Mechanical design of stimuli-responsive flexible rotary joint using liquid crystal elastomers

doi:10.1007/s10483-025-3328-7

Abstract

Abstract:

Conventional rotary actuators mainly rely on electric or hydraulic/pneumatic motors to convert energy into mechanical motion, making them one of the most widely used actuation methods in industrial manufacturing, robotics, and automation control. However, these traditional actuators often suffer from limitations in operability and applicability due to their complex structures, bulky systems, high energy consumption, and severe mechanical wear. Liquid crystal elastomers (LCEs) have been increasingly used for programmable actuation applications, owing to their ability to undergo large, reversible, and anisotropic deformations in response to external stimuli. In this work, we propose a compact flexible rotary joint (FRJ) based on LCEs. To describe the thermo-mechanical coupled behaviors, a constitutive model is developed and further implemented for finite element analysis (FEA). Through combining experiments and simulations, we quantify the dynamic rotational behavior of the rotor rotating relative to the base driven by the induced strain of the FRJ under cyclic thermal stimuli. The proposed rotary joint features a simple structure, lightweight design, low energy consumption, and easy control. These characteristics endow it with significant potential for miniaturization and integration in the field of soft actuation and robotics.

Key words: liquid crystal elastomer (LCE), rotary actuator, flexible rotary joint (FRJ), programmable actuation, reversible cyclic motion

2010 MSC Number:

Weicong ZHANG, Zengting XU, Baihong CHEN, Xiangren KONG, Rui XIAO, Jin QIAN. Mechanical design of stimuli-responsive flexible rotary joint using liquid crystal elastomers. Applied Mathematics and Mechanics (English Edition), 2025, 46(12): 2221-2240.

TrendMD

Figures/Tables 19

Fig. 1

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Fig. 4

Table 1

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Fig. 6

Fig. 7

Fig. 8

Fig. 9

Table 2

Structural parameter setting"

Number of connection points	$R$ /mm	$α / (∘)$
2	17	30
3	17	20
4	17	10

Table 2

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Fig. 15

Fig. 16

Table A1

Comparison results of the present FRJ and traditional rotary joints"

Joint	Drive method	Size/mm	Weight/g	Power/W
Electromotor^[48]	Electric	35	80	4.5
RV reducer^[49]	Electric	$> 40$	4 700	1 700
Maxon EC90 motor^[50]	Electric	22	600	90
Rotating pneumatic clutch^[51]	Pneumatic	50	450	–
Double-blade rotating cylinder^[52]	Hydraulic	500	4 300	–
Hydraulic rotary joint^[53]	Hydraulic	172	1 000	–
Hydraforce PV70	Hydraulic	–	$> 190$	50–60
Bucher hydraulics	Hydraulic	–	$> 500$	$> 30$
DVP vacuum	Pneumatic	$> 60$	$> 250$	10–30
Maxon EC-max 16	Electric	16	20	5–10
Oriental motor PKP223	Electric	28	110	1–5
Present work	Thermal	34	3.2	~10

Table A1

References 54

[1]	YOON, C. Advances in biomimetic stimuli responsive soft grippers. Nano Convergence, 6(1), 20 (2019)
[2]	SON, H. and YOON, C. Advances in stimuli-responsive soft robots with integrated hybrid materials. Actuators, 9(4), 115 (2020)
[3]	WANG, Z. B., CHEN, Y. X., MA, Y., and WANG, J. Bioinspired stimuli-responsive materials for soft actuators. Biomimetics, 9(3), 128 (2024)
[4]	LIU, K., WU, J. T., PAULINO, G. H., and QI, H. J. Programmable deployment of tensegrity structures by stimulus-responsive polymers. Scientific Reports, 7, 3511 (2017)
[5]	KIM, H., TORRES, F., WU, Y. Y., VILLAGRAN, D., LIN, Y. R., and TSENG, T. L. Integrated 3D printing and corona poling process of PVDF piezoelectric films for pressure sensor application. Smart Materials and Structures, 26(8), 085027 (2017)
[6]	CHEN, Z. P., LIN, Y. Y., ZHENG, G. Z., YANG, Y. W., ZHANG, Y. X., ZHENG, S. Q., LI, J. W., LI, J. W., REN, L., and JIANG, L. L. Programmable transformation and controllable locomotion of magnetoactive soft materials with 3D-patterned magnetization. ACS Applied Materials & Interfaces, 12, 58179–58190 (2020)
[7]	SHI, X. Y., DENG, Z. X., ZHANG, P., WANG, Y., ZHOU, G. F., and HAAN, L. T. Wearable optical sensing of strain and humidity: a patterned dual-responsive semi-interpenetrating network of a cholesteric main-chain polymer and a poly (ampholyte). Advanced Functional Materials, 31(45), 2104641 (2021)
[8]	TOKAREV, I. and MINKO, S. Preprogrammed dynamic microstructured polymer interfaces. Advanced Functional Materials, 30(2), 1903478 (2020)
[9]	XIA, X. X., SPADACCINI, C. M., and GREER, J. R. Responsive materials architected in space and time. Nature Reviews Materials, 7(9), 683–701 (2022)
[10]	CHE, K. K., ROULEAU, M., and MEAUD, J. Temperature-tunable time-dependent snapping of viscoelastic metastructures with snap-through instabilities. Extreme Mechanics Letters, 32, 100528 (2019)
[11]	HU, H. W., LI, D. Y., SALIM, T., LI, Y., CHENG, G. G., LAM, Y. M., and DING, J. N. Electrically driven hydrogel actuators: working principle, material design and applications. Journal of Materials Chemistry C, 12(5), 1565–1582 (2024)
[12]	EL HELOU, C., BUSKOHL, P. R., TABOR, C. E., and HARNE, R. L. Digital logic gates in soft, conductive mechanical metamaterials. Nature Communications, 12, 1633 (2021)
[13]	DONG, Q. Y., WAN, Z. Q., LI, Q., LIU, Y. S., ZHANG, P., ZHANG, X., NIU, Y. T., LIU, H., ZHOU, Y. S., and LV, L. W. 3D-printed near-infrared-light-responsive on-demand drug-delivery scaffold for bone regeneration. Biomaterials Advances, 159, 213804 (2024)
[14]	YUAN, Z. S., ZHA, J. Z., and LIU, J. X. A light-steered self-rowing liquid crystal elastomer-based boat. Polymers, 17(6), 711 (2025)
[15]	QIU, Y. L., DAI, Y. T., and LI, K. Multimodal self-operation of a liquid crystal elastomer spring-linkage mechanism under constant light. International Journal of Solids and Structures, 302, 112998 (2024)
[16]	LI, K., QIAN, P. P., HU, H. Y., DAI, Y. T., and GE, D. L. A light-powered liquid crystal elastomer semi-rotary motor. International Journal of Solids and Structures, 284, 112509 (2023)
[17]	DAI, L., XU, J. W., and XIAO, R. Modeling the stimulus-responsive behaviors of fiber-reinforced soft materials. International Journal of Applied Materials, 16, 2450041 (2024)
[18]	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)
[19]	WANG, Q. Y., PAN, C. F., ZHANG, Y. X., PENG, L. L., CHEN, Z. P., MAJIDI, C., and JIANG, L. L. Magnetoactive liquid-solid phase transitional matter. Matter, 6, 855–872 (2023)
[20]	SUN, Y. X., WANG, L., ZHU, Z. Q., LI, X. X., SUN, H., ZHAO, Y., PENG, C. H., LIU, J., ZHANG, S. W., and LI, M. J. A 3D-printed ferromagnetic liquid crystal elastomer with programmed dual-anisotropy and multi-responsiveness. Advanced Materials, 35, 2302824 (2023)
[21]	ZHAO, X. H., CHEN, X. Y., YUK, H., LIN, S. T., LIU, X. Y., and PARADA, G. Soft materials by design: unconventional polymer networks give extreme properties. Chemical Reviews, 121, 4309–4372 (2021)
[22]	SUO, Z. G. Theory of dielectric elastomers. Acta Mechanica Solida Sinica, 23(6), 549–578 (2010)
[23]	YAO, B. W., WU, S. W., WANG, R. X., YAN, Y. C., CARDENAS, A., WU, D., ALSAID, Y., WU, W. Z., ZHU, X. Y., and HE, X. M. Hydrogel ionotronics with ultra-low impedance and high signal fidelity across broad frequency and temperature ranges. Advanced Functional Materials, 32(10), 2109506 (2022)
[24]	WANG, Y. M., WANG, Y. N., WEI, Q. H., and ZHANG, J. Light-responsive shape memory polymer composites. European Polymer Journal, 173, 111314 (2022)
[25]	ZHAO, W., LI, N., LIU, L. W., LENG, J. S., and LIU, Y. J. Mechanical behaviors and applications of shape memory polymer and its composites. Applied Physics Reviews, 10, 011306 (2023)
[26]	JIN, B. J. and YANG, S. Programming liquid crystalline elastomer networks with dynamic covalent bonds. Advanced Functional Materials, 33(45), 2304769 (2023)
[27]	HERBERT, K. M., FOWLER, H. E., MCCRACKEN, J. M., SCHLAFMANN, K. R., KOCH, J. A., and WHITE, T. J. Synthesis and alignment of liquid crystalline elastomers. Nature Reviews Materials, 7, 23–38 (2021)
[28]	HE, Q. G., WANG, Z. J., WANG, Y., WANG, Z. J., LI, C. H., ANNAPOORANAN, R., ZENG, J., CHEN, R. K., and CAI, S. Q. Electrospun liquid crystal elastomer microfiber actuator. Science Robotics, 6(57), eabi9704 (2021)
[29]	CAI, P. Q., WANG, C. X., GAO, H. J., and CHEN, X. D. Mechanomaterials: a rational deployment of forces and geometries in programming functional materials. Advanced Materials, 33(46), 2007977 (2021)
[30]	ZHOU, Y., HAUSER, A. W., BENDE, N. P., KUZYK, M. G., and HAYWARD, R. C. Waveguiding microactuators based on a photothermally responsive nanocomposite hydrogel. Advanced Functional Materials, 26(30), 5447–5452 (2016)
[31]	XU, S. M., ZHANG, S. S., LEI, R. C., LIU, Y., BU, W. S., WEI, X. L., and ZHANG, Z. Z. Fluid-driven and smart material-driven research for soft body robots. Progress in Natural Science: Materials International, 33(4), 371–385 (2023)
[32]	CHEN, S., WANG, H. Z., LIU, T. Y., and LIU, J. Liquid metal smart materials toward soft robotics. Advanced Intelligent Systems, 5(8), 2200375 (2023)
[33]	CHEN, Y. Z., KUENSTLER, A. S., HAYWARD, R. C., and JIN, L. H. Formation of rolls from liquid crystal elastomer bistrips. Soft Matter, 18(21), 4077–4089 (2022)
[34]	WANG, L., ZHENG, D., HARKER, P., PATEL, A. B., GUO, C. F., and ZHAO, X. H. Evolutionary design of magnetic soft continuum robots. Proceedings of the National Academy of Sciences of the United States of America, 118, e2021922118 (2021)
[35]	NARAYANAN, P., PRAMANIK, R., and AROCKIARAJAN, A. Micromechanics-based constitutive modeling of hard-magnetic soft materials. Mechanics of Materials, 184, 104722 (2023)
[36]	WANG, L., KIM, Y., GUO, C. F., and ZHAO, X. H. Hard-magnetic elastica. Journal of the Mechanics and Physics of Solids, 142, 104045 (2020)
[37]	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)
[38]	ZHANG, W., NAN, Y. F., WU, Z. X., SHEN, Y. J., and LUO, D. Photothermal-driven liquid crystal elastomers: materials, alignment and applications. Molecules, 27(14), 4330 (2022)
[39]	WHITE, T. J. and BROER, D. J. Programmable and adaptive mechanics with liquid crystal polymer networks and elastomers. Nature Materials, 14, 1087–1098 (2015)
[40]	WANG, L. Q., WEI, Z. X., XU, Z. T., YU, Q. M., WU, Z. L., WANG, Z. J., QIAN, J., and XIAO, R. Shape morphing of 3D printed liquid crystal elastomer structures with precuts. ACS Applied Polymer Materials, 5(9), 7477–7484 (2023)
[41]	ZHANG, Y., XUAN, C., JIANG, Y. F., and HUO, Y. Z. Continuum mechanical modeling of liquid crystal elastomers as dissipative ordered solids. Journal of the Mechanics and Physics of Solids, 126, 285–303 (2019)
[42]	KANG, J. T., LIU, S. X., and WANG, C. G. Controllable bistable smart composite structures driven by liquid crystal elastomer. Smart Materials and Structures, 31, 015003 (2022)
[43]	NIE, Z. Z., WANG, M., and YANG, H. Structure-induced intelligence of liquid crystal elastomers. Chemistry — A European Journal, 29(38), e202301027 (2023)
[44]	WANG, Z. J., WANG, Z. J., ZHENG, Y., HE, Q. G., WANG, Y., and CAI, S. Q. Three-dimensional printing of functionally graded liquid crystal elastomer. Science Advances, 6(39), e202301027 (2020)
[45]	WANG, J. K., ZHU, B. G., HUI, C. Y., and ZEHNDER, A. T. Determination of material parameters in constitutive models using adaptive neural network machine learning. Journal of the Mechanics and Physics of Solids, 177, 105324 (2023)
[46]	CLARKE, S. M., HOTTA, A., TAJBAKHSH, A. R., and TERENTJEV, E. M. Effect of crosslinker geometry on equilibrium thermal and mechanical properties of nematic elastomers. Physical Review E, 64(6), 061702 (2001)
[47]	NOLAN, D. R., LALLY, C., and MCGARRY, J. P. Understanding the deformation gradient in Abaqus and key guidelines for anisotropic hyperelastic user material subroutines (UMATs). Journal of the Mechanical Behavior of Biomedical Materials, 126, 104940 (2022)
[48]	GARANT, X. and GOSSELIN, C. Design and experimental validation of reorientation manoeuvres for a free falling robot inspired from the cat righting reflex. IEEE Transactions on Robotics, 37(2), 482–493 (2021)
[49]	SHEN, Y. K., GUO, Y., and FAN, J. W. Robot joint cycloidal gear tooth fault detection in robot working conditions based on piecewise mean difference. IEEE Sensors Journal, 24(20), 32740–32747 (2024)
[50]	ISHIGURO, Y., MAKABE, T., NAGAMATSU, Y., KOJIO, Y., KOJIMA, K., SUGAI, F., KAKIUCHI, Y., OKADA, K., and INABA, M. Bilateral humanoid teleoperation system using whole-body exoskeleton cockpit TABLIS. IEEE Robotics and Automation Letters, 5(4), 6419–6426 (2020)
[51]	XIONG, Q., LI, D. N., ZHOU, X. Y., XIN, W. C., WANG, C., AMBROSE, J. W., and YEOW, R. C. Single-motor ultraflexible robotic (SMUFR) humanoid hand. IEEE Transactions on Medical Robotics and Bionics, 6(4), 1666–1677 (2024)
[52]	ZONG, H. Z., YANG, Z. X., YU, X., ZHANG, J. H., AI, J. K., ZHU, Q. X., WANG, F., SU, Q., and XU, B. Active disturbance rejection control of hydraulic quadruped robots rotary joints for improved impact resistance. Chinese Journal of Mechanical Engineering, 37, 103 (2024)
[53]	YANG, M. X., ZHANG, X., SHI, Y. D., and WANG, X. S. Mechanical design and position-tracking control of a novel robotic joint with a circular rotary electro-hydraulic actuator. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 237, 3680–3691 (2023)
[54]	DAI, L., 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 Science, 3, 5 (2023)

Training detail	Value
Hidden layers	{36, 36}
Training size	1 000
Training error/%	0.3
Validation error/%	2.7
Optimal parameter prediction error/%	0.6