Design, comprehensive evaluation, and experimental study of a cable-driven parallel robot for lower limb rehabilitation


The stability of the rehabilitation robot system is an important prerequisite for the safety of patients’ rehabilitation training, and there are few studies on the evaluation method of the stability of the cable-driven rehabilitation robot. Hence, this paper aims to study the evaluation method of the dynamical stability of a cable-driven lower limb rehabilitation robot (CDLR) through comprehensive consideration of the position, cable tension, system stiffness, and velocity of the traction point. The structure and working principle of the CDLR is introduced. The position performance factor, the cable tension performance factor, and the system stiffness performance factor are defined based on the kinematics, dynamics, and system stiffness model of the CDLR. The evaluation index of the static stability of the CDLR is presented by comprehensively considering three performance factors. Considering the safety and comfort of the patients’ training, a velocity influence function is given. Combined with the evaluation index of the static stability and the velocity influence function, the evaluation index of the dynamical stability of the CDLR is proposed. Finally, the stability distribution laws of the CDLR are presented by simulation and experimental study. The rationality and correctness of the stability evaluation index are verified by experiments. The experiment results provide an important reference for structural design, rehabilitation training task planning, and control strategy of the CDLR.

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  1. 1.

    Bacci ML (2017) A concise history of world population. Wiley, Hoboken

    Google Scholar 

  2. 2.

    Wang YL, Wang KY, Zhang ZX et al (2020) Analysis of dynamical stability of rigid-flexible hybrid-driven lower limb rehabilitation robot. J Mech Sci Tech 34(4):1735–1748.

    Article  Google Scholar 

  3. 3.

    Wang YL, Wang KY, Zhao WY et al (2019) Effects of single crouch walking gaits on fatigue damages of lower extremity main muscles. J Mech. Med. Biol. 19(7):1940046.

    Article  Google Scholar 

  4. 4.

    Basteris A, Nijenhuis SM, Stienen AHA (2014) Training modalities in robot-mediated upper limb rehabilitation in stroke: a framework for classication based on a systematic review. J Neuroeng Rehabil. 11:111–126.

    Article  Google Scholar 

  5. 5.

    Chen SH, Lien WM (2016) Assistive control system for upper limb rehabilitation robot. IEEE Trans Neural Syst Rehabil Eng 24(11):1199–1209.

    Article  Google Scholar 

  6. 6.

    Ugurlu B, Nishimura M, Hyodo K et al (2014) Proof of concept for robot-aided upper limb rehabilitation using disturbance observers. IEEE Trans Hum-Mach Syst 45(1):110–118.

    Article  Google Scholar 

  7. 7.

    Rathore A, Wilcox M, Ramirez DZM, et al (2016) Quantifying the human-robot interaction forces between a lower limb exoskeleton and healthy users. In: Proceedings of the in Proceedings of the IEEE 38th Annual International Conference on Engineering in Medicine and Biology Society (EMBC), pp 586–589.

  8. 8.

    Jin X, Prado A, Agrawal SK (2018) Retraining of human gait-are lightweight cable-driven leg exoskeleton designs effective? IEEE Trans Neural Syst Rehabil Eng 26(4):847–855.

    Article  Google Scholar 

  9. 9.

    Kino H, Yoshitake T, Wada R et al (2018) 3-DOF planar parallel-wire driven robot with an active balancer and its model-based adaptive control. Adv Robot 32(14):766–777.

    Article  Google Scholar 

  10. 10.

    Zou YP, Wang N, Wang XQ et al (2018) Design and experimental research of movable cable-driven lower limb rehabilitation robot. IEEE Access 7:2315–2326.

    Article  Google Scholar 

  11. 11.

    Zou YP, Liu K, Wang N, et al (2018) Design and optimization of movable cable-driven lower-limb rehabilitation robot. In: 3rd IEEE international conference on advanced robotics and mechatronics (IEEE ICARM), pp 714–719.

  12. 12.

    Zhang LX, Li LL, Zou YP et al (2017) Force control strategy and bench press experimental research of a cable driven astronaut rehabilitative training robot. IEEE Access. 5:9981–9989.

    Article  Google Scholar 

  13. 13.

    Xiao F, Gao Y, Wang Y et al (2018) Design and evaluation of a 7-DOF cable-driven upper limb exoskeleton. J Mech Sci Technol 32(2):855–864.

    Article  Google Scholar 

  14. 14.

    Ni WC, Li H, Jiang ZH, Zhang BN, Huang Q et al (2018) Motion and force control method of 7-DOF cable-driven rehabilitation exoskeleton robot. Assem Autom 38(5):595–605.

    Article  Google Scholar 

  15. 15.

    Tsai YL, Huang JJ, Pu SW et al (2019) Usability assessment of a cable-driven exoskeletal robot for rehabilitation. Front Neurorobot 13(3):1–11.

    Article  Google Scholar 

  16. 16.

    Cheng L, Chen M, Zheng WL (2018) Design and control of a wearable hand rehabilitation robot. IEEE Access. 6:74039–74050.

    Article  Google Scholar 

  17. 17.

    Wang KY, Yin PC, Yang HP et al (2018) The man-machine motion planning of rigid-flexible hybrid lower limb rehabilitation robot. Adv Mech Eng 10(6):1–11.

    Article  Google Scholar 

  18. 18.

    Wang KY, Di CB, Tang XQ et al (2014) Modeling and simulation to muscle strength training of lower limbs rehabilitation robots. Adv Mech Eng 7(1):1–8.

    Article  Google Scholar 

  19. 19.

    Wang H, Kinugawa J, Kosuge K (2018) Exact kinematic modeling and identification of reconfigurable cable-driven robots with dual-pulley cable guiding mechanisms. IEEE-ASME Trans Mechatron 24(2):774–784.

    Article  Google Scholar 

  20. 20.

    Wang W, Yu L, Yang J (2019) Linear parameter variant modeling and parameter identification of a cable-driven micromanipulator for surgical robot. Proc Inst Mech Eng Part C-J Eng Mech Eng Sci 233(5):1828–1840.

    Article  Google Scholar 

  21. 21.

    Chen Q, Zi B, Sun Z et al (2019) Design and development of a new cable-driven parallel robot for waist rehabilitation. IEEE/ASME Trans. Mech. 24(4):1497–1507.

    Article  Google Scholar 

  22. 22.

    Asl Hamed Jabbari, Yoon Jungwon (2017) Stable assist-as-needed controller design for a planar cable-driven robotic system. Int J Control Autom Syst 15(6):2871–2882.

    Article  Google Scholar 

  23. 23.

    Wang Deri, Ahn Jeongdo, Jung Jinwoo (2017) Winch-integrated mobile end-effector for a cable-driven parallel robot with auto-installation. Int J Control Autom Syst 15(5):2355–2363.

    Article  Google Scholar 

  24. 24.

    Meziane R, Cardou P, Otis MJ-D (2019) Cable interference control in physical interaction for cable-driven parallel mechanisms. Mech Mach Theory 132:30–47.

    Article  Google Scholar 

  25. 25.

    Tang X (2014) An overview of the development for cable-driven parallel manipulator. Adv Mech Eng 6:823–828.

    Article  Google Scholar 

  26. 26.

    Barbosa AM, Carvalho JCM, Goncalves RS (2018) Cable-driven lower limb rehabilitation robot. J Braz Soc Mech Sci Eng 40(5):244–254.

    Article  Google Scholar 

  27. 27.

    Hong HJ, Ali Jabran, Ren L (2018) A review on topological architecture and design methods of cable-driven mechanism. Adv Mech Eng 10(5):1–14.

    Article  Google Scholar 

  28. 28.

    Behzadipour S, Khajepour A (2006) Stiffness of cable-based parallel manipulators with application to stability analysis. J Mech Des 128(1):303–310.

    Article  Google Scholar 

  29. 29.

    Michael N, Fink J, Kumar V (2011) Cooperative manipulation and transportation with aerial robots. Auton Robot 30(1):73–86.

    Article  MATH  Google Scholar 

  30. 30.

    Bosscher PM, Ebert-Uphoff IMME (2004) A stability measure for underconstrained cable-driven robots. In: Proceedings of IEEE international conference on robotics and automation 2004. New Orleans, LA, USA. pp 4943–4949.

  31. 31.

    Khosravi AM et al (2013) Robust PID control of fully-constrained cable driven parallel robots. Mechatronics 24(2):87–97.

    MathSciNet  Article  Google Scholar 

  32. 32.

    Wei HL, Qiu YY, Su Y (2016) Motion control strategy and stability analysis for high-speed cable-driven camera robots with cable inertia effects. Int J Adv Robot Syst 13:1–14.

    Article  Google Scholar 

  33. 33.

    Wei HL, Qui YY, Wang J (2015) An approach to evaluate stability for cable-based parallel camera robots with hybrid tension-stiffness properties. Int J Adv Robot Syst 12:185.

    Article  Google Scholar 

  34. 34.

    Wei HL, Qui YY, Sheng Y (2019) On the cable pseudo-drag problem of cable-driven parallel camera robots at high speeds. Robotica 37(10):1695–1709.

    Article  Google Scholar 

  35. 35.

    Liu P, Qiu YY, Su Y (2016) A new hybrid force-position measure approach on the stability for a camera robot. Proc Inst Mech Eng Part C-J Eng Mech Eng Sci 230(14):2508–2516.

    Article  Google Scholar 

  36. 36.

    Liu P (2015) On the mechanics and stability for the cable-driven parallel manipulators. Xidian University PhD Thesis

  37. 37.

    Liu P (2014) Minimum cable tensions for the cable-based parallel robots. J Appl Math 350492:1–8.

    Article  Google Scholar 

  38. 38.

    Wang YL, Zhao ZG, Su C et al (2017) Analysis of the workspace and dynamic stability of a multi-robot collaboratively towing system. J Vib Shock 36(16):44–50.

    Article  Google Scholar 

  39. 39.

    Wang YL, Wang KY, Wang WL et al (2019) Appraise and analysis of dynamical stability of cable-driven lower limb rehabilitation training robot. J Mech Sci Tech 33(11):5461–5472.

    Article  Google Scholar 

  40. 40.

    Zhao ZG, Wang YL, Li JN (2018) Appraise of dynamical stability of multi-robots cooperatively towing system based on hybrid force-position-pose approach. J Harbin Eng Univ 39(1):148–155.

    Article  MATH  Google Scholar 

  41. 41.

    Cafolla Daniele, Russo Matteo, Carbone Giuseppe, Cube A (2019) Cable-driven device for limb rehabilitation. J Bionic Eng 16:493–503.

    Article  Google Scholar 

  42. 42.

    Liu X, Qiu YY, Sheng Y (2011) Analysis on the static stiffness of wire-driven parallel manipulators. J Mech Eng 47(13):35–43.

    Article  Google Scholar 

  43. 43.

    Carbone G, Ceccarelli M (2010) Comparison of indices for stiffness performance evaluation. Front Mech Eng China 5(3):270–278.

    Article  Google Scholar 

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This work was supported in part by the National Natural Science Foundation of China (51405095), Natural Science Foundation of Heilongjiang Province, China (LH2019E032), and Postdoctoral Scientific Research Fund of Heilongjiang (LBH-Q15030), and Fundamental Research Funds for Central Universities of the Harbin Engineering University (3072019CF0704, 3072020CF0706).

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Correspondence to Ke-yi Wang.

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Wang, Y., Wang, K. & Zhang, Z. Design, comprehensive evaluation, and experimental study of a cable-driven parallel robot for lower limb rehabilitation. J Braz. Soc. Mech. Sci. Eng. 42, 371 (2020).

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  • Rehabilitation robot
  • Lower limb rehabilitation
  • Stability
  • Velocity influence function
  • Experiment study