
, Q.
, 2022
, “Origami-Inspired Soft Actuators for Stimulus Perception and Crawling Robot Applications
,” IEEE Trans. Rob.
, 38
(2
), pp. 748
–764
.10.1109/TRO.2021.309664438.
Liu
, S.
, Peng
, G.
, Li
, Z.
, Li
, W.
, and Sun
, L.
, 2023
, “Low-Frequency Vibration Isolation Via an Elastic Origami-Inspired Structure
,” Int. J. Mech. Sci.
, 260
, p. 108622
.10.1016/j.ijmecsci.2023.10862239.
Ye
, K.
, and Ji
, J. C.
, 2022
, “An Origami Inspired Quasi-Zero Stiffness Vibration Isolator Using a Novel Truss-Spring Based Stack Miura-Ori Structure
,” Mech. Syst. Signal Process.
, 165
, p. 108383
.10.1016/j.ymssp.2021.10838340.
Deleo
, A. A.
, O'Neil
, J.
, Yasuda
, H.
, Salviato
, M.
, and Yang
, J.
, 2020
, “Origami-Based Deployable Structures Made of Carbon Fiber Reinforced Polymer Composites
,” Compos. Sci. Technol.
, 191
, p. 108060
.10.1016/j.compscitech.2020.10806041.
Melancon
, D.
, Gorissen
, B.
, García-Mora
, C. J.
, Hoberman
, C.
, and Bertoldi
, K.
, 2021
, “Multistable Inflatable Origami Structures at the Metre Scale
,” Nature
, 592
(7855
), pp. 545
–550
.10.1038/s41586-021-03407-442.
Wang
, C.
, Guo
, H.
, Liu
, R.
, and Deng
, Z.
, 2022
, “A Programmable Origami-Inspired Space Deployable Structure With Curved Surfaces
,” Eng. Struct.
, 256
, p. 113934
.10.1016/j.engstruct.2022.11393443.
Lee
, D.-Y.
, Kim
, S.-R.
, Kim
, J.-S.
, Park
, J.-J.
, and Cho
, K.-J.
, 2017
, “Origami Wheel Transformer: A Variable-Diameter Wheel Drive Robot Using an Origami Structure
,” Soft Rob.
, 4
(2
), pp. 163
–180
.10.1089/soro.2016.003844.
Fonseca
, L. M.
, Rodrigues
, G. V.
, Savi
, M. A.
, and Paiva
, A.
, 2019
, “Nonlinear Dynamics of an Origami Wheel With Shape Memory Alloy Actuators
,” Chaos, Solitons Fractals
, 122
, pp. 245
–261
.10.1016/j.chaos.2019.03.03345.
Lee
, D.-Y.
, Kim
, J.-K.
, Sohn
, C.-Y.
, Heo
, J.-M.
, and Cho
, K.-J.
, 2021
, “High-Load Capacity Origami Transformable Wheel
,” Sci. Rob.
, 6
(53
), p. eabe0201
.10.1126/scirobotics.abe020146.
Lee
, J.-G.
, and Rodrigue
, H.
, 2019
, “Origami-Based Vacuum Pneumatic Artificial Muscles With Large Contraction Ratios
,” Soft Rob.
, 6
(1
), pp. 109
–117
.10.1089/soro.2018.006347.
Robertson
, M. A.
, Kara
, O. C.
, and Paik
, J.
, 2021
, “Soft Pneumatic Actuator-Driven Origami-Inspired Modular Robotic ‘Pneumagami’
,” Int. J. Rob. Res.
, 40
(1
), pp. 72
–85
.10.1177/027836492090990548.
Gabler
, F.
, Karnaushenko
, D. D.
, Karnaushenko
, D.
, and Schmidt
, O. G.
, 2019
, “Magnetic Origami Creates High Performance Micro Devices
,” Nat. Commun.
, 10
(1
), p. 3013
.10.1038/s41467-019-10947-x49.
Xu
, T.
, Zhang
, J.
, Salehizadeh
, M.
, Onaizah
, O.
, and Diller
, E.
, 2019
, “Millimeter-Scale Flexible Robots With Programmable Three-Dimensional Magnetization and Motions
,” Sci. Rob.
, 4
(29
), p. eaav4494
.10.1126/scirobotics.aav449450.
Tang
, D.
, Zhang
, C.
, Sun
, H.
, Dai
, H.
, Xie
, J.
, Fu
, J.
, and Zhao
, P.
, 2021
, “Origami-Inspired Magnetic-Driven Soft Actuators With Programmable Designs and Multiple Applications
,” Nano Energy
, 89
, p. 106424
.10.1016/j.nanoen.2021.10642451.
Luo
, M.
, Yan
, R.
, Wan
, Z.
, Qin
, Y.
, Santoso
, J.
, Skorina
, E. H.
, and Onal
, C. D.
, 2018
, “OriSnake: Design, Fabrication, and Experimental Analysis of a 3-D Origami Snake Robot
,” IEEE Rob. Autom. Lett.
, 3
(3
), pp. 1993
–1999
.10.1109/LRA.2018.280011252.
Li
, Y.
, Huang
, H.
, and Li
, B.
, 2023
, “Design of a Deployable Continuum Robot Using Elastic Kirigami-Origami
,” IEEE Rob. Autom. Lett.
, 8
(12
), pp. 8382
–8389
.10.1109/LRA.2023.333005553.
Zhu
, Y.
, Birla
, M.
, Oldham
, K. R.
, and Filipov
, E. T.
, 2020
, “Elastically and Plastically Foldable Electrothermal Micro-Origami for Controllable and Rapid Shape Morphing
,” Adv. Funct. Mater.
, 30
(40
), p. 2003741
.10.1002/adfm.20200374154.
Ho
, D. T.
, Park
, H. S.
, Kim
, S. Y.
, and Schwingenschlögl
, U.
, 2020
, “Graphene Origami With Highly Tunable Coefficient of Thermal Expansion
,” ACS Nano
, 14
(7
), pp. 8969
–8974
.10.1021/acsnano.0c0379155.
Kim
, S.-H.
, Lee
, H. R.
, Yu
, S. J.
, Han
, M.-E.
, Lee
, D. Y.
, Kim
, S. Y.
, Ahn
, H.-J.
, et al., 2015
, “Hydrogel-Laden Paper Scaffold System for Origami-Based Tissue Engineering
,” Proc. Natl. Acad. Sci.
, 112
(50
), pp. 15426
–15431
.10.1073/pnas.150474511256.
Kang
, J.-H.
, Kim
, H.
, Santangelo
, C. D.
, and Hayward
, R. C.
, 2019
, “Enabling Robust Self-Folding Origami by Pre-Biasing Vertex Buckling Direction
,” Adv. Mater.
, 31
(39
), p. 0193006
.10.1002/adma.20190300657.
Zhang
, Y.
, Le
, X.
, Jian
, Y.
, Lu
, W.
, Zhang
, J.
, and Chen
, T.
, 2019
, “3D Fluorescent Hydrogel Origami for Multistage Data Security Protection
,” Adv. Funct. Mater.
, 29
(46
), p. 1905514
.10.1002/adfm.20190551458.
Chen
, Z.
, Li
, Y.
, and Li
, Q. M.
, 2021
, “Hydrogel-Driven Origami Metamaterials for Tunable Swelling Behavior
,” Mater. Des.
, 207
, p. 109819
.10.1016/j.matdes.2021.10981959.
Huang
, Z.
, Wei
, C.
, Dong
, L.
, Wang
, A.
, Yao
, H.
, Guo
, Z.
, and Mi
, S.
, 2022
, “Fluid-Driven Hydrogel Actuators With an Origami Structure
,” iScience
, 25
(7
), p. 104674
.10.1016/j.isci.2022.10467460.
An
, N.
, Li
, M.
, and Zhou
, J.
, 2020
, “Modeling SMA-Enabled Soft Deployable Structures for Kirigami/Origami Reflectors
,” Int. J. Mech. Sci.
, 180
, p. 105753
.10.1016/j.ijmecsci.2020.10575361.
Velvaluri
, P.
, Soor
, A.
, Plucinsky
, P.
, de Miranda
, R. L.
, James
, R. D.
, and Quandt
, E.
, 2021
, “Origami-Inspired Thin-Film Shape Memory Alloy Devices
,” Sci. Rep.
, 11
(1
), p. 10988
.10.1038/s41598-021-90217-362.
Zheng
, K.
, Gao
, E.
, Tian
, B.
, Liang
, J.
, Liu
, Q.
, Xue
, E.
, Shao
, Q.
, and Wu
, W.
, 2022
, “Modularized Paper Actuator Based on Shape Memory Alloy, Printed Heater, and Origami
,” Adv. Intell. Syst.
, 4
(12
), p. 2200194
.10.1002/aisy.20220019463.
Chung
, C.
, Hyeon
, K.
, Jeong
, J.
, Lee
, D.-Y.
, and Kyung
, K.-U.
, 2024
, “Origami-Inspired Wearable Robot for Shoulder Abduction Assistance: A Double-Petal Mechanism Utilizing Shape Memory Alloy Actuators
,” IEEE Rob. Autom. Lett.
, 9
(2
), pp. 1484
–1491
.10.1109/LRA.2023.334175164.
Chen
, T.
, Bilal
, O. R.
, Lang
, R.
, Daraio
, C.
, and Shea
, K.
, 2019
, “Autonomous Deployment of a Solar Panel Using Elastic Origami and Distributed Shape-Memory-Polymer Actuators
,” Phys. Rev. Appl.
, 11
(6
), p. 064069
.10.1103/PhysRevApplied.11.06406965.
Jape
, S.
, Garza
, M.
, Ruff
, J.
, Espinal
, F.
, Sessions
, D.
, Huff
, G.
, Lagoudas
, D. C.
, Peraza Hernandez
, E. A.
, and Hartl
, D. J.
, 2020
, “Self-Foldable Origami Reflector Antenna Enabled by Shape Memory Polymer Actuation
,” Smart Mater. Struct.
, 29
(11
), p. 115011
.10.1088/1361-665X/abaac266.
Liu
, Y.
, Zhang
, W.
, Zhang
, F.
, Lan
, X.
, Leng
, J.
, Liu
, S.
, Jia
, X.
, et al., 2018
, “Shape Memory Behavior and Recovery Force of 4D Printed Laminated Miura-Origami Structures Subjected to Compressive Loading
,” Compos. Part B: Eng.
, 153
, pp. 233
–242
.10.1016/j.compositesb.2018.07.05367.
Mailen
, R. W.
, Long
, R. M.
, Parmar
, K.
, Indaco
, M.
, and Guzzetti
, D.
, 2023
, “Quantifying Hinge Torque in Self-Folding, Shape Memory Polymer Origami Under Varying Thermal Loads
,” Appl. Mater. Today
, 35
, p. 101949
.10.1016/j.apmt.2023.10194968.
Chen
, H.
, Zhang
, X.-L.
, Zhang
, Y.-Y.
, Wang
, D.
, Bao
, D.-L.
, Que
, Y.
, Xiao
, W.
, et al., 2019
, “Atomically Precise, Custom-Design Origami Graphene Nanostructures
,” Science
, 365
(6457
), pp. 1036
–1040
.10.1126/science.aax786469.
Miskin
, M. Z.
, Dorsey
, K. J.
, Bircan
, B.
, Han
, Y.
, Muller
, D. A.
, McEuen
, P. L.
, and Cohen
, I.
, 2018
, “Graphene-Based Bimorphs for Micron-Sized, Autonomous Origami Machines
,” Proc. Natl. Acad. Sci.
, 115
(3
), pp. 466
–470
.10.1073/pnas.171288911570.
Mu
, J.
, Hou
, C.
, Wang
, H.
, Li
, Y.
, Zhang
, Q.
, and Zhu
, M.
, 2015
, “Origami-Inspired Active Graphene-Based Paper for Programmable Instant Self-Folding Walking Devices
,” Sci. Adv.
, 1
(10
), p. e1500533
.10.1126/sciadv.150053371.
Shah
, S. I. H.
, Bashir
, S.
, Ashfaq
, M.
, Altaf
, A.
, and Rmili
, H.
, 2021
, “Lightweight and Low-Cost Deployable Origami Antennas—A Review
,” IEEE Access
, 9
, pp. 86429
–86448
.10.1109/ACCESS.2021.308895372.
Mintchev
, S.
, Shintake
, J.
, and Floreano
, D.
, 2018
, “Bioinspired Dual-Stiffness Origami
,” Sci. Rob.
, 3
(20
), p. eaau0275
.10.1126/scirobotics.aau027573.
Xiang
, X. M.
, Lu
, G.
, and You
, Z.
, 2020
, “Energy Absorption of Origami Inspired Structures and Materials
,” Thin-Walled Struct.
, 157
, p. 107130
.10.1016/j.tws.2020.10713074.
Leanza
, S.
, Wu
, S.
, Sun
, X.
, Qi
, H. J.
, and Zhao
, R. R.
, 2024
, “Active Materials for Functional Origami
,” Adv. Mater.
, 36
(9
), p. 2302066
.10.1002/adma.20230206675.
Rojas
, J. P.
, Conchouso
, D.
, Arevalo
, A.
, Singh
, D.
, Foulds
, I. G.
, and Hussain
, M. M.
, 2017
, “Paper-Based Origami Flexible and Foldable Thermoelectric Nanogenerator
,” Nano Energy
, 31
, pp. 296
–301
.10.1016/j.nanoen.2016.11.01276.
Cai
, J.
, Estakhrianhaghighi
, E.
, and Akbarzadeh
, A.
, 2022
, “Functionalized Graphene Origami Metamaterials With Tunable Thermal Conductivity
,” Carbon
, 191
, pp. 610
–624
.10.1016/j.carbon.2022.02.00877.
Li
, X.
, Sheng
, X.
, Fang
, Y.
, Hu
, X.
, Gong
, S.
, Sheng
, M.
, Lu
, X.
, and Qu
, J.
, 2023
, “Wearable Janus-Type Film With Integrated All-Season Active/Passive Thermal Management, Thermal Camouflage, and Ultra-High Electromagnetic Shielding Efficiency Tunable by Origami Process
,” Adv. Funct. Mater.
, 33
(18
), p. 2212776
.10.1002/adfm.20221277678.
Dudte
, L. H.
, Vouga
, E.
, Tachi
, T.
, and Mahadevan
, L.
, 2016
, “Programming Curvature Using Origami Tessellations
,” Nat. Mater.
, 15
(5
), pp. 583
–588
.10.1038/nmat454079.
Meloni
, M.
, Zhang
, Q.
, Pak
, J.
, Bilore
, M. N.
, Ma
, R.
, Ballegaard
, E.
, Lee
, D. S.-H.
, and Cai
, J.
, 2022
, “Designing Origami Tessellations Composed of Quadrilateral Meshes and Degree-4 Vertices for Engineering Applications
,” Autom. Constr.
, 142
, p. 104482
.10.1016/j.autcon.2022.10448280.
Walker
, A.
, and Stankovic
, T.
, 2022
, “Algorithmic Design of Origami Mechanisms and Tessellations
,” Commun. Mater.
, 3
(1
), p. 4
.10.1038/s43246-022-00227-581.
Feng
, H.
, Ma
, J.
, Chen
, Y.
, and You
, Z.
, 2018
, “Twist of Tubular Mechanical Metamaterials Based on Waterbomb Origami
,” Sci. Rep.
, 8
(1
), p. 9522
.10.1038/s41598-018-27877-182.
Mukhopadhyay
, T.
, Ma
, J.
, Feng
, H.
, Hou
, D.
, Gattas
, J. M.
, Chen
, Y.
, and You
, Z.
, 2020
, “Programmable Stiffness and Shape Modulation in Origami Materials: Emergence of a Distant Actuation Feature
,” Appl. Mater. Today
, 19
, p. 100537
.10.1016/j.apmt.2019.10053783.
Ma
, J.
, Feng
, H.
, Chen
, Y.
, Hou
, D.
, and You
, Z.
, 2020
, “Folding of Tubular Waterbomb
,” Research
, 2020, Article No. 1735081.10.34133/2020/173508184.
Li
, S.
, Fang
, H.
, Sadeghi
, S.
, Bhovad
, P.
, and Wang
, K.-W.
, 2019
, “Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties
,” Adv. Mater.
, 31
(5
), p. 1805282
.10.1002/adma.20180528285.
Zhang
, Q.
, Fang
, H.
, and Xu
, J.
, 2020
, “Programmable Stopbands and Supratransmission Effects in a Stacked Miura-Origami Metastructure
,” Phys. Rev. E
, 101
(4
), p. 042206
.10.1103/PhysRevE.101.04220686.
Dang
, X.
, Lu
, L.
, Duan
, H.
, and Wang
, J.
, 2022
, “Deployment Kinematics of Axisymmetric Miura Origami: Unit Cells, Tessellations, and Stacked Metamaterials
,” Int. J. Mech. Sci.
, 232
, p. 107615
.10.1016/j.ijmecsci.2022.10761587.
Zhou
, H.
, Fang
, H.
, Wu
, H.
, and Xu
, J.
, 2023
, “Effects of Inter-Cell Connections on the Multi-Stable Dynamics of Dual-Cell Stacked Miura-Origami Structures
,” J. Sound Vib.
, 553
, p. 117682
.10.1016/j.jsv.2023.11768288.
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
.10.1103/PhysRevLett.122.15550189.
Meng
, F.
, Chen
, S.
, Zhang
, W.
, Ou
, P.
, Zhang
, J.
, Chen
, C.
, and Song
, J.
, 2021
, “Negative Poisson's Ratio in Graphene Miura Origami
,” Mech. Mater.
, 155
, p. 103774
.10.1016/j.mechmat.2021.10377490.
Moradweysi
, P.
, Santucci
, P. M.
, Carta
, G.
, Goudarzi
, T.
, Aghdam
, M. M.
, Baldi
, A.
, and Brun
, M.
, 2024
, “Design and Analysis of a Thick Miura-Ori Folded Structure With Large Negative Poisson's Ratio
,” Mech. Adv. Mater. Struct.
, 31
(4
), pp. 908
–926
.10.1080/15376494.2022.212656791.
Wang
, X.
, Qu
, H.
, and Guo
, S.
, 2023
, “Tristable Property and the High Stiffness Analysis of Kresling Pattern Origami
,” Int. J. Mech. Sci.
, 256
, p. 108515
.10.1016/j.ijmecsci.2023.10851592.
Yin
, P.
, Han
, H.
, Tang
, L.
, Tan
, X.
, Guo
, M.
, Xia
, C.
, and Aw
, K. C.
, 2024
, “Kresling Origami-Inspired Electromagnetic Energy Harvester With Reversible Nonlinearity
,” Smart Mater. Struct.
, 33
(3
), p. 035043
.10.1088/1361-665X/ad27fb93.
Johnson
, M.
, Chen
, Y.
, Hovet
, S.
, Xu
, S.
, Wood
, B.
, Ren
, H.
, Tokuda
, J.
, and Tse
, Z. T. H.
, 2017
, “Fabricating Biomedical Origami: A State-of-the-Art Review
,” Int. J. Comput. Assist. Radiol. Surg.
, 12
(11
), pp. 2023
–2032
.10.1007/s11548-017-1545-194.
Tang
, J.
, and Wei
, F.
, 2022
, “Miniaturized Origami Robots: Actuation Approaches and Potential Applications
,” Macromol. Mater. Eng.
, 307
(2
), p. 2100671
.10.1002/mame.20210067195.
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
.10.1115/1.403931496.
Lang
, R.
, 2018
, Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami
, CRC Press
, Boca Raton, FL
.97.
Hull
, T.
, 2003
, “Counting Mountain-Valley Assignments for Flat Folds
,” Ars Combinatoria
, 67
, pp. 175
–187
.10.48550/arXiv.1410.502298.
Bowen
, L. A.
, Grames
, C. L.
, Magleby
, S. P.
, Howell
, L. L.
, and Lang
, R. J.
, 2013
, “A Classification of Action Origami as Systems of Spherical Mechanisms
,” ASME J. Mech. Des.
, 135
(11
), p. 111008
.10.1115/1.402537999.
Santangelo
, C. D.
, 2020
, “Theory and Practice of Origami in Science
,” Soft Matter
, 16
(1
), pp. 94
–101
.10.1039/C9SM01745C100.
Karami
, A.
, Reddy
, A.
, and Nassar
, H.
, 2024
, “Curved-Crease Origami for Morphing Metamaterials
,” Phys. Rev. Lett.
, 132
(10
), p. 108201
.10.1103/PhysRevLett.132.108201101.
Evans
, T. A.
, Lang
, R. J.
, Magleby
, S. P.
, and Howell
, L. L.
, 2015
, “Rigidly Foldable Origami Gadgets and Tessellations
,” R. Soc. Open Sci.
, 2
(9
), p. 150067
.10.1098/rsos.150067102.
Lang
, R. J.
, Brown
, N.
, Ignaut
, B.
, Magleby
, S.
, and Howell
, L.
, 2020
, “Rigidly Foldable Thick Origami Using Designed-Offset Linkages
,” ASME J. Mech. Robot.
, 12
(2
), p. 021106.10.1115/1.4045940103.
Fonseca
, L. M.
, Rodrigues
, G. V.
, and Savi
, M. A.
, 2022
, “An Overview of the Mechanical Description of Origami-Inspired Systems and Structures
,” Int. J. Mech. Sci.
, 223
, p. 107316
.10.1016/j.ijmecsci.2022.107316104.
Hull
, T.
, 1994
, “On the Mathematics of Flat Origamis
,” Congr. Numer.
, 100
, pp. 215
–224
.http://origametry.net/papers/origamimath.pdf105.
Zhu
, YI.
, Schenk
, M.
, and Filipov
, E. T.
, 2022
, “A Review on Origami Simulations: From Kinematics, to Mechanics, toward Multiphysics
,” ASME Appl. Mech. Rev.
, 74
(3
), p. 03080110.1115/1.4055031.106.
Kawasaki
, T.
, 1989
, “On the Relation Between Mountain-Creases and Valley Creases of a Flat Origami
,” Proceedings of the First International Meeting Origami of Science and Technology
, Universita di Padova
, Italy
, Dec. 6–7, pp. 153
–157
.107.
Justin
, J.
, 1989
, “Mathematical Aspects of Paper Folding
,” Proceedings of the First International Meeting of Origami Science and Technology
, Universita di Padova
, Italy
, Dec. 6–9, pp. 263
–277
.108.
Kasahara
, K.
, and Takahama
, T.
, 1987
, Origami for the Connoisseur
, Japan Publications,
Tokyo, Japan.109.
Fulton
, J.
, and Schaub
, H.
, 2021
, “Forward Dynamics Analysis of Origami-Folded Deployable Spacecraft Structures
,” Acta Astronaut.
, 186
, pp. 549
–561
.10.1016/j.actaastro.2021.03.022110.
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
.10.1016/j.mechmachtheory.2022.104904111.
Wang
, S.
, Wu
, J.
, Yan
, P.
, Huang
, H.
, Li
, B.
, and Liu
, R.
, 2023
, “Design of Deployable Circular Structures Based on Miura Origami Pattern
,” Mech. Mach. Theory
, 186
, p. 105350
.10.1016/j.mechmachtheory.2023.105350112.
Guo
, Z.
, Tachi
, T.
, and Yu
, H.
, 2022
, “Folding Process Planning of Rigid Origami Using the Explicit Expression and Rapidly Exploring Random Tree Method
,” ASME J. Mech. Rob.
, 14
(1
), p. 011003
.10.1115/1.4051439113.
Chen
, Y.
, Feng
, H.
, Ma
, J.
, Peng
, R.
, and You
, Z.
, 2016
, “Symmetric Waterbomb Origami
,” Proc. R. Soc. A
, 472
(2190
), p. 20150846
.10.1098/rspa.2015.0846114.
O'Neil
, J.
, Salviato
, M.
, and Yang
, J.
, 2023
, “Energy Absorption Behavior of Filament Wound CFRP Origami Tubes Pre-Folded in Kresling Pattern
,” Compos. Struct.
, 304
, p. 116376
.10.1016/j.compstruct.2022.116376115.
Turco
, E.
, Barchiesi
, E.
, Causin
, A.
, dell'Isola
, F.
, and Solci
, M.
, 2023
, “Kresling Tube Metamaterial Exhibits Extreme Large-Displacement Buckling Behavior
,” Mech. Res. Commun.
, 134
, p. 104202
.10.1016/j.mechrescom.2023.104202116.
Li
, M.
, Zhou
, Z.
, Hao
, B.
, Yu
, C.
, Chen
, Y.
, and Ma
, J.
, 2023
, “Design and Deformation Analysis of an Inflatable Metallic Cylinder Based on the Kresling Origami Pattern
,” Thin-Walled Struct.
, 188
, p. 110859
.10.1016/j.tws.2023.110859117.
Ye
, H.
, Ma
, J.
, Zhou
, X.
, Wang
, H.
, and You
, Z.
, 2019
, “Energy Absorption Behaviors of Pre-Folded Composite Tubes With the Full-Diamond Origami Patterns
,” Compos. Struct.
, 221
, p. 110904
.10.1016/j.compstruct.2019.110904118.
Suh
, J.-E.
, Kim
, T.-H.
, and Han
, J.-H.
, 2021
, “New Approach to Folding a Thin-Walled Yoshimura Patterned Cylinder
,” J. Spacecr. Rockets
, 58
(2
), pp. 516
–530
.10.2514/1.A34784119.
Feng
, H.
, Yan
, G.
, and Prabhakar
, P.
, 2023
, “Role of Material Directionality on the Mechanical Response of Miura-Ori Composite Structures
,” Compos. Struct.
, 306
, p. 116606
.10.1016/j.compstruct.2022.116606120.
Yang
, H.
, and Ma
, L.
, 2018
, “Multi-Stable Mechanical Metamaterials With Shape-Reconfiguration and Zero Poisson's Ratio
,” Mater. Des.
, 152
, pp. 181
–190
.10.1016/j.matdes.2018.04.064121.
Schenk
, M.
, and Guest
, S. D.
, 2013
, “Geometry of Miura-Folded Metamaterials
,” Proc. Natl. Acad. Sci.
, 110
(9
), pp. 3276
–3281
.10.1073/pnas.1217998110122.
Yasuda
, H.
, and Yang
, J.
, 2015
, “Reentrant Origami-Based Metamaterials With Negative Poisson's Ratio and Bistability
,” Phys. Rev. Lett.
, 114
(18
), p. 185502
.10.1103/PhysRevLett.114.185502123.
Cai
, J.
, Deng
, X.
, Zhou
, Y.
, Feng
, J.
, and Tu
, Y.
, 2015
, “Bistable Behavior of the Cylindrical Origami Structure With Kresling Pattern
,” ASME J. Mech. Des.
, 137
, p. 061406
.10.1115/1.4030158124.
Xi
, K.
, Chai
, S.
, Ma
, J.
, and Chen
, Y.
, 2023
, “Multi-Stability of the Extensible Origami Structures
,” Adv. Sci.
, 10
(29
), p. 2303454
.10.1002/advs.202303454125.
Li
, Y.
, Pan
, F.
, Lin
, X.
, Yang
, K.
, Ren
, Y.
, Yang
, W.
, and Chen
, Y.
, 2023
, “Multistable Origami Honeycomb
,” Int. J. Mech. Sci.
, 243
, p. 108044
.10.1016/j.ijmecsci.2022.108044126.
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
.10.1103/PhysRevE.94.043002127.
Fang
, H.
, Chu
, S.-C. A.
, and Wang
, K. W.
, 2017
, “Self-Locking Origami Structures and Locking-Induced Piecewise Stiffness
,” ASME
Paper No. DETC2017-67197.10.1115/DETC2017-67197128.
Fang
, H.
, Li
, S.
, and Wang
, K. W.
, 2016
, “Self-Locking Degree-4 Vertex Origami Structures
,” Proc. R. Soc. A
, 472
(2195
), p. 20160682
.10.1098/rspa.2016.0682129.
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
.10.1073/pnas.1509465112130.
Sengupta
, S.
, and Li
, S.
, 2018
, “Harnessing the Anisotropic Multistability of Stacked-Origami Mechanical Metamaterials for Effective Modulus Programming
,” J. Intell. Mater. Syst. Struct.
, 29
(14
), pp. 2933
–2945
.10.1177/1045389X18781040131.
Schenk
, M.
, and Guest
, S. D.
, 2011
, “Origami Folding: A Structural Engineering Approach
,” Origami
, 5
, pp. 291
–304
.https://www3.eng.cam.ac.uk/~sdg/preprint/5OSME.pdf132.
Dong
, S.
, Zhao
, X.
, and Yu
, Y.
, 2021
, “Dynamic Unfolding Process of Origami Tessellations
,” Int. J. Solids Struct.
, 226–227
, p. 111075
.10.1016/j.ijsolstr.2021.111075133.
Filipov
, E.
, Liu
, K.
, Tachi
, T.
, Schenk
, M.
, and Paulino
, G. H.
, 2017
, “Bar and Hinge Models for Scalable Analysis of Origami
,” Int. J. Solids Struct.
, 124
, pp. 26
–45
.10.1016/j.ijsolstr.2017.05.028134.
Gillman
, A.
, Fuchi
, K.
, and Buskohl
, P.
, 2018
, “Truss-Based Nonlinear Mechanical Analysis for Origami Structures Exhibiting Bifurcation and Limit Point Instabilities
,” Int. J. Solids Struct.
, 147
, pp. 80
–93
.10.1016/j.ijsolstr.2018.05.011135.
Woodruff
, S. R.
, and Filipov
, E. T.
, 2020
, “A Bar and Hinge Model Formulation for Structural Analysis of Curved-Crease Origami
,” Int. J. Solids Struct.
, 204–205
, pp. 114
–127
.10.1016/j.ijsolstr.2020.08.010136.
Sadeghi
, S.
, Betsill
, B. D.
, and Li
, S.
, 2019
, “Design and Optimization of an Origami-Inspired Jumping Mechanism With Nonlinear Stiffness Properties
,” ASME
Paper No. DETC2019-97706.10.1115/DETC2019-97706137.
Yasuda
, H.
, Chong
, C.
, Charalampidis
, E. G.
, Kevrekidis
, P. G.
, and Yang
, J.
, 2016
, “Formation of Rarefaction Waves in Origami-Based Metamaterials
,” Phys. Rev. E
, 93
(4
), p. 043004
.10.1103/PhysRevE.93.043004138.
Sadeghi
, S.
, and Li
, S.
, 2019
, “Fluidic Origami Cellular Structure With Asymmetric Quasi-Zero Stiffness for Low-Frequency Vibration Isolation
,” Smart Mater. Struct.
, 28
(6
), p. 065006
.10.1088/1361-665X/ab143c139.
Soleimani
, H.
, Goudarzi
, T.
, and Aghdam
, M. M.
, 2021
, “Advanced Structural Modeling of a Fold in Origami/Kirigami Inspired Structures
,” Thin-Walled Struct.
, 161
, p. 107406
.10.1016/j.tws.2020.107406140.
Fonseca
, L. M.
, and Savi
, M. A.
, 2020
, “Nonlinear Dynamics of an Autonomous Robot With Deformable Origami Wheels
,” Int. J. Non-Linear Mech.
, 125
, p. 103533
.10.1016/j.ijnonlinmec.2020.103533141.
Zhai
, Z.
, Wang
, Y.
, and Jiang
, H.
, 2018
, “Origami-Inspired, On-Demand Deployable and Collapsible Mechanical Metamaterials With Tunable Stiffness
,” Proc. Natl. Acad. Sci.
, 115
(9
), pp. 2032
–2037
.10.1073/pnas.1720171115142.
Wang
, X.
, Qu
, H.
, Li
, X.
, Kuang
, Y.
, Wang
, H.
, and Guo
, S.
, 2023
, “Multi-Triangles Cylindrical Origami and Inspired Metamaterials With Tunable Stiffness and Stretchable Robotic Arm
,” PNAS Nexus
, 2
(4
), p. pgad098
.10.1093/pnasnexus/pgad098143.
Lu
, L.
, Leanza
, S.
, and Zhao
, R. R.
, 2023
, “Origami With Rotational Symmetry: A Review on Their Mechanics and Design
,” ASME Appl. Mech. Rev.
, 75
(5
), p. 050801
.10.1115/1.4056637144.
Liu
, K.
, and Paulino
, G.
, 2017
, “Nonlinear Mechanics of Non-Rigid Origami: An Efficient Computational Approach
,” Proc. R. Soc. A: Math., Phys. Eng. Sci.
, 473
(2206
), p. 20170348
.10.1098/rspa.2017.0348145.
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
.10.1103/PhysRevLett.114.055503146.
Wei
, Z. Y.
, Guo
, Z. V.
, Dudte
, L.
, Liang
, H. Y.
, and Mahadevan
, L.
, 2013
, “Geometric Mechanics of Periodic Pleated Origami
,” Phys. Rev. Lett.
, 110
(21
), p. 215501
.10.1103/PhysRevLett.110.215501147.
Brunck
, V.
, Lechenault
, F.
, Reid
, A.
, and Adda-Bedia
, M.
, 2016
, “Elastic Theory of Origami-Based Metamaterials
,” Phys. Rev. E
, 93
(3
), p. 033005
.10.1103/PhysRevE.93.033005148.
Yasuda
, H.
, Tachi
, T.
, Lee
, M.
, and Yang
, J.
, 2017
, “Origami-Based Tunable Truss Structures for Non-Volatile Mechanical Memory Operation
,” Nat. Commun.
, 8
(1
), p. 962
.10.1038/s41467-017-00670-w149.
Han
, H.
, Tang
, L.
, Cao
, D.
, and Liu
, L.
, 2020
, “Modeling and Analysis of Dynamic Characteristics of Multi-Stable Waterbomb Origami Base
,” Nonlinear Dyn.
, 102
(4
), pp. 2339
–2362
.10.1007/s11071-020-06082-8150.
Zhai
, Z.
, Wang
, Y.
, Lin
, K.
, Wu
, L.
, and Jiang
, H.
, 2020
, “In Situ Stiffness Manipulation Using Elegant Curved Origami
,” Sci. Adv.
, 6
(47
), p. eabe2000
.10.1126/sciadv.abe2000151.
Sun
, Y.
, Song
, K.
, Ju
, J.
, and Zhou
, X.
, 2024
, “Curved-Creased Origami Mechanical Metamaterials With Programmable Stabilities and Stiffnesses
,” Int. J. Mech. Sci.
, 262
, p. 108729
.10.1016/j.ijmecsci.2023.108729152.
Miyazawa
, Y.
, Yasuda
, H.
, Kim
, H.
, Lynch
, J. H.
, Tsujikawa
, K.
, Kunimine
, T.
, Raney
, J. R.
, and Yang
, J.
, 2021
, “Heterogeneous Origami-Architected Materials With Variable Stiffness
,” Commun. Mater.
, 2
(1
), p. 110
.10.1038/s43246-021-00212-4153.
Li
, Z.
, Kidambi
, N.
, Wang
, L.
, and Wang
, K.-W.
, 2020
, “Uncovering Rotational Multifunctionalities of Coupled Kresling Modular Structures
,” Extreme Mech. Lett.
, 39
, p. 100795
.10.1016/j.eml.2020.100795154.
Liu
, Q.
, Ye
, H.
, Cheng
, J.
, Li
, H.
, He
, X.
, Jian
, B.
, and Ge
, Q.
, 2023
, “Stiffness-Tunable Origami Structures Via Multimaterial Three-Dimensional Printing
,” Acta Mech. Solida Sin.
, 36
(4
), pp. 582
–593
.10.1007/s10338-023-00403-1155.
Chi
, Y.
, Li
, Y.
, Zhao
, Y.
, Hong
, Y.
, Tang
, Y.
, and Yin
, J.
, 2022
, “Bistable and Multistable Actuators for Soft Robots: Structures, Materials, and Functionalities
,” Adv. Mater.
, 34
(19
), p. 2110384
.10.1002/adma.202110384156.
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
.10.1088/0964-1726/23/9/094009157.
Wo
, Z.
, and Filipov
, E. T.
, 2023
, “Stiffening Multi-Stable Origami Tubes by Outward Popping of Creases
,” Extreme Mech. Lett.
, 58
, p. 101941
.10.1016/j.eml.2022.101941158.
Fang
, H.
, Li
, S.
, Ji
, H.
, and Wang
, K. W.
, 2017
, “Dynamics of a Bistable Miura-Origami Structure
,” Phys. Rev. E
, 95
(5
), p. 052211
.10.1103/PhysRevE.95.052211159.
Yasuda
, H.
, Johnson
, K.
, Arroyos
, V.
, Yamaguchi
, K.
, Raney
, J. R.
, and Yang
, J.
, 2022
, “Leaf-Like Origami With Bistability for Self-Adaptive Grasping Motions
,” Soft Rob.
, 9
(5
), pp. 938
–947
.10.1089/soro.2021.0008160.
Wang
, C.
, Guo
, H.
, Liu
, R.
, Deng
, Z.
, Chen
, Y.
, and You
, Z.
, 2024
, “Reconfigurable Origami-Inspired Multistable Metamorphous Structures
,” Sci. Adv.
, 10
(22
), p. eadk8662
.10.1126/sciadv.adk8662161.
Silverberg
, J. L.
, Evans
, A. A.
, McLeod
, L.
, Hayward
, R. C.
, Hull
, T.
, Santangelo
, C. D.
, and Cohen
, I.
, 2014
, “Using Origami Design Principles to Fold Reprogrammable Mechanical Metamaterials
,” Science
, 345
(6197
), pp. 647
–650
.10.1126/science.1252876162.
Bowen
, L.
, Frecker
, M.
, Simpson
, T. W.
, and von Lockette
, P.
, 2014
, “A Dynamic Model of Magneto-Active Elastomer Actuation of the Waterbomb Base
,” ASME
Paper No. DETC2014-35407.10.1115/DETC2014-35407163.
Grasinger
, M.
, Gillman
, A.
, and Buskohl
, P. R.
, 2022
, “Multistability, Symmetry and Geometric Conservation in Eightfold Waterbomb Origami
,” Proc. R. Soc. A
, 478
(2268
), p. 20220270
.10.1098/rspa.2022.0270164.
Flores
, J.
, Stein-Montalvo
, L.
, and Adriaenssens
, S.
, 2022
, “Effect of Crease Curvature on the Bistability of the Origami Waterbomb Base
,” Extreme Mech. Lett.
, 57
, p. 101909
.10.1016/j.eml.2022.101909165.
Zhang
, H.
, Zhu
, B.
, Chen
, B.
, Cui
, C.
, Li
, H.
, and Zhang
, X.
, 2022
, “A Phase Diagram-Based Stability Design Method for a Symmetrical Origami Waterbomb Base
,” ASME J. Mech. Des.
, 144
(10
), p. 103303
.10.1115/1.4054806166.
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
.10.1002/adfm.202201891167.
Lu
, L.
, Dang
, X.
, Feng
, F.
, Lv
, P.
, and Duan
, H.
, 2022
, “Conical Kresling Origami and Its Applications to Curvature and Energy Programming
,” Proc. R. Soc. A
, 478
(2257
), p. 20210712
.10.1098/rspa.2021.0712168.
Sharma
, H.
, Chaudhary
, A.
, and Upadhyay
, S. H.
, 2023
, “Experimental Verification of the Bistable Behavior of Conical Kresling Origami
,” Thin-Walled Struct.
, 190
, p. 110980
.10.1016/j.tws.2023.110980169.
Liu
, K.
, Tachi
, T.
, and Paulino
, G. H.
, 2019
, “Invariant and Smooth Limit of Discrete Geometry Folded From Bistable Origami Leading to Multistable Metasurfaces
,” Nat. Commun.
, 10
(1
), p. 4238
.10.1038/s41467-019-11935-x170.
Zhang
, L.
, Pan
, F.
, Ma
, Y.
, Yang
, K.
, Guo
, S.
, and Chen
, Y.
, 2023
, “Bistable Reconfigurable Origami Metamaterials With High Load-Bearing and Low State-Switching Forces
,” Extreme Mech. Lett.
, 63
, p. 102064
.10.1016/j.eml.2023.102064171.
Silverberg
, J. L.
, Na
, J.-H.
, Evans
, A. A.
, Liu
, B.
, Hull
, T. C.
, Santangelo
, C. D.
, Lang
, R. J.
, Hayward
, R. C.
, and Cohen
, I.
, 2015
, “Origami Structures With a Critical Transition to Bistability Arising From Hidden Degrees of Freedom
,” Nat. Mater.
, 14
(4
), pp. 389
–393
.10.1038/nmat4232172.
Fan
, J.
, Zhang
, L.
, Wei
, S.
, Zhang
, Z.
, Choi
, S.-K.
, Song
, B.
, and Shi
, Y.
, 2021
, “A Review of Additive Manufacturing of Metamaterials and Developing Trends
,” Mater. Today
, 50
, pp. 303
–328
.10.1016/j.mattod.2021.04.019173.
Kumar
, P.
, Ali
, T.
, and Pai
, M. M. M.
, 2021
, “Electromagnetic Metamaterials: A New Paradigm of Antenna Design
,” IEEE Access
, 9
, pp. 18722
–18751
.10.1109/ACCESS.2021.3053100174.
Gao
, N.
, Zhang
, Z.
, Deng
, J.
, Guo
, X.
, Cheng
, B.
, and Hou
, H.
, 2022
, “Acoustic Metamaterials for Noise Reduction: A Review
,” Adv. Mater. Technol.
, 7
(6
), p. 2100698
.10.1002/admt.202100698175.
Ren
, Z.
, Chang
, Y.
, Ma
, Y.
, Shih
, K.
, Dong
, B.
, and Lee
, C.
, 2020
, “Leveraging of MEMS Technologies for Optical Metamaterials Applications
,” Adv. Opt. Mater.
, 8
(3
), p. 1900653
.10.1002/adom.201900653176.
Wan
, M.
, Yu
, K.
, Gu
, J.
, Zeng
, H.
, Sun
, H.
, and Khatibi
, A. A.
, 2023
, “4D Printed TMP Origami Metamaterials With Programmable Mechanical Properties
,” Int. J. Mech. Sci.
, 250
, p. 108275
.10.1016/j.ijmecsci.2023.108275177.
Zhou
, X.
, Zang
, S.
, and You
, Z.
, 2016
, “Origami Mechanical Metamaterials Based on the Miura-Derivative Fold Patterns
,” Proc. R. Soc. A
, 472
(2191
), p. 20160361
.10.1098/rspa.2016.0361178.
Fang
, H.
, Chu
, S.-C. A.
, Xia
, Y.
, and Wang
, K.-W.
, 2018
, “Programmable Self-Locking Origami Mechanical Metamaterials
,” Adv. Mater.
, 30
(15
), p. 1706311
.10.1002/adma.201706311179.
Bertoldi
, K.
, Vitelli
, V.
, Christensen
, J.
, and van Hecke
, M.
, 2017
, “Flexible Mechanical Metamaterials
,” Nat. Rev. Mater.
, 2
(11
), p. 17066
.10.1038/natrevmats.2017.66180.
Chen
, Y.
, Liang
, J.
, Shi
, P.
, Feng
, J.
, Sareh
, P.
, and Dai
, J.
, 2023
, “Inverse Design of Programmable Poisson's Ratio and In-Plane Stiffness for Generalized Four-Fold Origami
,” Compos. Struct.
, 311
, p. 116789
.10.1016/j.compstruct.2023.116789181.
Boatti
, E.
, Vasios
, N.
, and Bertoldi
, K.
, 2017
, “Origami Metamaterials for Tunable Thermal Expansion
,” Adv. Mater.
, 29
(26
), p. 1700360
.10.1002/adma.201700360182.
Cai
, J.
, and Akbarzadeh
, A.
, 2021
, “Hierarchical Kirigami-Inspired Graphene and Carbon Nanotube Metamaterials: Tunability of Thermo-Mechanic Properties
,” Mater. Des.
, 206
, p. 109811
.10.1016/j.matdes.2021.109811183.
Chen
, Z.
, Wu
, T.
, Nian
, G.
, Shan
, Y.
, Liang
, X.
, Jiang
, H.
, and Qu
, S.
, 2019
, “Ron Resch Origami Pattern Inspired Energy Absorption Structures
,” ASME J. Appl. Mech.
, 86
(1
), p. 011005
.10.1115/1.4041415184.
Wang
, Z.
, Jing
, L.
, Yao
, K.
, Yang
, Y.
, Zheng
, B.
, Soukoulis
, C. M.
, Chen
, H.
, and Liu
, Y.
, 2017
, “Origami-Based Reconfigurable Metamaterials for Tunable Chirality
,” Adv. Mater.
, 29
(27
), p. 1700412
.10.1002/adma.201700412185.
Wickeler
, A. L.
, and Naguib
, H. E.
, 2020
, “Novel Origami-Inspired Metamaterials: Design, Mechanical Testing and Finite Element Modelling
,” Mater. Des.
, 186
, p. 108242
.10.1016/j.matdes.2019.108242186.
Xiang
, X.
, Fu
, Z.
, Zhang
, S.
, Lu
, G.
, Ha
, N. S.
, Liang
, Y.
, and Zhang
, X.
, 2021
, “The Mechanical Characteristics of Graded Miura-Ori Metamaterials
,” Mater. Des.
, 211
, p. 110173
.10.1016/j.matdes.2021.110173187.
Lv
, C.
, Krishnaraju
, D.
, Konjevod
, G.
, Yu
, H.
, and Jiang
, H.
, 2014
, “Origami Based Mechanical Metamaterials
,” Sci. Rep.
, 4
(1
), p. 5979
.10.1038/srep05979188.
Hedayati
, R.
, Roudbarian
, N.
, Tahmasiyan
, S.
, and Bodaghi
, M.
, 2023
, “Gradient Origami Metamaterials for Programming Out-of-Plane Curvatures
,” Adv. Eng. Mater.
, 25
(14
), p. 2201838
.10.1002/adem.202201838189.
Resch
, R. D.
, 1968
, “Self-Supporting Structural Unit Having a Series of Repetitious Geometrical Modules
,” U.S. Patent No. 3,407,558.190.
Tachi
, T.
, 2013
, “Designing Freeform Origami Tessellations by Generalizing Resch's Patterns
,” ASME J. Mech. Des.
, 135
, p. 111006
.10.1115/1.4025389191.
Kshad
, M. A. E.
, Popinigis
, C.
, and Naguib
, H. E.
, 2019
, “3D Printing of Ron-Resch-Like Origami Cores for Compression and Impact Load Damping
,” Smart Mater. Struct.
, 28
(1
), p. 015027
.10.1088/1361-665X/aaec40192.
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
.10.1016/j.ijmecsci.2021.106791193.
Wen
, G.
, Chen
, G.
, Long
, K.
, Wang
, X.
, Liu
, J.
, and Xie
, Y. M.
, 2021
, “Stacked-Origami Mechanical Metamaterial With Tailored Multistage Stiffness
,” Mater. Des.
, 212
, p. 110203
.10.1016/j.matdes.2021.110203194.
Harris
, J. A.
, and McShane
, G. J.
, 2021
, “Impact Response of Metallic Stacked Origami Cellular Materials
,” Int. J. Impact Eng.
, 147
, p. 103730
.10.1016/j.ijimpeng.2020.103730195.
Misseroni
, D.
, Pratapa
, P. P.
, Liu
, K.
, and Paulino
, G. H.
, 2022
, “Experimental Realization of Tunable Poisson's Ratio in Deployable Origami Metamaterials
,” Extreme Mech. Lett.
, 53
, p. 101685
.10.1016/j.eml.2022.101685196.
Li
, Z.
, Yang
, Q.
, Fang
, R.
, Chen
, W.
, and Hao
, H.
, 2021
, “Origami Metamaterial With Two-Stage Programmable Compressive Strength Under Quasi-Static Loading
,” Int. J. Mech. Sci.
, 189
, p. 105987
.10.1016/j.ijmecsci.2020.105987197.
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
.10.1016/j.matdes.2021.110343198.
Ye
, H.
, Liu
, Q.
, Cheng
, J.
, Li
, H.
, Jian
, B.
, Wang
, R.
, Sun
, Z.
, Lu
, Y.
, and Ge
, Q.
, 2023
, “Multimaterial 3D Printed Self-Locking Thick-Panel Origami Metamaterials
,” Nat. Commun.
, 14
(1
), p. 1607
.10.1038/s41467-023-37343-w199.
Lee
, T.-U.
, Chen
, Y.
, Heitzmann
, M. T.
, and Gattas
, J. M.
, 2021
, “Compliant Curved-Crease Origami-Inspired Metamaterials With a Programmable Force-Displacement Response
,” Mater. Des.
, 207
, p. 109859
.10.1016/j.matdes.2021.109859200.
Eidini
, M.
, and Paulino
, G. H.
, 2015
, “Unraveling Metamaterial Properties in Zigzag-Base Folded Sheets
,” Sci. Adv.
, 1
(8
), p. e1500224
.10.1126/sciadv.1500224201.
Eidini
, M.
, 2016
, “Zigzag-Base Folded Sheet Cellular Mechanical Metamaterials
,” Extreme Mech. Lett.
, 6
, pp. 96
–102
.10.1016/j.eml.2015.12.006202.
Kamrava
, S.
, Ghosh
, R.
, Wang
, Z.
, and Vaziri
, A.
, 2019
, “Origami-Inspired Cellular Metamaterial With Anisotropic Multi-Stability
,” Adv. Eng. Mater.
, 21
(2
), p. 1800895
.10.1002/adem.201800895203.
Miura
, K.
, and Tachi
, T.
, 2010
, “Synthesis of Rigid-Foldable Cylindrical Polyhedra
,” Symmetry: Art and Science, International Society for the Interdisciplinary Study of Symmetry
, Gmuend
, Austria
, pp. 204
–213
.https://www.researchgate.net/publication/284415083_Synthesis_of_rigidfoldable_cylindrical_polyhedra204.
Yasuda
, H.
, Yein
, T.
, Tachi
, T.
, Miura
, K.
, and Taya
, M.
, 2013
, “Folding Behaviour of Tachi–Miura Polyhedron Bellows
,” Proc. R. Soc. A
, 469
(2159
), p. 20130351
.10.1098/rspa.2013.0351205.
Wang
, H.
, Zhao
, D.
, Jin
, Y.
, Wang
, M.
, Mukhopadhyay
, T.
, and You
, Z.
, 2020
, “Modulation of Multi-Directional Auxeticity in Hybrid Origami Metamaterials
,” Appl. Mater. Today
, 20
, p. 100715
.10.1016/j.apmt.2020.100715206.
Liu
, W.
, Jiang
, H.
, and Chen
, Y.
, 2022
, “3D Programmable Metamaterials Based on Reconfigurable Mechanism Modules
,” Adv. Funct. Mater.
, 32
(9
), p. 2109865
.10.1002/adfm.202109865207.
Jamalimehr
, A.
, Mirzajanzadeh
, M.
, Akbarzadeh
, A.
, and Pasini
, D.
, 2022
, “Rigidly Flat-Foldable Class of Lockable Origami-Inspired Metamaterials With Topological Stiff States
,” Nat. Commun.
, 13
(1
), p. 1816
.10.1038/s41467-022-29484-1208.
Song
, J.
, Chen
, Y.
, and Lu
, G.
, 2012
, “Axial Crushing of Thin-Walled Structures With Origami Patterns
,” Thin-Walled Struct.
, 54
, pp. 65
–71
.10.1016/j.tws.2012.02.007209.
Yang
, K.
, Xu
, S.
, Shen
, J.
, Zhou
, S.
, and Xie
, Y. M.
, 2016
, “Energy Absorption of Thin-Walled Tubes With Pre-Folded Origami Patterns: Numerical Simulation and Experimental Verification
,” Thin-Walled Struct.
, 103
, pp. 33
–44
.10.1016/j.tws.2016.02.007210.
Yang
, K.
, Xu
, S.
, Zhou
, S.
, and Xie
, Y. M.
, 2018
, “Multi-Objective Optimization of Multi-Cell Tubes With Origami Patterns for Energy Absorption
,” Thin-Walled Struct.
, 123
, pp. 100
–113
.10.1016/j.tws.2017.11.005211.
Tao
, R.
, Ji
, L.
, Li
, Y.
, Wan
, Z.
, Hu
, W.
, Wu
, W.
, Liao
, B.
, Ma
, L.
, and Fang
, D.
, 2020
, “4D Printed Origami Metamaterials With Tunable Compression Twist Behavior and Stress-Strain Curves
,” Compos. Part B: Eng.
, 201
, p. 108344
.10.1016/j.compositesb.2020.108344212.
Wen
, G.
, Zhang
, S.
, Wang
, H.
, Wang
, Z.-P.
, He
, J.
, Chen
, Z.
, Liu
, J.
, and Xie
, Y. M.
, 2023
, “Origami-Based Acoustic Metamaterial for Tunable and Broadband Sound Attenuation
,” Int. J. Mech. Sci.
, 239
, p. 107872
.10.1016/j.ijmecsci.2022.107872213.
Zhang
, Z.
, Chen
, G.
, Xun
, Y.
, Long
, Y.
, Wang
, J.
, Wang
, H.
, and Angeles
, J.
, 2023
, “Bioinspired Rigid-Soft Hybrid Origami Actuator With Controllable Versatile Motion and Variable Stiffness
,” IEEE Trans. Rob.
, 39
(6
), pp. 4768
–4784
.10.1109/TRO.2023.3311630214.
Haas
, F.
, Gorb
, S.
, and Wootton
, R. J.
, 2000
, “Elastic Joints in Dermapteran Hind Wings: Materials and Wing Folding
,” Arthropod Struct. Dev.
, 29
(2
), pp. 137
–146
.10.1016/S1467-8039(00)00025-6215.
Faber
, J. A.
, Arrieta
, A. F.
, and Studart
, A. R.
, 2018
, “Bioinspired Spring Origami
,” Science
, 359
(6382
), pp. 1386
–1391
.10.1126/science.aap7753216.
Liu
, K.
, Tachi
, T.
, and Paulino
, G. H.
, 2021
, “Bio-Inspired Origami Metamaterials With Metastable Phases Through Mechanical Phase Transitions
,” ASME J. Appl. Mech.
, 88
(9
), p. 091002
.10.1115/1.4050556217.
Kim
, W.
, Byun
, J.
, Kim
, J.-K.
, Choi
, W.-Y.
, Jakobsen
, K.
, Jakobsen
, J.
, Lee
, D.-Y.
, and Cho
, K.-J.
, 2019
, “Bioinspired Dual-Morphing Stretchable Origami
,” Sci. Rob.
, 4
(36
), p. eaay3493
.10.1126/scirobotics.aay3493218.
Rajabi
, H.
, Ghoroubi
, N.
, Stamm
, K.
, Appel
, E.
, and Gorb
, S. N.
, 2017
, “Dragonfly Wing Nodus: A One-Way Hinge Contributing to the Asymmetric Wing Deformation
,” Acta Biomater.
, 60
, pp. 330
–338
.10.1016/j.actbio.2017.07.034219.
Wootton
, R. J.
, 1991
, “The Functional Morphology of the Wings of Odonata
,” Adv. Odonatol.
, 5
(1
), pp. 153
–169
.https://natuurtijdschriften.nl/pub/593092220.
Saito
, K.
, Yamamoto
, S.
, Maruyama
, M.
, and Okabe
, Y.
, 2014
, “Asymmetric Hindwing Foldings in Rove Beetles
,” Proc. Natl. Acad. Sci.
, 111
(46
), pp. 16349
–16352
.10.1073/pnas.1409468111221.
Hedrick
, T. L.
, Combes
, S. A.
, and Miller
, L. A.
, 2015
, “Recent Developments in the Study of Insect Flight
,” Can. J. Zool.
, 93
(12
), pp. 925
–943
.10.1139/cjz-2013-0196222.
Sun
, J.
, and Bhushan
, B.
, 2011
, “The Structure and Mechanical Properties of Dragonfly Wings and Their Role on Flyability
,” C. R. Mec.
, 340
(1–2
), pp. 3
–17
.10.1016/j.crme.2011.11.003223.
Lentink
, D.
, Müller
, U. K.
, Stamhuis
, E. J.
, De Kat
, R.
, Van Gestel
, W.
, Veldhuis
, L. L. M.
, Henningsson
, P.
, Hedenström
, A.
, Videler
, J. J.
, and Van Leeuwen
, J. L.
, 2007
, “How Swifts Control Their Glide Performance With Morphing Wings
,” Nature
, 446
(7139
), pp. 1082
–1085
.10.1038/nature05733224.
Nudds
, R. L.
, Dyke
, G. J.
, and Rayner
, J. M. V.
, 2007
, “Avian Brachial Index and Wing Kinematics: Putting Movement Back Into Bones
,” J. Zool.
, 272
(2
), pp. 218
–226
.10.1111/j.1469-7998.2006.00261.x225.
Di Luca
, M.
, Mintchev
, S.
, Heitz
, G.
, Noca
, F.
, and Floreano
, D.
, 2017
, “Bioinspired Morphing Wings for Extended Flight Envelope and Roll Control of Small Drones
,” Interface Focus
, 7
(1
), p. 20160092
.10.1098/rsfs.2016.0092226.
Haas
, F.
, Gorb
, S.
, and Blickhan
, R.
, 2000
, “The Function of Resilin in Beetle Wings
,” Proc. R. Soc. B-Biol. Sci.
, 267
(1451
), pp. 1375
–1381
.10.1098/rspb.2000.1153227.
Song
, Z.
, Yan
, Y.
, Tong
, J.
, and Sun
, J.
, 2020
, “Asian Ladybird Folding and Unfolding of Hind Wing: Biomechanical Properties of Resilin in Affecting the Tensile Strength of the Folding Area
,” J. Mater. Sci.
, 55
(10
), pp. 4524
–4537
.10.1007/s10853-019-04326-6228.
Sun
, J.
, Liu
, C.
, and Bhushan
, B.
, 2019
, “A Review of Beetle Hindwings: Structure, Mechanical Properties, Mechanism and Bioinspiration
,” J. Mech. Behav. Biomed. Mater.
, 94
, pp. 63
–73
.10.1016/j.jmbbm.2019.02.031229.
Saito
, K.
, Nomura
, S.
, Yamamoto
, S.
, Niiyama
, R.
, and Okabe
, Y.
, 2017
, “Investigation of Hindwing Folding in Ladybird Beetles by Artificial Elytron Transplantation and Microcomputed Tomography
,” Proc. Natl. Acad. Sci.
, 114
(22
), pp. 5624
–5628
.10.1073/pnas.1620612114230.
Baek
, S.-M.
, Yim
, S.
, Chae
, S.-H.
, Lee
, D.-Y.
, and Cho
, K.-J.
, 2020
, “Ladybird Beetle–Inspired Compliant Origami
,” Sci. Rob.
, 5
(41
), p. eaaz6262
.10.1126/scirobotics.aaz6262231.
Lang
, R. J.
, 1996
, “A Computational Algorithm for Origami Design
,” Proceedings of the Twelfth Annual Symposium on Computational Geometry
, Association for Computing Machinery, Philadelphia, PA, May 24–26, pp. 98
–105
.10.1145/237218.237249232.
Mitani
, J.
, 2012
, “Oripa
,” University of Tsukuba
, Tsukuba, Japan
, accessed Sept. 24, 2024, https://mitani.cs.tsukuba.ac.jp/oripa/233.
Tachi
, T.
, 2009
, “Rigid Origami Simulator
,” The University of Tokyo
, Tokyo, Japan
, accessed Sept. 24, 2024, https://tsg.ne.jp/TT/software/index.html234.
235.
Suto
, K.
, and Tanimichi
, K.
, 2021
, “Crane
,” Nature Architects Inc., Tokyo, Japan, accessed Sept. 24, 2024
, https://www.food4rhino.com/en/app/crane236.
Wang
, S.
, Yan
, P.
, Huang
, H.
, Zhang
, N.
, and Li
, B.
, 2023
, “Inflatable Metamorphic Origami
,” Research
, 6
, p. 0133
.10.34133/research.0133
