Study on influence of size-independent parameters on steady-state characteristics of Miura origami structure

doi:10.3785/j.issn.1006-754X.2025.04.163

Chinese Journal of Engineering Design

2025, Vol. 32

Issue (4): 452-462 DOI: 10.3785/j.issn.1006-754X.2025.04.163

Robotic and Mechanism Design

Study on influence of size-independent parameters on steady-state characteristics of Miura origami structure

Jialiang WANG(

),Shen SHU,Kai CHU,Yu ZHANG,Hao ZHOU,Junfeng HU(

)

School of Mechanical and Electrical Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China

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Abstract

Bistable origami structures have broad application prospects in solving practical engineering problems due to their characteristics such as rapid transformation, negative stiffness and energy storage capacity. At present, the configuration design and steady-state characteristic regulation of bistable origami structures mostly focus on size parameters such as crease length and the angle between adjacent creases. However, the steady-state characteristics of some origami structures are minimally affected by size parameters, and there are often certain restrictions on the overall structure size in practical applications. For this purpose, taking the Miura origami structure as the research object, the influence law of parameters such as the crease length, the angle between adjacent creases and the initial folding angle on the potential energy barrier was analyzed based on the potential energy equation. It was found that the initial folding angle had the greatest impact on the steady-state characteristics of the Miura origami structure. Then, the influence of size-independent parameters such as the crease forming angle and the pre-folding angle on the initial folding angle was analyzed through experiments, and the changes in steady-state characteristics such as the unstable output force and instability time of the Miura origami structure under different crease forming angles were demonstrated. Finally, taking the water-based origami robot based on the Miura origami structure as an example, its swimming speed was increased by 70% by changing the crease forming angle while remaining the size parameters unchanged. The research results provide a new approach for the performance regulation and practical application of bistable origami structures.

Key words： Miura origami structure bistable initial folding angle origami robot

Received: 31 July 2024 Published: 01 September 2025

CLC:

TH 122

Corresponding Authors: Junfeng HU E-mail: 3080595650@qq.com;hjfsuper@126.com

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Cite this article:

Jialiang WANG,Shen SHU,Kai CHU,Yu ZHANG,Hao ZHOU,Junfeng HU. Study on influence of size-independent parameters on steady-state characteristics of Miura origami structure. Chinese Journal of Engineering Design, 2025, 32(4): 452-462.

URL:

https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2025.04.163 OR https://www.zjujournals.com/gcsjxb/Y2025/V32/I4/452

尺寸无关参数对三浦折纸结构稳态特性的影响研究

双稳态折纸结构具有快速变形、负刚度和可储能等特性，在解决实际工程问题方面具有广阔的应用前景。目前，双稳态折纸结构的构型设计与稳态特性调控多从折痕长度、相邻折痕夹角等尺寸参数入手，但部分折纸结构的稳态特性受尺寸参数的影响很小，且在实际应用中对整体结构的尺寸往往存在一定限制。为此，以三浦折纸结构为研究对象，基于势能方程分析了其折痕长度、相邻折痕夹角和初始折展角度等参数对势能壁垒的影响规律，发现初始折展角度对三浦折纸结构稳态特性的影响最大。随后，通过实验分析了折痕制成角度与预折叠角度等尺寸无关参数对初始折展角度的影响，并展示了不同折痕制成角度下三浦折纸结构失稳输出力、失稳时间等稳态特性的变化。最后，以基于三浦折纸结构的水上折纸机器人为例，在其尺寸参数不变的情况下，通过更改折痕制成角度使其游动速度提升了70%。研究结果为双稳态折纸结构的性能调控与实际应用提供了一种新思路。

关键词： 三浦折纸结构, 双稳态, 初始折展角度, 折纸机器人

Fig.1 Bistable verification experiment of Miura origami structure

Fig.2 Schematic of size parameters and folding process of Miura origami structure

Fig.3 Schematic of folded flat form and potential energy barrier of Miura origami structure

水平	因素
水平	$l 4$ /mm	$α 1$ /(°)	$φ 20$ /(°)
1	70	55	60
2	100	70	105
3	130	85	170

Table 1 Factor level table for potential energy barrier Taguchi experiment

序号	因素			$Δ E$ /J
序号	$l 4$ /mm	$α 1$ /(°)	$φ 20$ /(°)	$Δ E$ /J
1	70	55	60	0.138
2	70	70	105	0.077
3	70	85	170	0.021
4	100	55	105	0.070
5	100	70	170	0.003
6	100	85	60	0.184
7	130	55	170	0.002
8	130	70	60	0.192
9	130	85	105	0.120

Table 2 Schemes and results of potential energy barrier Taguchi experiment

水平	因素
水平	$l 4$	$α 1$	$φ 20$
1	0.078 667	0.070 000	0.171 333
2	0.085 667	0.090 667	0.089 000
3	0.104 667	0.108 333	0.008 667
极差	0.026 000	0.038 333	0.162 666
排秩	3	2	1

Table 3 Response result of mean potential energy barrier

Fig.4 Main effect plot of mean potential energy barrier

Fig.5 Schematic of initial folding angle formation of single-crease origami structure

Fig.6 Adjustment method of crease formation angle

水平	因素
水平	$l 4$ /mm	$β$ /(°)	$θ 0$ /(°)
1	70	120	30
2	100	150	100
3	130	180	170

Table 4 Factor level table for initial folding angle Taguchi experiment

Fig.7 Miura origami structure with different initial folding angles

序号	因素			$γ 0$ /(°)
序号	$l 4$ /mm	$β$ /(°)	$θ 0$ /(°)	$γ 0$ /(°)
1	70	120	30	71.20
2	70	150	100	102.25
3	70	180	170	128.65
4	100	120	100	111.50
5	100	150	170	136.65
6	100	180	30	66.65
7	130	120	170	140.80
8	130	150	30	67.35
9	130	180	100	98.45

Table 5 Schemes and results of initial folding angle Taguchi experiment

水平	因素
水平	$l 4$	$β$	$θ 0$
1	100.70	107.83	68.40
2	104.93	102.08	104.07
3	102.20	97.92	135.37
极差	4.23	9.91	66.97
排秩	3	2	1

Table 6 Response result of mean initial folding angle

Fig.8 Main effect plot of mean initial folding angle

Fig.9 Experimental platform for measuring supporting force of Miura origami structure

Fig.10 Force-displacement curve during steady-state to critical point of instability

Fig.11 Instability time form critical point of instability to steady-state Ⅰ

Fig.12 Measurement results of unstable output force

Fig.13 Swimming demonstration of turtle, frog and water-based origami robot

Fig.14 Structural design of water-based origami robot

Fig.15 Schematic of Miura origami structure in robot prototype

Fig.16 Comparison of swimming process of robot before and after initial folding angle adjustment

Fig.17 Relation between robot swimming speed and initial folding angle


[[15]]	WANG H R， SHEN X J， WANG Z H， et al. Study on folding stability of origami metamaterials［J］. Chinese Journal of Theoretical and Applied Mechanics， 2022， 54（10）： 2726-2732.

[[16]]	SILVERBERG J L， NA J H， EVANS A A， et al. Origami structures with a critical transition to bistability arising from hidden degrees of freedom［J］. Nature Materials， 2015， 14（4）： 389-393.

[[17]]	邱海，方虹斌，徐鉴. 多稳态串联折纸结构的非线性动力学特性［J］. 力学学报， 2019， 51（4）： 1110-1121. QIU H， FANG H B， XU J. Nonlinear dynamical characteristics of a multi-stable series origami structure［J］. Chinese Journal of Theoretical and Applied Mechanics， 2019， 51（4）： 1110-1121.

[[18]]	WANG Y B， LIU K. Shape optimization of non-rigid origami leading to emerging bistability［J］. Mechanics Research Communications， 2023， 132： 104165.

[[19]]	FABER J A， ARRIETA A F， STUDART A R. Bioinspired spring origami［J］. Science， 2018， 359（6382）： 1386-1391.

[[20]]	FLORES J， STEIN-MONTALVO L， ADRIAENSSENS S. Effect of crease curvature on the bistability of the origami Waterbomb base［J］. Extreme Mechanics Letters， 2022， 57： 101909.

[[21]]	GUO K X， LIU M C， VELLA D， et al. Dehydration-induced corrugated folding in Rhapis excelsa plant leaves［J］. Proceedings of the National Academy of Sciences of the United States of America， 2024， 121（17）： e2320259121.

[[1]]	冯慧娟，杨名远，姚国强，等. 折纸机器人［J］. 中国科学：技术科学， 2018， 48（12）： 1259-1274. doi：10.1360/n092018-00213 FENG H J， YANG M Y， YAO G Q， et al. Origami robots［J］. Scientia Sinica （Technologica）， 2018， 48（12）： 1259-1274. doi: 10.1360/n092018-00213

[[2]]	SADEGHI S， ALLISON S R， BESTILL B， et al. TMP origami jumping mechanism with nonlinear stiffness［J］. Smart Materials and Structures， 2021， 30（6）： 065002.

[[3]]	WANG C L， GUO H W， LIU R Q， et al. A kirigami-inspired metamorphic double-loop linkage with multiple single-degree-of-freedom reconfiguration branches［J］. Journal of Mechanical Design， 2023， 145（7）： 073301.

[[22]]	FANG H B， LI S Y， JI H M， et al. Uncovering the deformation mechanisms of origami metamaterials by introducing generic degree-four vertices［J］. Physical Review E， 2016， 94（4）： 043002.

[[4]]	SALAZAR R， MURTHY S， PELLAZAR C， et al. TransFormers for lunar extreme environments： large origami deployable solar reflectors［C］//2017 IEEE Aerospace Conference. Big Sky， MT， Mar. 4-11， 2017.

[[5]]	HUANG X H， LIU L S， LIN Y H， et al. High-stretchability and low-hysteresis strain sensors using origami-inspired 3D mesostructures［J］. Science Advances， 2023， 9（34）： eadh9799.

[[6]]	LIU Q K， WANG W， REYNOLDS M F， et al. Micrometer-sized electrically programmable shape-memory actuators for low-power microrobotics［J］. Science Robotics， 2021， 6（52）： eabe6663.

[[7]]	KIM S J， LEE D Y， JUNG G P， et al. An origami-inspired， self-locking robotic arm that can be folded flat［J］. Science Robotics， 2018， 3（16）： eaar2915.

[[8]]	FANG H B， CHU S A， XIA Y T， et al. Programmable self-locking origami mechanical metamaterials［J］. Advanced Materials， 2018， 30（15）： 1706311.

[[9]]	HAN H B， SOROKIN V， TANG L H， et al. Lightweight origami isolators with deployable mechanism and quasi-zero-stiffness property［J］. Aerospace Science & Technology， 2022， 121： 107319.

[[10]]	WU H P， FANG H B， CHEN L F， et al. Transient dynamics of a miura-origami tube during free deployment［J］. Physical Review Applied， 2020， 14（3）： 034068.

[[11]]	CHI Y D， LI Y B， ZHAO Y， et al. Bistable and multistable actuators for soft robots： structures， materials， and functionalities［J］. Advanced Materials， 2022， 34（19）： 2110384.

[[12]]	ZHOU X， ZANG S X， YOU Z. Origami mechanical metamaterials based on the Miura-derivative fold patterns［J］. Proceedings of the Royal Society A： Mathematical， Physical and Engineering Sciences， 2016， 472（2191）： 20160361.

[[13]]	WEI S Z， GHOSH T K. Bioinspired bistable dielectric elastomer actuators： programmable shapes and application as binary valves［J］. Soft Robotics， 2022， 9（5）： 900-906.

[[14]]	LASCHI C， MAZZOLAI B， CIANCHETTI M. Soft robotics： technologies and systems pushing the boundaries of robot abilities［J］. Science Robotics， 2016， 1（1）： eaah3690.

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