Skip to main content
SpringerLink
Log in

Elastodynamic modeling of spatial parallel manipulators contain subclosed loops

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

In this work, the delta parallel manipulator (PM) was considered as a case study to present a system elastodynamic modeling of spatial PMs contain subclosed loops. The mechanism consisted of major substructures including proximal, short, and distal links. Each link was divided into elements to establish the body-to-body and body-to-ground constraint equations. The global independent generalized displacement coordinates (IGDC) of the mechanism were extracted with the theory of multi-point constraint elements. Besides, the global IGDC and substructure synthesis approach was used to obtain the complete elastodynamic modeling of the mechanism without supplementing constraint equations. The resulting configuration-dependent elastodynamic modeling had fewer degrees of freedom, different from thousands used in finite element model (FEM). The natural frequencies could be predicted at any configuration of the mechanism, and were compared against the values of FEM to assess the correctness of the modeling. The proposed modeling could predict the distribution of natural frequencies of the mechanism in the workspace with computational efficiency. Therefore, it could be used as a numerical twin to simulate the elastodynamic performance of PMs in the pre-design stage.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Yang, W. Ye and Q. C. Li, Review of the performance optimization of parallel manipulators, Mech. Mach. Theory, 170 (2022) 104725.

    Article  Google Scholar 

  2. T. Yoshikawa, Dynamic manipulability of robot manipulators, Proc. of IEEE Int. Conf. Robot. Automat. (ICRA), St. Louis, MO (1985) 1033–1038.

  3. R. Clavel, Device for the Movement and Positioning of an Element in Space, Patent No. US4976582A, US Patent and Trademark Office (1990).

  4. R. Cravel, Delta, a fast robot with parallel geometry, Proc. of the 18th Int. Symp. on Industrial Robots (ISIR), Lausanne (1988) 91–100.

  5. S. J. Yan, S. K. Ong and A. Y. C. Nee, Stiffness analysis of parallelogram-type parallel manipulators using a strain energy method, Robot. Cim.-Int. Manuf., 37 (2016) 13–22.

    Article  Google Scholar 

  6. B. Hu, Kinetostatic model of overconstrained lower mobility parallel manipulators, Nonlinear Dynam., 86 (2016) 309–322.

    Article  Google Scholar 

  7. H. H. Nam and Y. Altintas, Modeling the dynamics of 5-axis machine tool using the multibody approach, ASME. J. Manuf. Sci. Eng., 143(2) (2020) 021012.

    Google Scholar 

  8. N. Vinh, T. Cvitanic and S. Melkote, Data-driven modeling of the modal properties of a six-degrees-of-freedom industrial robot and its application to robotic milling, ASME. J. Manuf. Sci. Eng., 141(12) (2019) 121006.

    Article  Google Scholar 

  9. X. Zhang, J. K. Mills and W. L. Cleghorn, Flexible linkage structural vibration control on a 3-PRR planar parallel manipulator: experimental results, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 223 (3009) 71–84.

    Google Scholar 

  10. L. Chen and H. G. Wang, Finite element modal analysis of the FPD glass substrates handling robot, Proc. of Int. Conf. on Mechatronics and Automation (ICMA), Chengdu (2012) 1341–1346.

  11. Y. Ma, W. Niu, Z. Luo, F. Yin and T. Huang, Static and dynamic performance evaluation of a 3-DOF spindle head using CAD-CAE integration methodology, Robot. Cim.-Int. Manuf., 41 (2016) 1–12.

    Article  Google Scholar 

  12. A. Kermanian, A. Kamali and A. Taghvaeipour, Dynamic analysis of flexible parallel robots via enhanced co-rotational and rigid finite element formulations, Mech. Mach. Theory, 139 (2019) 144–173.

    Article  Google Scholar 

  13. L. Sheng, W. Li, Y. Wang, X. Yang and M. Fan, Rigid-flexible coupling dynamic model of a flexible planar parallel robot for modal characteristics research, Adv. Mech. Eng., 11 (1) (2019).

  14. D. Liang, Y. Song, T. Sun and X. Jin, Rigid-flexible coupling dynamic modeling and investigation of a redundantly actuated parallel manipulator with multiple actuation modes, J. Sound Vib., 403 (2017) 129–151.

    Article  Google Scholar 

  15. M. Sharifnia and A. Akbarzadeh, An analytical model for vibration and control of a PR-PRP parallel robot with a flexible platform and prismatic joint, J. Vib. Control, 22(3) (2016) 632–648.

    Article  MathSciNet  Google Scholar 

  16. M. Sharifnia and A. Akbarzadeh, Dynamics and vibration of a 3-PSP parallel robot with flexible moving platform, J. Vib. Control, 22(4) (2016) 1095–1116.

    Article  MathSciNet  Google Scholar 

  17. M. H. Korayem, S. F. Dehkordi, M. Mojarradi and P. Monfared, Analytical and experimental investigation of the dynamic behavior of a revolute-prismatic manipulator with N flexible links and hubs, Int. J. Ad. Manuf. Tech., 103(5–8) (2019) 2235–2256.

    Article  Google Scholar 

  18. L. Wu, G. Wang, H. Liu and T. Huang, An approach for elastodynamic modeling of hybrid robots based on substructure synthesis technique, Mech. Mach. Theory, 123 (2018) 124–136.

    Article  Google Scholar 

  19. J. Zhang and Y.-q. Zhao, Elastodynamic modeling and joint reaction prediction for 3-PRS PKM, J. Cent. South Univ., 22(8) (2015) 2971–2979.

    Article  Google Scholar 

  20. J. Zhang, Y. Q. Zhao and M. Ceccarelli, Elastodynamic model-based vibration characteristics prediction of a three prismatic-revolute-spherical parallel kinematic machine, J. Dyn. Sys., Meas., Control., 138(4) (2016) 041009.

    Article  Google Scholar 

  21. Y. Zhao, F. Gao, X. Dong and X. Zhao, Dynamics analysis and characteristics of the 8-PSS flexible redundant parallel manipulator, Robot. Cim.-Int. Manuf., 27(5) (2011) 918–928.

    Article  Google Scholar 

  22. M. Rognant, E. Courteille and P. Maurine, A systematic procedure for the elastodynamic modeling and identification of robot manipulators, IEEE T. Robot., 26(6) (2010) 1085–1093.

    Article  Google Scholar 

  23. Z. Chen, M. Kong, M. Liu and W. You, Dynamic modelling and trajectory tracking of parallel manipulator with flexible link regular paper, Int. J. Adv. Robot. Syst., 10 (2013) 328.

    Article  Google Scholar 

  24. Z. H. Chen, J. H. Li, S. K. Wang, J. Z. Wang and L. L. Ma, Flexible gait transition for six wheel-legged robot with unstructured terrains, Robot. Auton. Syst., 150 (2022) 103989.

    Article  Google Scholar 

  25. J. Yu, H. Y. Shen, H. F. Wang and X. Z. Wu, Speed estimation of multiphase induction motor using rotor slot harmonics with limited snr and dynamic load conditions, IEEE Trans. Ind. Electron (2022) 3201286.

  26. S. K. Wang, Z. H. Chen, J. H. Li, J. Z. Wang, J. Li and J. B. Zhao, Flexible motion framework of the six wheel-legged robot: experimental results, IEEE/ASME Transactions on Mechatronics, 27(4) (2022) 2246- 2257.

    Article  Google Scholar 

  27. B. Bounab, Multi-objective optimal design based kinetoelastostatic performance for the delta parallel mechanism, Robotica, 34(2) (2016) 258–273.

    Article  Google Scholar 

  28. G. Carbone, E. Ottaviano and M. Ceccarelli, An optimum design procedure for both serial and parallel manipulators, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 221(7) (2007) 829–843.

    Google Scholar 

  29. C. Yang, Q. Li and Q. Chen, Multi-objective optimization of parallel manipulators using a game algorithm, Appl. Math. Model., 74 (2019) 217–243.

    Article  MathSciNet  MATH  Google Scholar 

  30. C. Yang, Q. Li, Q. Chen and L. Xu, Elastostatic stiffness modeling of overconstrained parallel manipulators, Mech. Math. Theory, 122 (2018) 58–74.

    Article  Google Scholar 

  31. A. Rezaei, A. Akbarzadeh and M.-R. Akbarzadeh-T., An investigation on stiffness of a 3-PSP spatial parallel mechanism with flexible moving platform using invariant form, Mech. Math. Theory, 51 (2010) 198–216.

    Google Scholar 

  32. K. Zheng, Y. Hu and W. Yu, A novel parallel recursive dynamics modeling method for robot with flexible bar-groups, Appl. Math. Model., 77 (2020) 267–288.

    Article  MathSciNet  MATH  Google Scholar 

  33. F. W. Yin, W. J. Tian, H. T. Liu, T. Huang and D. G. Chetwynd, A screw-theory-based approach to determining the identifiable parameters for calibration of parallel manipulators, Mech. Mach. Theory, 145 (2020) 103665.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (51705465), China, in part by the Natural Science Foundation of Zhejiang Province (LGG20 E050021), China, in part by the Key research and development project of Jiaxing Science and Technology Bureau (2022BZ 10004), China.

Author information

Authors and Affiliations

  1. Faculty of Mechanical and Electrical Engineering, Jiaxing University, Jiaxing, 314001, China

    Chao Yang, Yang Wang, Junbin Lou & Fengli Huang

  2. National and Local Joint Engineering Research Center for Reliability Analysis and Testing of Mechanical and Electrical Products, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Wei Ye

Authors
  1. Chao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junbin Lou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wei Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fengli Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fengli Huang.

Additional information

Chao Yang received the B.S. degree in Process Equipment & Control Engineering from Zhengzhou University of Light Industry, Zhengzhou, China, in 2005, the M.S. degree in Engineering Mechanics from Dalian University of Technology, Dalian, China, in 2009, and a Ph.D. degree in Mechanical Engineering from Zhejiang Sci-Tech University, Hangzhou, China, in 2019. He joined the Faculty of Mechanical Engineering, Jiaxing University, in 2019, where he is currently a Lecturer. His main research interests include kinematics, stiffness, dynamics, and multi-objective optimization of parallel manipulators.

Fengli Huang received the B.S. degree in Thermal Engineering from Kunming University of Science and Technology, Kunming, China, in 2000, the M.S. degree in Mechanical Engineering from Zhejiang University of Technology, Hangzhou, China, in 2005, and a Ph.D. degree in Mechanical Engineering of Tongji University, China, in 2010. He joined the Faculty of Mechanical Engineering, Jiaxing University, in 2005, where he is currently a Professor. He is the author of more than 70 articles. His research interests include modern design theory and method, mechanism theory, equipment for flexible devices, and application of parallel manipulators.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, C., Wang, Y., Lou, J. et al. Elastodynamic modeling of spatial parallel manipulators contain subclosed loops. J Mech Sci Technol 37, 1421–1431 (2023). https://doi.org/10.1007/s12206-023-0228-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-023-0228-9

Keywords

Search

Navigation