Applied Mathematics and Mechanics >
Design and analysis of a mechanically intelligent system for biomechanical energy harvesting
Received date: 2025-10-12
Revised date: 2025-12-08
Online published: 2026-02-04
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 12202262, 12172127, 12032015, and 12121002), the Young Elite Scientists Sponsorship Program by the China Association for Science and Technology (No. 2023QNRC001), and the Hunan Province Science and Technology Innovation Program of China (Nos. 2025JJ20012 and 2025RC4022)
Copyright
The rapid advancement of wearable electronic devices has paved the way for a more intelligent and interconnected world. However, ensuring the sustainable energy supply for these devices remains a critical challenge, particularly for specialized populations and professionals in demanding environments, where a lack of power can pose life-threatening risks. Herein, we propose a mechanically intelligent biomechanical energy harvesting approach that adapts to complex human motion excitations, thereby improving the energy harvesting performance. Leveraging a mechanical intelligence mechanism, the energy harvester aligns with human physiological habits, selectively activating or deactivating as needed. The system can also adapt to excitations of varying directions, amplitudes, and frequencies. Furthermore, the string tension helps reduce the impact forces on the knee joint during foot strikes. A theoretical model for the biomechanical energy harvesting system is developed to describe its dynamic and electrical characteristics, and a prototype is fabricated and tested under diverse conditions. The experimental results are in good agreement with the simulation trends, validating the effectiveness of the theoretical model. A test subject running at 8 km/h for 90 seconds can successfully power a smartphone for 20 seconds, demonstrating the viability of self-powered applications. This mechanically intelligent biomechanical energy harvesting method holds a promising solution for the sustainable power supply for wearable electronic devices.
Linchuan ZHAO , Zewen CHEN , X. CHEN , Qiuhua GAO , Zhiyuan WU , Ge YAN , Kexiang WEI , E. M. YEATMAN , Guang MENG , Wenming ZHANG , Hongxiang ZOU . Design and analysis of a mechanically intelligent system for biomechanical energy harvesting[J]. Applied Mathematics and Mechanics, 2026 , 47(2) : 235 -254 . DOI: 10.1007/s10483-026-3353-7
| [1] | YANG, Y. Q., GUO, X. G., ZHU, M. L., SUN, Z. D., ZHANG, Z. X., HE, T. Y. Y., and LEE, C. K. Triboelectric nanogenerator enabled wearable sensors and electronics for sustainable internet of things integrated green earth. Advanced Energy Materials, 13(1), 2203040 (2023) |
| [2] | ZHAO, X., ASKARI, H., and CHEN, J. Nanogenerators for smart cities in the era of 5G and Internet of Things. Joule, 5(6), 1391–1431 (2021) |
| [3] | ZHANG, S. L., BICK, M., XIAO, X., CHEN, G. R., NASHALIAN, A., and CHEN, J. Leveraging triboelectric nanogenerators for bioengineering. Matter, 4(3), 845–887 (2021) |
| [4] | CHIEW, T. K., KHOO, S., ANSARI, P., and KIRUTHIKA, U. Mobile and wearable technologies for persons with disabilities: a bibliometric analysis (2000–2021). Disability and Rehabilitation: Assistive Technology, 19(3), 994–1002 (2024) |
| [5] | ZOU, H. X., LI, M., ZHAO, L. C., LIAO, X. W., GAO, Q. H., YAN, G., DU, R. H., WEI, K. X., and ZHANG, W. M. Cooperative compliant traction mechanism for human-friendly biomechanical energy harvesting. Energy Conversion and Management, 258, 115523 (2022) |
| [6] | YANG, J. H., ZHANG, W. X., and YANG, X. D. Integrated device for multiscale series vibration reduction and energy harvesting. Applied Mathematics and Mechanics (English Edition), 44(12), 2227–2242 (2023) https://doi.org/10.1007/s10483-023-3063-8 |
| [7] | LAI, Z. H., XU, J. C., BOWEN, C. R., and ZHOU, S. X. Self-powered and self-sensing devices based on human motion. Joule, 6(7), 1501–1565 (2022) |
| [8] | LI, H. T., ZHENG, T. Y., QIN, W. Y., TIAN, R. L., DING, H., JI, J. C., and CHEN, L. Q. Theoretical and experimental study of a bi-stable piezoelectric energy harvester under hybrid galloping and band-limited random excitations. Applied Mathematics and Mechanics (English Edition), 45(3), 461–478 (2024) https://doi.org/10.1007/s10483-024-3098-5 |
| [9] | LIU, M. Y., QIAN, F., MI, J., and ZUO, L. Biomechanical energy harvesting for wearable and mobile devices: state-of-the-art and future directions. Applied Energy, 321, 119379 (2022) |
| [10] | WENG, S., WU, L. Y., LI, Z. Q., ZHANG, L. B., and DAI, H. L. Optimizing wind energy harvester with machine learning. Applied Mathematics and Mechanics (English Edition), 46(8), 1417–1432 (2025) https://doi.org/10.1007/s10483-025-3279-6 |
| [11] | ZHANG, L. B., HE, Y. X., MENG, B., DAI, H. L., and WANG, L. Unlocking multidirectional and broadband wind energy harvesting with triboelectric nanogenerator and vortex-induced vibration of sphere. Applied Mathematics and Mechanics (English Edition), 45(11), 1895–1912 (2024) https://doi.org/10.1007/s10483-024-3185-8 |
| [12] | DU, X. Z., CHEN, H. X., LI, C. C., LI, Z. H., WANG, W. X., GUO, D. X., YU, H., WANG, J. L., and TANG, L. H. Wake galloping piezoelectric-electromagnetic hybrid ocean wave energy harvesting with oscillating water column. Applied Energy, 353, 122081 (2024) |
| [13] | ZHANG, B., LIU, H. S., ZHOU, S. X., and GAO, J. A review of nonlinear piezoelectric energy harvesting interface circuits in discrete components. Applied Mathematics and Mechanics (English Edition), 43(7), 1001–1026 (2022) https://doi.org/10.1007/s10483-022-2863-6 |
| [14] | YU, T. C., LIANG, F., and YANG, H. L. Vibration energy harvesting of a three-directional functionally graded pipe conveying fluids. Applied Mathematics and Mechanics (English Edition), 46(5), 795–812 (2025) https://doi.org/10.1007/s10483-025-3249-8 |
| [15] | WANG, Q., CHEN, Z. W., ZHAO, L. C., LI, M., ZOU, H. X., WEI, K. X., ZHANG, X. Z., and ZHANG, W. M. Enhanced galloping energy harvester with cooperative mode of vibration and collision. Applied Mathematics and Mechanics (English Edition), 43(7), 945–958 (2022) https://doi.org/10.1007/s10483-022-2869-9 |
| [16] | YU, N., FEI, X. Y., WU, C. Y., and YAN, B. Modeling and analysis of magnetic spring enhanced lever-type electromagnetic energy harvesters. Applied Mathematics and Mechanics (English Edition), 43(5), 743–760 (2022) https://doi.org/10.1007/s10483-022-2849-9 |
| [17] | ZHAO, L., LU, Z. Q., DING, H., and CHEN, L. Q. A viscoelastic metamaterial beam for integrated vibration isolation and energy harvesting. Applied Mathematics and Mechanics (English Edition), 45(7), 1243–1260 (2024) https://doi.org/10.1007/s10483-024-3159-7 |
| [18] | CAI, M. J. and LIAO, W. H. Enhanced electromagnetic wrist-worn energy harvester using repulsive magnetic spring. Mechanical Systems and Signal Processing, 150, 107251 (2021) |
| [19] | CAI, M. J. and LIAO, W. H. Toward high-performance wrist-worn energy harvester via hybrid approach. IEEE/ASME Transactions on Mechatronics, 30(1), 469–481 (2024) |
| [20] | XIE, L. H. and CAI, M. J. Increased energy harvesting and reduced accelerative load for backpacks via frequency tuning. Mechanical Systems and Signal Processing, 58-59, 399–415 (2015) |
| [21] | HOU, Z. H., LIU, Q. H., ZHAO, H., XIE, J. X., CAO, J. Y., LIAO, W. H., and BOWEN, C. R. Biomechanical modeling and experiments of energy harvesting backpacks. Mechanical Systems and Signal Processing, 200, 110612 (2023) |
| [22] | CAO, D. X., WANG, J. R., GUO, X. Y., LAI, S. K., and SHEN, Y. J. Recent advancement of flow-induced piezoelectric vibration energy harvesting techniques: principles, structures, and nonlinear designs. Applied Mathematics and Mechanics (English Edition), 43(7), 959–978 (2022) https://doi.org/10.1007/s10483-022-2867-7 |
| [23] | GAO, F., LIAO, W. H., LIANG, J. R., and WU, X. Y. Performance enhancement of piezoelectric bending beam-based human knee energy harvester. IEEE/ASME Transactions on Mechatronics, 29(4), 2779–2784 (2024) |
| [24] | GAO, F., LIU, G. Y., FU, X. L., LI, L., and LIAO, W. H. Lightweight piezoelectric bending beam-based energy harvester for capturing energy from human knee motion. IEEE/ASME Transactions on Mechatronics, 27(3), 1256–1266 (2022) |
| [25] | XIONG, J. Q., CUI, P., CHEN, X. L., WANG, J. X., PARIDA, K., LIN, M. F., and LEE, P. S. Skin-touch-actuated textile-based triboelectric nanogenerator with black phosphorus for durable biomechanical energy harvesting. Nature Communications, 9(1), 4280 (2018) |
| [26] | ZHOU, Z. H., WENG, L., TAT, T., LIBANORI, A., LIN, Z. M., GE, L. J., YANG, J., and CHEN, J. Smart insole for robust wearable biomechanical energy harvesting in harsh environments. ACS Nano, 14(10), 14126–14133 (2020) |
| [27] | ZOU, Y. J., RAVEENDRAN, V., and CHEN, J. Wearable triboelectric nanogenerators for biomechanical energy harvesting. Nano Energy, 77, 105303 (2020) |
| [28] | TAN, D. G., ZHOU, J. X., WANG, K., ZHANG, C., LI, Z. Y., and XU, D. L. Wearable bistable triboelectric nanogenerator for harvesting torsional vibration energy from human motion. Nano Energy, 109, 108315 (2023) |
| [29] | KONG, L. J., FANG, Z., ZHANG, T. S., ZHANG, Z. T., PAN, Y. J., HAO, D. N., CHEN, J. F., and QI, L. F. A self-powered and self-sensing lower-limb system for smart healthcare. Advanced Energy Materials, 13(31), 2301254 (2023) |
| [30] | CHEN, T. T., WANG, K., CHEN, S. C., XU, Z. Y., LI, Z., and ZHOU, J. X. Nonlinear electromechanical coupling dynamics of a two-degree-of-freedom hybrid energy harvester. Applied Mathematics and Mechanics (English Edition), 46(6), 989–1010 (2025) https://doi.org/10.1007/s10483-025-3264-7 |
| [31] | RAHMAN, M. T., RANA, S. S., SALAUDDIN, M., MAHARJAN, P., BHATTA, T., and PARK, J. Y. Biomechanical energy-driven hybridized generator as a universal portable power source for smart/wearable electronics. Advanced Energy Materials, 10(12), 1903663 (2020) |
| [32] | FAN, K. Q., HAO, J. Y., WANG, C. Y., ZHANG, C., WANG, W. D., and WANG, F. An eccentric mass-based rotational energy harvester for capturing ultralow-frequency mechanical energy. Energy Conversion and Management, 241, 114301 (2021) |
| [33] | JI, L. J., ZHAO, C., YANG, T. Y., YANG, H. R., AZEEM, M., LI, Z. Y., FENG, R., FENG, G. Q., LI, S., and LI, W. Energy harvesting and human motion sensing of a 2D piezoelectric hybrid organic-inorganic perovskite. APL Materials, 12(9), 091116 (2024) |
| [34] | WANG, W., CAO, J. Y., ZHANG, N., LIN, J., and LIAO, W. H. Magnetic-spring based energy harvesting from human motions: design, modeling and experiments. Energy Conversion and Management, 132, 189–197 (2017) |
| [35] | MA, X. Q., LI, H. T., ZHOU, S. X., YANG, Z. C., and LITAK, G. Characterizing nonlinear characteristics of asymmetric tristable energy harvesters. Mechanical Systems and Signal Processing, 168, 108612 (2022) |
| [36] | XIA, G. Y., LU, Q. T., CAI, M. J., LI, X., ZHANG, D. X., WANG, C. S., and LIAO, W. H. Comprehensive investigation of a broadband wearable energy harvester using adaptive kinetic energy reallocation mechanism. Mechanical Systems and Signal Processing, 206, 110907 (2024) |
| [37] | ZHU, Y., CHEN, G. T., ZHANG, J. Q., LI, Z. Y., and ZHOU, S. X. A flexible piezoelectric energy harvester featuring an eccentric pendulum via frequency up-conversion for human motion. Smart Materials and Structures, 33(8), 085032 (2024) |
| [38] | ZHAO, L. C., ZOU, H. X., WEI, K. X., ZHOU, S. X., MENG, G., and ZHANG, W. M. Mechanical intelligent energy harvesting: from methodology to applications. Advanced Energy Materials, 13(29), 2300557 (2023) |
| [39] | FEBRIOLA, N. A., SINGH, S., JEONG, E., and YOON, J. Highly deformable triboelectric nanogenerators fabricated using high-dielectric elastomers and double-network ionic hydrogels for use in energy harvesting and motion sensing. Chemical Engineering Journal, 503, 158641 (2025) |
| [40] | ZHOU, X. R., PARIDA, K., CHEN, J., XIONG, J. Q., ZHOU, Z. H., JIANG, F., XIN, Y. Y., MAGDASSI, S., and LEE, P. S. 3D printed auxetic structure-assisted piezoelectric energy harvesting and sensing. Advanced Energy Materials, 13(34), 2301159 (2023) |
| [41] | ZHAO, L., GONG, Y., SHEN, F., PENG, Y., XIE, S. R., and LI, Z. J. Diminishing potential well barrier in bi-stable energy harvesters by introducing symmetric stiffness. Thin-Walled Structures, 209, 112880 (2025) |
| [42] | LIAO, X., CHEN, L., ZHAO, H. L., JIANG, Q. B., and ZHANG, L. Electromagnetic vari-potential bi-stable energy harvester under low-amplitude excitation. International Journal of Mechanical Sciences, 307, 110871 (2025) |
| [43] | WANG, H., ZHAO, Q. L., SONG, R. J., GUO, J. L., CHANG, W. Y., YANG, X. H., and ZHANG, L. A. Design and performance study of low frequency magnetic coupling bistable piezoelectric and electromagnetic energy harvester. Energy, 320, 135178 (2025) |
| [44] | LI, Z. J., WANG, C. Y, SHEN, F., PENG, Y., and WANG, M. Goose queue inspired V-array with cross-section variations for enhanced electromechanical energy harvesting behaviors. IEEE/ASME Transactions on Mechatronics, 30(6), 4525–4534 (2025) |
| [45] | XIE, Z. Q., RAN, Y. A., FANG, G., ZHU, Y., HUANG, W. B., FU, B. Y., GE, S. S., ZHANG, Z. G., and WANG, Z. G. A novel variable potential energy well bistable piezoelectric rotational energy harvester. Mechanical Systems and Signal Processing, 239, 113312 (2025) |
| [46] | ZHAO, L., GONG, Y., SHEN, F., WU, H., PENG, Y., XIE, S. R., and LI, Z. J. Effect of stability state transition of variable potential well in tri-hybridized energy harvesters. Mechanical Systems and Signal Processing, 223, 111855 (2025) |
| [47] | WANG, C., CHAI, H. F., LI, G. L., WANG, W., TIAN, R. L., WEN, G. L., WANG, C. H., and LAI, S. K. Boosting biomechanical and wave energy harvesting efficiency through a novel triple hybridization of piezoelectric, electromagnetic, and triboelectric generators. Applied Energy, 374, 123876 (2024) |
| [48] | HAN, L. T., HE, L. P., LV, X. Q., SUN, L., ZHANG, L. M., and FAN, W. Piezoelectric-electromagnetic wearable harvester for energy harvesting and motion monitoring. Sustainable Energy Technologies and Assessments, 71, 104030 (2024) |
| [49] | HAO, D. N., FAN, C. L., XIA, X. F., ZHANG, Z. T., and YANG, Y. W. Hybrid electromagnetic-triboelectric hip energy harvester for wearables and AI-assisted motion monitoring. Small, 21(21), 2500643 (2025) |
| [50] | WANG, Z. H., HOU, L., YAO, M. H., and YANG, T. Z. A pendulum inertial electromagnetic energy harvester for harvesting multiple-source low-frequency human motion energy. Science China Technological Sciences, 68, 2020102 (2025) |
| [51] | ZHANG, J. J., YUAN, Q. J., GAO, S. H., LI, R., MAO, B. J., MA, Y. B., QI, G. Q., QU, J. T., MU, X. J., and ZHOU, Z. H. Wearable pendulum-rotor-separated hybrid generator for smart healthcare monitoring. ACS Applied Materials & Interfaces, 16(42), 56666–56675 (2024) |
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