Hostname: page-component-7857688df4-6b9td Total loading time: 0 Render date: 2025-11-18T16:17:33.998Z Has data issue: false hasContentIssue false
  • English
  • Français

On the force-pose stability sensitivity analysis method for six-degree-of-freedom spatial cable-suspended parallel robots with eight cables

Part of: Recent advances in parallel and service robotics, from development to applications

Published online by Cambridge University Press:  18 November 2025

Peng Liu Open the ORCID record for Peng Liu [Opens in a new window] ,
Xuechao Duan ,
Zhufeng Shao  and
Jing Xia Open the ORCID record for Jing Xia [Opens in a new window]
Peng Liu*
Affiliation:
Shaanxi Key Laboratory of Mine Electromechanical Equipment Intelligent Detection and Control, Xi’an University of Science and Technology, Xi’an, 710054, China Key Laboratory of Ministry of Education for Electronic Equipment Structure Design, Xidian University, Xi’an, 710000, China
Xuechao Duan
Affiliation:
Key Laboratory of Ministry of Education for Electronic Equipment Structure Design, Xidian University, Xi’an, 710000, China
Zhufeng Shao
Affiliation:
State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China
Jing Xia
Affiliation:
Shaanxi Key Laboratory of Mine Electromechanical Equipment Intelligent Detection and Control, Xi’an University of Science and Technology, Xi’an, 710054, China
*
Corresponding author: Peng Liu; Emails: liupeng@xust.edu.cn; 200304405liupeng@163.com
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper focuses on six-degree-of-freedom (six-DOF) spatial cable-suspended parallel robots with eight cables (8-6 CSPRs) because the redundantly actuated CSPRs are relevant in many applications, such as large-scale assembly and handling tasks, and pick-and-place operations. One of the main concerns for the 8-6 CSPRs is the stability because employing cables with strong flexibility and unidirectional restraint operates the end-effector of the robot under external disturbances. As a consequence, this paper attempts to address two key issues related to the 8-6 CSPRs: the force-pose stability measure method and the stability sensitivity analysis method. First, a force-pose stability measure model taking into account the poses of the end-effector and the cable tensions of the 8-6 CSPR is presented, in which two cable tension influencing factors and two position influencing factors are developed, while an attitude influence function representing the influence of the attitudes of the end-effector on the stability of the robot is constructed. And furthermore, a new type of workspace related to the force-pose stability of the 8-6 CSPRs is defined and generated in this paper. Second, a force-pose stability sensitivity analysis method for the 8-6 CSPRs is developed with the gray relational analysis method, where the relationship between the force-pose stability of the robot and the 14 influencing factors (the end-effector’s poses and cable tensions) is investigated to reveal the sequence of the 14 influencing factors on the force-pose stability of the robot. Finally, the proposed force-pose stability measure method and stability sensitivity analysis method for the 8-6 CSPRs are verified through simulations.

Keywords

cable-suspended parallel robotstabilityforce-posesensitivity

Information

Type
Research Article
Information
Robotica , First View , pp. 1 - 24
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Qian, S., Zhao, Z., Qian, P., Wang, Z. and Zi, B., “Research on workspace visual-based continuous switching sliding mode control for cable-driven parallel robots,” Robotica 42(1), 1–20 (2024).10.1017/S0263574723001273CrossRefGoogle Scholar
Khadem, M., Inel, F., Carbone, G. and Tich, A. S. T., “A novel pyramidal cable-driven robot for exercising and rehabilitation of writing tasks,” Robotica 41(11), 3463–3484 (2023).10.1017/S026357472300111XCrossRefGoogle Scholar
Song, D., Lu, M., Zhao, L., Sun, Z., Wang, H. and Zhang, L., “A novel design method for a reconfigurable two-drive cable-driven parallel robot,” Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 239(6), 2049–2062 (2025).10.1177/09544062241293253CrossRefGoogle Scholar
Xu, G., Zhu, H., Xiong, H. and Lou, Y., “Data-driven dynamics modeling and control strategy for a planar n-DOF cable-driven parallel robot driven by n+1 cables allowing collisions,” J. Mech. Robot. 16(5), 051008 (2024).10.1115/1.4062792CrossRefGoogle Scholar
Barbosa, A. M., Carvalho, J. C. M. and Goncalves, R. S., “Cable-driven lower limb rehabilitation robot,” J. Braz. Soc. Mech. Sci. Eng. 40, 245 (2018).10.1007/s40430-018-1172-yCrossRefGoogle Scholar
Zuccon, G., Doria, A., Bottin, M., Minto, R. and Rosati, G., “Vibrations of cable-suspended rehabilitation robots,” Robotica 41(12), 3702–3723 (2023).10.1017/S0263574723001248CrossRefGoogle Scholar
Wang, X., Hu, Y. and Lin, Q., “Workspace analysis and verification of cable-driven parallel mechanism for wind tunnel test,” Proc. Inst. Mech. Eng. Part G: J. Aerosp. Eng. 231(6), 1012–1021 (2017).10.1177/0954410016646601CrossRefGoogle Scholar
Zhang, B., Shang, W., Gao, X., Li, Z., Wang, X., Ma, Y., Zhang, F., Yao, R., Li, H., Yin, J., Yang, Q. and Li, Q., “Synthetic design and analysis of the new feed cabin mechanism in five-hundred-meter aperture spherical radio telescope (FAST),” Mech. Mach. Theory 191, 105507 (2024).10.1016/j.mechmachtheory.2023.105507CrossRefGoogle Scholar
Lee, C. and Gwak, K., “Design of a novel cable-driven parallel robot for 3D printing building construction,” Int. J. Adv. Manuf. Technol. 123, 4353–4366 (2022).10.1007/s00170-022-10323-yCrossRefGoogle Scholar
Nguyen-Van, S. and Gwak, K., “A two-nozzle cable-driven parallel robot for 3D printing building construction: Path optimization and vibration analysis,” Int. J. Adv. Manuf. Technol. 120, 3325–3338 (2022).10.1007/s00170-022-08919-5CrossRefGoogle Scholar
Picard, E., Plestan, F., Tahoumi, E., Claveau, F. and Caro, S., “Control strategies for a cable-driven parallel robot with varying payload information,” Mechatronics 79(3), 102648 (2021).10.1016/j.mechatronics.2021.102648CrossRefGoogle Scholar
Behzadipour, S. and Khajepour, A., “Stiffness of cable-based parallel manipulators with application to stability analysis,” ASME J. Mech. Des. 128(1), 303–310 (2005).10.1115/1.2114890CrossRefGoogle Scholar
Liu, P., Qiu, Y., Su, Y. and Chang, J., “On the minimum cable tensions for the cable-based parallel robots,” J. Appl. Math. 2014(1), 350492 (2014).10.1155/2014/350492CrossRefGoogle Scholar
Bosscher, P. and Ebert-Uphoff, I.. “A Stability Measure for Underconstrained Cable-Driven Robots,” In: IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA ’04 (2004) pp. 4943–4949.Google Scholar
Bosscher, P. M.. Disturbance Robustness Measures and Wrench-Feasible Workspace Generation Techniques for Cable-Driven Robots . Ph.D. Thesis (Georgia Institute of Technology, 2004).Google Scholar
Liu, P., Qiu, Y. and Su, Y., “A new hybrid force-position measure approach on the stability for a camera robot,” Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 230(14), 2508–2516 (2016).10.1177/0954406215597712CrossRefGoogle Scholar
Wei, H., Qiu, Y. and Yang, J., “An approach to evaluate stability for cable-based parallel camera robots with hybrid tension-stiffness properties,” Int. J. Adv. Robot. Syst. 12, 185 (2015).Google Scholar
Wang, Y., Wang, K., Wang, W., Han, Z. and Zhang, Z., “Appraisement and analysis of dynamical stability of under-constrained cable-driven lower-limb rehabilitation training robot,” Robotica 39(6), 1023–1036 (2021).10.1017/S0263574720000879CrossRefGoogle Scholar
Yu, J., Tao, J., Wang, G., Li, X. and Wang, H., “Stability analysis and optimal design of a cable-driven parallel robot,” Robot. Auton. Syst. 173, 104611 (2024).10.1016/j.robot.2023.104611CrossRefGoogle Scholar
Liu, P., Qiao, X. and Zhang, X., “Stability sensitivity for a cable-based coal-gangue picking robot based on grey relational analysis,” Int. J. Adv. Robot. Syst. 18(6), 17298814211059729 (2021).CrossRefGoogle Scholar
Liu, P., Tian, H., Cao, X., Zhang, X., Qiao, X. and Su, Y., “Dynamic stability measurement and grey relational stability sensitivity analysis methods for high-speed long-span 4-1 cable robots,” Mathematics 10(24), 4653 (2022).10.3390/math10244653CrossRefGoogle Scholar
Liu, P., Zhang, X., Qiao, X. and Qiu, Y., “A grey relational analysis method for structural stability sensitivity of cable-suspended camera robots including presence of cable mass,” J. Grey Syst.-UK 34(4), 54–77 (2022).Google Scholar
Liu, P., Ma, H., Cao, X., Zhang, X., Duan, X. and Nie, Z., “Minimum dynamic cable tension workspace generation techniques and cable tension sensitivity analysis methods for cable-suspended gangue-sorting robots,” Machines 11(3), 338 (2023).10.3390/machines11030338CrossRefGoogle Scholar
Liu, P., Tian, H. and Qiao, X., “Minimum cable tensions and tension sensitivity for long-span cable-driven camera robots with applications to stability analysis,” Actuators 12(1), 17 (2023).10.3390/act12010017CrossRefGoogle Scholar
Kim, S., Kim, J., Lee, J., Shim, S. and Kim, K., “Robust optimal design of a neutral valve for hydrostatic transmissions using grey relational analysis,” Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 231(18), 3414–3428 (2017).10.1177/0954406216645628CrossRefGoogle Scholar
Wang, Y. and Li, H., “A novel single-sample retinal vessel segmentation method based on grey relational analysis,” Sensors 24(13), 4326 (2024).10.3390/s24134326CrossRefGoogle ScholarPubMed
Gosselin, C. and Grenier, M., “On the determination of the force distribution in overconstrained cable-driven parallel mechanisms,” Meccanica 46, 3–15 (2011).10.1007/s11012-010-9369-xCrossRefGoogle Scholar
Pott, A., “An Improved Force Distribution Algorithm for Over-Constrained Cable-Driven Parallel Robots,” In: Computational Kinematics (Springer, Heidelberg, 2014) pp. 139–146.10.1007/978-94-007-7214-4_16CrossRefGoogle Scholar
Mikelsons, L., Bruckmann, T., Hiller, M. and Schramm, D., “A Real-Time Capable Force Calculation Algorithm for Redundant Tendon-Based Parallel Manipulators,” In: 2008 IEEE International Conference on Robotics and Automation (2008) pp. 3869–3874 .10.1109/ROBOT.2008.4543805CrossRefGoogle Scholar
Song, D., Lu, M., Zhao, L., Sun, Z., Wang, H. and Zhang, L., “A novel real-time tension distribution method for cable-driven parallel robots,” Robotica 42(11), 3692–3708 (2024).10.1017/S0263574724001590CrossRefGoogle Scholar
Wang, Y., Wang, K., Wang, W., Yin, P. and Han, Z., “Appraise and analysis of dynamical stability of cable-driven lower limb rehabilitation training robot,” J. Mech. Sci. Technol. 33(11), 5461–5472 (2019).10.1007/s12206-019-1040-4CrossRefGoogle Scholar
Ida, E. and Carricato, M., “Static workspace computation for underactuated cable-driven parallel robots,” Mech. Mach. Theory 193 (2024).10.1016/j.mechmachtheory.2023.105551CrossRefGoogle Scholar
Peng, J., Guo, Y., Meng, D. and Han, Y., “Kinematics, statics modeling and workspace analysis of a cable-driven hybrid robot,” Multibody Syst. Dyn. 61(2), 163–193 (2024).10.1007/s11044-023-09924-6CrossRefGoogle Scholar
Qin, Z., Liu, Z., Liu, Y., Gao, H., Sun, C. and Sun, G., “Workspace analysis and optimal design of dual cable-suspended robots for construction,” Mech. Mach. Theory 171, 104763 (2022).10.1016/j.mechmachtheory.2022.104763CrossRefGoogle Scholar
Liu, H. and Liu, Y., “Colleges’ performance assessment of university based on grey relational analysis,” J. Intell. Fuzzy Syst. 44(4), 6699–6708 (2023).Google Scholar
Sarraf, F. and Nejad, S. H., “Improving performance evaluation based on balanced scorecard with grey relational analysis and data envelopment analysis approaches: Case study in water and wastewater companies,” Eval. Program. Plan. 79, 101762 (2020).10.1016/j.evalprogplan.2019.101762CrossRefGoogle ScholarPubMed
Singh, S., Singh, I. and Dvivedi, A., “Multi objective optimization in drilling of Al6063/10% SiC metal matrix composite based on grey relational analysis,” Proc. Inst. Mech. Eng. Part B: J. Eng. 227(12), 1767–1776 (2013).10.1177/0954405413494383CrossRefGoogle Scholar