Skip to main content
SpringerLink
Log in

Performance analysis of 3-PPRU parallel mechanism with a completely/partially/non constant Jacobian matrix

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

Abstract

This paper proposes a 3-PPRU parallel mechanism (PM) with a completely/partially/non constant Jacobian matrix. Based on screw theory and selecting actuating components theory, the reasonability of the actuating input selection is analyzed. By different actuating selection, the Jacobian matrix of the PM can realize completely/partially/non constant. The direct, inverse and combined kinematic singularities of the PM with three different Jacobian matrices are discussed. The velocity, payload and stiffness performance of the PM are discussed and compared. A new index, as auxiliary evaluation index, is proposed first.

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. S. A. Joshi and L. W. Tsai, Jacobian analysis of limited-DOF parallel manipulators, J. of Mechanical Design, 124(2) (2002) 254–258.

    Article  Google Scholar 

  2. Q. C. Li, X. D. Sun, Q. H. Chen and C. Y. Wu, Kinematics and singularity analysis of 2-PRS-PRRU parallel mechanism, J. of Mechanical Engineering, 47(3) (2011) 21–27.

    Article  Google Scholar 

  3. Y. G. Li, Y. M. Song, Z. Y. Feng and C. Zhang, Complete Jacobian matrix of a class of incompletely symmetrical parallel mechanisms with 4DOF, J. of Mechanical Engineering, 43(6) (2007) 37–40.

    Article  Google Scholar 

  4. T. Huang, H. T. Liu and D. G. Chetwynd, Generalized Jacobian analysis of lower mobility manipulators, Mechanism and Machine Theory, 46(6) (2011) 831–844.

    Article  MATH  Google Scholar 

  5. B. Hu, C. X. Song, Q. L. Zhang and J. J. Yu, Jacobian matrix establishment of 2(2-UPR+SPR) serial-parallel manipulator, China Mechanical Engineering, 26(7) (2015) 853–858.

    Google Scholar 

  6. W. Ye, Q. C. Li and K. T. Zhang, Kinematics and performance analysis of a 2R2T parallel manipulator with partially decoupled motion, Transactions of the Chinese Society for Agricultural Machinery, 50(1) (2018) 1–10.

    Google Scholar 

  7. Z. X. Shi, Y. F. Luo, H. L. Chen and M. Y. Ye, On global performance indices of robotic mechanisms, Robot, 27(5) (2005) 420–422.

    Google Scholar 

  8. X. Zhou, Y. D. Xu, J. T. Yao, K. J. Zheng and Y. S. Zhao, Complete stiffness model and stiffness performance of 5-UPS/PRPU redundantly actuated parallel machine tool, Optics and Precision Engineering, 23(4) (2015) 1070–1080.

    Article  Google Scholar 

  9. S. G. Kim and J. Ryu, New dimensionally homogeneous Jacobian matrix formulation by three end-effector points for optimal design of parallel manipulators, IEEE Transactions on Robotics and Automation, 19(4) (2003) 731–736.

    Article  Google Scholar 

  10. Y. Z. Zhao, Y. C. Cao, X. W. Kong and T. S. Zhao, Type synthesis of parallel mechanisms with a constant Jacobian matrix, J. of Mechanisms and Robotics, 10(6) (2018) 061011.

    Article  Google Scholar 

  11. Y. Z. Zhao, B. W. Liang, Y. C. Cao and T. S. Zhao, 3-PRRR translational parallel mechanism with constant Jacobian matrix and its transfer performance analysis, Transactions of the Chinese Society for Agricultural Machinery, 48(1) (2017) 333–338.

    Google Scholar 

  12. Y. Z. Zhao, B. W. Liang, W. Yang, C. Wang, G. M. Chen and T. S. Zhao, The constant balancing 6UPS/(3PRRR)+S parallel mechanism and its balancing performance analysis, Mechanism and Machine Theory, 126 (2018) 79–91.

    Article  Google Scholar 

  13. Y. Z. Zhao, Y. C. Cao, B. W. Liang, R. Han and S. Li, A Deformable Parallel Three-dimensional Dynamic Force Sensor, Patent No. 106017769B, National Intellectual Property Administration, China (2016).

    Google Scholar 

  14. Y. C. Cao, Y. Z. Zhao, T. Zhang and G. C. Ma, Construction method of parallel mechanisms with a partially constant Jacobian matrix, Mechanism and Machine Theory, 145 (2020) 103699.

    Article  Google Scholar 

  15. Y. Z. Zhao, B. W. Liang, J. Zhang, L. Z. Qi, D. Zhang and W. Yang, The effect analysis of input selection on performance of 3-PPRR translational parallel mechanism, International J. of Robotics and Automation, 33(6) (2018) 635–644.

    Google Scholar 

  16. T. S. Zhao and Z. Huang, Theory and application of selecting actuating components of spatial parallel mechanisms, J. of Mechanical Engineering, 36(10) (2000) 81–85.

    Article  Google Scholar 

  17. C. Gosselin and J. Angeles, Singularity analysis of closed-loop kinematic chains, IEEE Transactions on Robotics and Automation, 6(3) (1990) 281–290.

    Article  Google Scholar 

  18. X. J. Liu, The relationship between the performance criteria and link lengths of the parallel manipulators and their design theory, Ph.D. Thesis, Yanshan University, China (1999).

    Google Scholar 

  19. J. K. Salisbury and J. J. Craig, Articulated hands: force control and kinematic issues, The International J. of Robotics Research, 1(1) (1982) 4–17.

    Article  Google Scholar 

  20. X. J. Liu, J. S. Wang and G. Pritschow, On the optimal kinematic design of the PRRRP 2-DoF parallel mechanism, Mechanism and Machine Theory, 41(9) (2006) 1111–1130.

    Article  MATH  Google Scholar 

  21. C. Gosselin and J. Angeles, A global performance index for the kinematic optimization of robotic manipulators, J. of Mechanical Design, 113(3) (1991) 220–226.

    Article  Google Scholar 

  22. Q. L. Huai, Performance analysis and design on the six degree of freedom motion simulatior, M.S. Thesis, Yanshan University, China (2014).

    Google Scholar 

  23. N. N. Lin and K. M. Li, Dexterity analysis of 3-(2SPS) parallel manipulator, Machine Building and Automation, 43(6) (2014) 39–42.

    Google Scholar 

  24. Q. Hao, Optimization design and dynamic control of a 2-DoF planar parallel manipulator, Ph.D. Thesis, Tsinghua University, China (2011).

    Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge the financial support of the National Science and Technology Major Project of China [grant numbers 2015ZX04005006]; the Science and Technology Planning Project of Guangdong Province, China [grant numbers 2019B040402006]; the Science and Technology Major Project of Zhongshan city, China [grant numbers 2018A10018]; the Natural Science Foundation of Hebei Province [grant numbers E2018203436]; the Science Technology Research of Higher Education of Hebei Province [grant numbers ZD2018024]; and Guangdong Province Jihua Laboratory [grant numbers Y80311W180].

Author information

Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, 510640, China

    Yachao Cao, Tie Zhang & Guangcai Ma

  2. Parallel Robot and Mechatronic System Laboratory, Yanshan University, Qinhuangdao, 066004, China

    Yanzhi Zhao

  3. Key Laboratory of Advanced Forging and Stamping Technology and Science of Ministry of National Education, Yanshan University, Qinhuangdao, 066004, China

    Yanzhi Zhao

Authors
  1. Yachao Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tie Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanzhi Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guangcai Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Tie Zhang or Yanzhi Zhao.

Additional information

Tie Zhang is a Professor and a Ph.D. candidate Supervisor of the School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, China. He received his Ph.D. in Mechanical Manufacturing and Automation from South China University of Technology in 2001. His main research interests include optimal design and control of serial and parallel robots, automation and intelligent systems.

Yanzhi Zhao is a Professor and a Ph.D. candicate Supervisor of the School of Mechanical Engineering, Yanshan University, Qinhuangdao, China. He received his Ph.D. in Mechatronics Engineering from Yanshan University in 2009. His main research interests include theory and applications of parallel mechanisms.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cao, Y., Zhang, T., Zhao, Y. et al. Performance analysis of 3-PPRU parallel mechanism with a completely/partially/non constant Jacobian matrix. J Mech Sci Technol 34, 4263–4279 (2020). https://doi.org/10.1007/s12206-020-0918-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-020-0918-5

Keywords

Search

Navigation