Light-powered self-rolling of a liquid crystal elastomer-based dicycle

doi:10.1007/s10483-025-3221-8

摘要/Abstract

Abstract:

Conventional liquid crystal elastomer (LCE)-based robots are limited by the need for complex controllers and bulky power supplies, restricting their use in microrobots and soft robots. This paper introduces a novel light-powered dicycle that uses an LCE rod, enabling self-rolling by harvesting energy from the environment. The LCE rod serves as the driving force, with energy being supplied by a line light source. Employing a dynamic LCE model, we calculate the transverse curvature of the LCE rod after deformation, as well as the driving moment generated by the shift in a rod’s center of gravity, which allows the dicycle to roll on its own. Through extensive numerical simulations, we identify the correlations between the angular velocity of the dicycle and the key system parameters, specifically the light intensity, LCE rod length, light penetration depth, overall mass of the dicycle, rolling friction coefficient, and wheel radius. Further, the experimental verification is the same as the theoretical result. This proposed light-powered self-rolling dicycle comes with the benefits of the simple structure, the convenient control, the stationary light source, and the small luminous area of the light source. It not only demonstrates self-sustaining oscillations based on active materials, but also highlights the great potential of light-responsive LCE rods in applications such as robotics, aerospace, healthcare, and automation.

Key words: self-rolling, dicycle, liquid crystal elastomer (LCE), rod, light-powered

中图分类号:

O322

. [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 253-268.

Kai LI, Chongfeng ZHAO, Yunlong QIU, Yuntong DAI. Light-powered self-rolling of a liquid crystal elastomer-based dicycle[J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 253-268.

图/表 16

Parameter	$I ¯ 1$	$L ¯ 0$	$z ¯ I$	$m ¯$	$μ$	$R ¯ C$
Value	0–1	0–40	0–10	0–10	0–0.3	0–20

参考文献 49

[1]	KRUSE, K. and JULICHER, F. Oscillations in cell biology. Current Opinion in Cell Biology, 17, 20–26 (2005)
[2]	RAJPUT, V. and DAYAL, P. Dynamical attributes of nanocatalyzed self-oscillating reactions via bifurcation analyses. The Journal of Chemical Physics, 155, 064902 (2021)
[3]	ZHANG, Z. G., DUAN, N. Y., LIN, C. G., and HUA, H. X. Coupled dynamic analysis of a heavily-loaded propulsion shafting system with continuous bearing-shaft friction. International Journal of Mechanical Sciences, 30, 2003619 (2020)
[4]	LI, S. M., PENG, H. C., LIU, C. J., DING, C., and TANG, H. Nonlinear characteristic and chip breaking mechanism for an axial low-frequency self-excited vibration drilling robot. International Journal of Mechanical Sciences, 230, 107561 (2022)
[5]	WANG, X. Q. and HO, G. W. Design of untethered soft material micromachine for life-like locomotion. Materials Today, 53, 197–216 (2022)
[6]	TAY, Z. Y. Energy extraction from an articulated plate anti-motion device of a very large floating structure under irregular waves. Renewable Energy, 130, 206–222 (2019)
[7]	RINCON, F., OGILVIE, G. I., and PROCOT, M. R. E. Self-sustaining nonlinear dynamo process in Keplerian shear flows. Physical Review Letters, 98, 254502 (2007)
[8]	TRIVEDI, D., RAHN, C. D., KIER, W. M., and WALKER, I. D. Soft robotics: biological inspiration, state of the art, and future research. Applied Bionics and Biomechanics, 5, 99–117 (2008)
[9]	BRAMBILLA, M., FERRANTE, E., BIRATTARI, M., and DORIGO, M. Swarm robotics: a review from the swarm engineering perspective. Swarm Intelligence, 7, 1–41 (2013)
[10]	LU, D., WANG, L. Q., CHEN, B. H., XU, Z. T., WANG, Z. J., and XIAO, R. Shape memory behaviors of 3D printed liquid crystal elastomers. Soft Science3, 5 (2023)
[11]	WANG, L. Q., WEI, Z. J., XU, Z. T., YU, Q. M., WU, Z. L., WANG, Z. J., and XIAO, R. Shape morphing of 3D printed liquid crystal elastomer structures with precuts. ACS Applied Polymer Materials, 5, 7477–7484 (2023)
[12]	WIE, J. J., SHANKAR, M. R., and WHITE, T. J. Photomotility of polymers. Nature Communications, 10, 13260 (2016)
[13]	MAEDA, S., HARA, Y., SAKAI, T., YOSHIDA, R., and HASHIMOTO, S. J. Self-walking gel. Advanced Materials, 19, 3480–3484 (2007)
[14]	LI, K., LIU, Y. L., DAI, Y. T., and YU, Y. Light-powered self-oscillation of a liquid crystal elastomer bow. Journal of Sound and Vibration, 57, 118142 (2024)
[15]	YOSHIDA, R. Self-oscillating gels driven by the Belousov-Zhabotinsky reaction as novel smart materials. Advanced Materials, 22, 3463–3483 (2010)
[16]	HUA, M. T., KIM, C., DU, Y. J., WU, D., BAI, R. B., and HE, X. M. Swaying gel: chemo-mechanical self-oscillation based on dynamic buckling. Matter, 4, 1029–1041 (2021)
[17]	WANG, Y. C., DANG, A. L., ZHANG, Z. F., YIN, R., GAO, Y. C., FENG, L., and YANG, S. Repeatable and reprogrammable shape morphing from photoresponsive gold nanorod/liquid crystal elastomers. Advanced Materials, 32, 2004270 (2020)
[18]	WANG, Y. C., LIU, J. Q., and YANG, S. Multi-functional liquid crystal elastomer composites. Applied Physics Reviews, 9, 011301 (2022)
[19]	KANG, D. J., KIM, W., BAE, B., PARK, H. K., and JUNG, B. H. Direct photofabrication of refractive-index-modulated multimode optical waveguide using photosensitive sol-gel hybrid materials. Applied Physics Letters, 87, 221106 (2005)
[20]	IKEDA, T., NAKANO, M., YU, Y., TSUTSUMI, O., and KANAZAWA, A. Anisotropic bending and unbending behavior of azobenzene liquid-crystalline gels by light exposure. Advanced Materials, 15, 201–205 (2003)
[21]	SUN, J. H., WANG, Y. P., WEI, L., and YANG, Z. Q. Ultrafast, high-contractile electrothermal-driven liquid crystal elastomer fibers towards artificial muscles. Small, 17, 2103700 (2021)
[22]	WEI, L. and YANG, Z. Q. The integration of sensing and actuating based on a simple design fiber actuator towards intelligent soft robots. Advanced Materials Technologies, 7, 2101260 (2022)
[23]	LEHMANN, W., SKUPIN, H., TOLKSDORF, C., GEBHARD, E., ZENTEL, R., KRUGER, P., LOSCHE, M., and KREMER, F. Giant lateral electrostriction in ferroelectric liquid-crystalline elastomers. nature, 410, 447–450 (2001)
[24]	BAI, C. P., KANG, J. T., and WANG, Y. Q. Light-induced motion of three-dimensional pendulum with liquid crystal elastomeric fiber. International Journal of Mechanical Sciences, 26, 108911 (2024)
[25]	XU, T. F., PEI, D. F., YU, S. Y., ZHAN, X. F., YI, M. G., and LI, C. X. Design of MXene composites with biomimetic rapid and self-oscillating actuation under ambient circumstances. ACS Applied Materials & Interfaces, 13, 31978–31985 (2021)
[26]	ZENG, H., LAHIKAINEN, M., LIU, L., AHMED, Z., WANI, Q. M., WANG, M., YANG, H., and PRIIMAGI, A. Light fuelled freestyle self-oscillators. Nature Communications, 10, 5057 (2019)
[27]	HU, Y., JI, Q. X., HUANG, M. J., CHANG, L. F., ZHANG, C. C., WU, G., ZI, B., BAO, N. Z., CHEN, W., and WU, Y. C. Light-driven self-oscillating actuators with phototactic locomotion based on black phosphorus heterostructure. Angewandte Chemie International Edition, 60, 20511–20517 (2021)
[28]	WIE, J. J., LEE, K. M., SMITH, M. L., VAIA, R. A., and WHITE, T. J. Torsional mechanical responses in azobenzene functionalized liquid crystalline polymer networks. Soft Matter, 9, 9303 (2013)
[29]	GELEBART, A. H., MULDER, D. J., VARGA, M., KONYA, A., VANTOMME, G., MEIJER, E. W., SELINGER, L. B., and BROER, D. J. Making waves in a photoactive polymer film. nature, 546, 632–636 (2017)
[30]	LIU, X. and LIU, Y. Spontaneous photo-buckling of a liquid crystal elastomer membrane. International Journal of Mechanical Sciences, 201, 106473 (2021)
[31]	SHELLEY, M. J. and UEDA, T. The Stokesian hydrodynamics of flexing, stretching filaments. Physica D-Nonlinear Phenomena, 146, 221–245 (2000)
[32]	KIM, Y., BERG, J., and CROSBY, A. J. Autonomous snapping and jumping polymer gels. Nature Materials, 20, 1695–1701 (2021)
[33]	WISDOM, K. M., WATSON, J. A., QU, X. P., and CHEN, C. H. Self-cleaning of superhydrophobic surfaces by self-propelled jumping condensate. Proceedings of the National Academy of Sciences of the United States of America, 110, 7992–7997 (2013)
[34]	LI, Z. W., MYUNY, N., and YIN, Y. D. Light-powered soft steam engines for self-adaptive oscillation and biomimetic swimming. Science Robotics, 6, 34851711 (2021)
[35]	HU, Z. M., LI, Y. L., and LV, J. A. Phototunable self-oscillating system driven by a self-winding fiber actuator. Nature Communications, 12, 3211 (2021)
[36]	GE, D. L., DAI, Y. T., LIANG, H. Y., and LI, K. Self-rolling and circling of a conical liquid crystal elastomer rod on a hot surface. International Journal of Mechanical Sciences, 263, 108780 (2024)
[37]	XU, P. B., SUN, X., DAI, Y. T., and LI, K. Light-powered sustained chaotic jumping of a liquid crystal elastomer balloon. International Journal of Mechanical Sciences, 266, 108922 (2024)
[38]	QIU, Y. L. and LI, K. Self-rotation-eversion of an anisotropic-friction-surface torus. International Journal of Mechanical Sciences, 281, 109584 (2024)
[39]	QIU, Y. L., GE, D. L., WU, H. Y., LI, K., and XU, P. B. Self-rotation of a liquid crystal elastomer rod under constant illumination. International Journal of Mechanical Sciences, 281, 109584 (2024)
[40]	ZHAO, J., DAI, C. F., DAI, Y. T., WU, J., and LI, K. Self-oscillation of cantilevered silicone oil paper sheet system driven by steam. Thin-Walled Structures, 203, 112270 (2024)
[41]	KOROL, O. G., SEVERIN, G. Y., and STRYGIN, V. V. Synchronization of self-oscillations of two close dynamic systems. Doklady Physics, 54, 426–428 (2009)
[42]	GE, D. L. and LI, K. Self-oscillating buckling and postbuckling of a liquid crystal elastomer disk under steady illumination. International Journal of Mechanical Sciences, 221, 107233 (2022)
[43]	LIU, C. Y., LI, K., YU, X. Z., YANG, J. P., and WANG, Z. J. A Multimodal self-propelling tensegrity structure. Advanced Materials, 36, 2314093 (2024)
[44]	HAUSER, A. W., SUNDARAM, S., and HAYWARD, R. C. Photothermocapillary oscillators. Physical Review Letters, 121, 158001 (2018)
[45]	YANG, H. X., ZHANG, C., CHEN, B. H., WANG, Z. J., XU, Y., and XIAO, R. Bioinspired design of stimuli-responsive artificial muscles with multiple actuation modes. Smart Materials and Structures, 32, 085023 (2023)
[46]	ZHOU, L., CHEN, H. M., and LI, K. Optically-responsive liquid crystal elastomer thin film motors in linear/nonlinear optical fields. Thin-Walled Structures, 202, 112082 (2024)
[47]	QIU, Y. L., WU, H. Y., DAI, Y. T., and LI, K. Behavior prediction and inverse design for self-rotating skipping ropes based on random forest and neural network. Mathematics, 12, 1019 (2024)
[48]	AHN, C., LI, K., and CAI, S. Q. Light or thermally-powered autonomous rolling of an elastomer rod. ACS Applied Materials & Interfaces, 10, 25689–25696 (2018)
[49]	YAKACKI, C., SAED, M., NAIR, D., GONG, T., REEDC, S. M., and BOWMANB, C. N. Tailorable and programmable liquid-crystalline elastomers using a two-stage thiol-acrylate reaction. RSC Advances, 5, 18997–19001 (2015)

Parameter	Definition	Value	Unit
I₁	Light intensity	0–100	kW/m²
C	Contraction coefficient	0–0.5
T	Thermal relaxation time	0.01–0.05	s
η₁	Light absorption constant	0.000 2	m/(s²·W)
m	Overall mass of the dicycle	0.004–0.04	kg
m_L	LCE rod mass	0.01–0.08	kg
z_I	Light penetration depth	0–0.15	m
L₀	Initial length of the LCE	0–0.2	m
R₀	Radius of the LCE rod	0–0.02	m
R_C	Wheel radius	0–0.05	m

Name	Ingredient	Function
Liquid crystal monomer	1, 4-bis-[4-(3-acryloyloxypropyloxy) benzoyloxy]-2-methylbenzene (RM257, 95%)	Liquid crystal phase structure constituting LCE
Crosslinking agent	Pentaerythritol tetrakis (3-mercaptopropionate) (PETMP, 95%)	Introduction of cross-linking points into liquid crystal molecules to enhance LCE stability
Spacer	2, 2-(ethyleneoxy) diethanethiol (EDDET, 95%)	Adjustment of flexibility and deformation properties of LCE
Photo-initiator	2-hydroxy-2-methylpropiophenone (I2959, 98%)	Control of photoinitiation reaction on deformation or reaction properties of LCE
Catalyst	Dipropylamine (DPA, 98%)	Catalyst for photo-initiators to facilitate reaction progress
Photothermal agent	Multi-walled carbon nanotubes (CNTs, 98%)	Improvement of photothermal conversion, material strength, and durability