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A novel modified analytical method and finite element method for vibration analysis of cable-driven parallel robots

Abstract

Cable-driven parallel robots (CDPRs) are vulnerable to vibration due to the inevitable flexible properties of the cables. Thus, vibration analysis is critical for CDPR’s operation in which highly accurate motion is required. However, most of the current methods related to vibration analysis of CDPRs rely on simple spring models which have limitations in their performance and complexity that are not general to analyze the vibration of various CDPRs. Hence, accurate, simple and general approaches for vibration analysis in CDPRs are need. To solve this problem, this paper presents the finite element method (FEM) and the modified analytical method to analyze the vibration of CDPRs. To validate these methods, free vibration analysis was conducted using the proposed methods for the planar and spatial cable-driven parallel robots. The natural frequencies of these two CDPRs were computed by the proposed two methods and compared with those of the commercial software, SAP2000. The solutions obtained by the FEM and the modified analytical models turned out to be close to SAP2000’s results, thereby verifying the validity of the proposed methods.

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References

  1. [1]

    C. Wright et al., Design of a modular snake robot, IEEE Int. Conf. Intel. Robot. Syst. (2007) 2609–2614.

  2. [2]

    Q. Nguyen et al., Optimized jumping on the MIT cheetah 3 robot, Proc. IEEE Int. Conf. Robot. Autom. (2019) 7448–7454.

  3. [3]

    G. Chen and B. Jin, Position-posture trajectory tracking of a six-legged walking robot, Int. J. Robot. Autom., 34 (1) (2019) 24–37.

    Google Scholar 

  4. [4]

    G. Chen, B. Jin and Y. Chen, Accurate and robust body position trajectory tracking of six-legged walking robots with nonsingular terminal sliding mode control method, Appl. Math. Model., 77 (2020) 1348–1372.

    MathSciNet  MATH  Article  Google Scholar 

  5. [5]

    G. Chen, B. Jin and Y. Chen, Nonsingular fast terminal sliding mode posture control for six-legged walking robots with redundant actuation, Mechatronics, 50 (2018) 1–15.

    Article  Google Scholar 

  6. [6]

    M. A. Khosravi and H. D. Taghirad, Robust PID control of fully-constrained cable driven parallel robots, Mechatronics, 24 (2) (2014) 87–97.

    Article  Google Scholar 

  7. [7]

    X. Diao and O. Ma, Vibration analysis of cable-driven parallel manipulators, Multibody Syst. Dyn., 21 (4) (2009) 347–360.

    MATH  Article  Google Scholar 

  8. [8]

    E. Barnett and C. Gosselin, Large-scale 3D printing with a cable-suspended robot, Addit. Manuf., 7 (2015) 27–44.

    Google Scholar 

  9. [9]

    E. Ottaviano, Analysis and design of a four-cable-driven parallel manipulator for planar and spatial tasks, Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci., 222 (8) (2008) 1583–1592.

    Article  Google Scholar 

  10. [10]

    S. Nguyen-Van and K. W. Gwak, A novel determination of boundaries of cable forces for cable-driven parallel robots with frequency constraint by using differential evolution algorithm, ICERA 2019: Advances in Engineering Research and Application (2019) 35–46.

  11. [11]

    C. Gosselin, Stiffness mapping for parallel manipulators, IEEE Trans. Robot. Autom., 6 (3) (1990) 377–382.

    Article  Google Scholar 

  12. [12]

    P. Bosscher et al., Cable-suspended robotic contour crafting system, Autom. Constr., 17 (1) (2007) 45–55.

    Article  Google Scholar 

  13. [13]

    D. Q. Nguyen and M. Gouttefarde, Study of reconfigurable suspended cable-driven parallel robots for airplane maintenance, 2014 IEEE/RSJ Int. Conf. Intell. Robot. Syst. (2014) 1682–1689.

  14. [14]

    L. Gagliardini et al., Optimal design of cable-driven parallel robots for large industrial structures, 2014 IEEE Int. Conf. Robot. Autom. (2014) 5744–5749.

  15. [15]

    G. Abbasnejad, J. Yoon and H. Lee, Optimum kinematic design of a planar cable-driven parallel robot with wrench-closure gait trajectory, Mech. Mach. Theory, 99 (2016) 1–18.

    Article  Google Scholar 

  16. [16]

    S. Behzadipour and A. Khajepour, Stiffness of cable-based parallel manipulators with application to stability analysis, J. Mech. Des., 128 (1) (2005) 303–310.

    MATH  Article  Google Scholar 

  17. [17]

    N. G. Dagalakis, J. S. Albus, B.-L. Wang, J. Unger and J. D. Lee, Stiffness study of a parallel link robot crane for shipbuilding applications, J. Offshore Mech. Arct. Eng., 111 (3) (1989) 183–193.

    Article  Google Scholar 

  18. [18]

    S. Kawamura, H. Kino and C. Won, High-speed manipulation by using parallel wire-driven robots, Robotica, 18 (1) (2000) 13–21.

    Article  Google Scholar 

  19. [19]

    H. Yuan et al., Vibration analysis of cable-driven parallel robots based on the dynamic stiffness matrix method, J. Sound Vib., 394 (2017) 527–544.

    Article  Google Scholar 

  20. [20]

    J. Du et al., Dynamic analysis of cable-driven parallel manipulators with time-varying cable lengths, Finite Elem. Anal. Des., 48 (1) (2012) 1392–1399.

    MathSciNet  Article  Google Scholar 

  21. [21]

    H. D. Do and K. S. Park, Analysis of effective vibration frequency of cable-driven parallel robot using mode tracking and quasi-static method, Microsyst. Technol., 23 (7) (2017) 2577–2585.

    Article  Google Scholar 

  22. [22]

    M. L. Gambhir and B. de V. Batchelor, A finite element for 3-D prestressed cablenets, Int. J. Numer. Methods, 11 (11) (1977) 1699–1718.

    MATH  Article  Google Scholar 

  23. [23]

    M. L. Gambhir and B. de V. Batchelor, Finite element study of the free vibration of 3-D cable networks, Int. J. Solids Struct., 15 (2) (1979) 127–136.

    MATH  Article  Google Scholar 

  24. [24]

    H. B. Jayaraman and W. C. Knudson, A curved element for the analysis of cable structures, Comput. Struct., 14 (3–4 (1981) 325–333.

    Article  Google Scholar 

  25. [25]

    J. P. Coyette and P. Guisset, Cable network analysis by a nonlinear programming technique, Eng. Struct., 10 (1) (1988) 41–46.

    Article  Google Scholar 

  26. [26]

    H. T. Thai and S. E. Kim, Nonlinear static and dynamic analysis of cable structures, Finite Elem. Anal. Des., 47 (3) (2011) 237–246.

    Article  Google Scholar 

  27. [27]

    R. Babaghasabha, M. A. Khosravi and H. D. Taghirad, Robust PID control of fully-constrained cable driven parallel robots, Mechatronics, 24 (2) (2014) 87–97.

    Article  Google Scholar 

  28. [28]

    A. Pott, Cable-driven Parallel Robots: Theory and Application, Springer International Publishing (2018).

  29. [29]

    H. M. Irvine, Cable Structures, MIT Press, Cambridge, MA, USA (1981).

    Google Scholar 

  30. [30]

    H. Yuan, E. Courteille and D. Deblaise, Static and dynamic stiffness analyses of cable-driven parallel robots with non-negligible cable mass and elasticity, Mech. Mach. Theory, 85 (2015) 64–81.

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2020R1A4A2002855).

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Corresponding author

Correspondence to Kwan-Woong Gwak.

Additional information

Sy Nguyen-Van received his B.S. and M.S. in Mechanical Engineering from Thai Nguyen University of Technology, Thai Nguyen, Vietnam, in 2015, and Sejong University, Seoul, South Korea, in 2019, respectively. He is currently a Lecturer there. His research interests are robotics, evolutionary algorithms, and engineering optimization.

Kwan-Woong Gwak received his B.S. and M.S. in Mechanical Engineering from Korea University, Korea, in 1993 and 1995, respectively, and his Ph.D. with a specialization in nonlinear control system design from the University of Texas, Austin, in 2003. Since 2006, he has been with the Department of Mechanical Engineering, Sejong University, where he is currently a Professor. His research interest includes the robotics, control system design, and mechatronics.

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Nguyen-Van, S., Gwak, KW., Nguyen, DH. et al. A novel modified analytical method and finite element method for vibration analysis of cable-driven parallel robots. J Mech Sci Technol 34, 3575–3586 (2020). https://doi.org/10.1007/s12206-020-0809-9

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Keywords

  • Cable-driven parallel robots
  • The cable element
  • The finite element method
  • The analytical method
  • Vibration analysis
  • Natural frequencies