Skip to main content
Log in

Dynamic modeling and validation of a tripod-based machine tool

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

In this paper, a reconfigurable tripod machine tool system is introduced, with a focus on dynamic modeling. The Newton-Euler approach is applied and a new modeling procedure is proposed. In the procedure of the dynamic modeling, the reference coordinate system for the forces/torques calculation and that for the equilibrium equations derivation are dealt with respectively. As a result, specific structural features of the tripod system are utilized to simplify the dynamic model and, thus, reduce the calculation complexity. The prototype tripod system is developed and the presented method is implemented for its configuration design. An experiment is conducted to validate the dynamic model.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Steward D (1965) A platform with six degrees of freedom. Proc Inst Mech Eng 180(15):371–386

    Google Scholar 

  2. Carretero JA, Podhorodeski RP, Nahon MN, Gosselin CM (2000) Kinematic analysis and optimization of a new three degree-of-freedom spatial parallel manipulator. ASME J Mech Des 122(1):17–24

    Article  Google Scholar 

  3. Dunlop GR, Jones TP (1999) Position analysis of a two DOF parallel mechanism—the Canterbury tracker. Mech Mach Theory 34(4):599–614

    Article  MATH  Google Scholar 

  4. Lee K-M, Arjunan S (1991) A three-degrees-of-freedom micromotion in-parallel actuated manipulator. IEEE Trans Robot Autom 7(5):634–641

    Article  Google Scholar 

  5. Fedewa D, Mehrabi MG, Kota S, Orlandea N, Gopalakrishran V (2000) Parallel structures and their applications in reconfigurable machining systems. In: Proceedings of the 2000 Parallel Kinematic Machines International Conference (PKM-IC 2000), Ann Arbor, Michigan, September 2000, pp 87–97

  6. Nguyen CC, Zhou Z-L, Bryfogis M (1995) A robotically assisted munition loading system. J Robot Syst 12(12):871–881

    Article  Google Scholar 

  7. Soons JA (1999) On the geometric and thermal errors of a hexapod machine tools. In: Boer CR, Molinari-Tosatti L, Smith KS (eds) Parallel kinematic machines: theoretical aspects and industrial requirements. Advanced Manufacturing Series. Springer, Berlin Heidelberg New York, pp 151–170

    Google Scholar 

  8. Wurst KH (1999) LINAPOD-machine tools as parallel link systems based on a modular design. In: Boer CR, Molinari-Tosatti L, Smith KS (eds) Parallel kinematic machines: theoretical aspects and industrial requirements. Advanced Manufacturing Series. Springer, Berlin Heidelberg New York, pp 377–394

    Google Scholar 

  9. Merlet JP (1999) The importance of optimal design for parallel structures. In: Boer CR, Molinari-Tosatti L, Smith KS (eds) Parallel kinematic machines: theoretical aspects and industrial requirements. Advanced Manufacturing Series. Springer, Berlin Heidelberg New York, pp 99–110

    Google Scholar 

  10. Bi ZM (2002) Adaptive robot systems for manufacturing applications. PhD thesis, Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada

  11. Ji Z, Song P (1998) Design of a reconfigurable platform manipulator. J Robot Syst 15(6):341–346

    Article  MATH  Google Scholar 

  12. Yang G, Chen I-M, Lim WK, Yeo SH (2001) Kinematic design of modular reconfigurable in-parallel robots. Auton Robots 10(1):83–89

    Article  MATH  Google Scholar 

  13. Xi F, Han W, Verner M, Ross A (2001) Development of a sliding-leg tripod as an add-on device for manufacturing. Robotica 19(3):285–294

    Article  Google Scholar 

  14. Bi ZM, Zhang WJ (2000) Concurrent optimal design of modular robotic configuration. J Robot Syst 18(2):77–87

    Article  MathSciNet  Google Scholar 

  15. Lee WH, Sanderson AC (2001) Dynamic analysis and distributed control of the Tetrobot modular reconfigurable robotic system. Auton Robots 10(1):67–82

    Article  MATH  Google Scholar 

  16. Chen I-M, Yang G (1997) Automatic generation of dynamics for modular reconfigurable robots with hybrid geometry. In: Proceedings of the IEEE International Conference on Robotics and Automation, Albuquerque, New Mexico, April 1997, pp 2288–2293

  17. Ji Z (1994) Dynamics decomposition for Stewart platforms. ASME J Mech Des 116(1):67–69

    Article  Google Scholar 

  18. Dasgupta B, Choudhury P (1999) A general strategy based on the Newton-Euler approach for the dynamic formulation of parallel manipulators. Mech Mach Theory 34(6):801–824

    Article  MATH  MathSciNet  Google Scholar 

  19. Geng Z, Haynes LS, Lee JD, Carroll RL (1992) On the dynamic model and kinematic analysis of a class of Stewart platforms. Robot Auton Syst 9(4):237–254

    Article  Google Scholar 

  20. Wang LCT, Chen CC (1994) On the dynamic analysis of general parallel robotic manipulators. Int J Robot Autom 9(2):81–87

    Google Scholar 

  21. Lee K-M, Shah DK (1988) Dynamic analysis of a three-degree-freedom in-parallel actuated manipulator. IEEE J Robot Autom 4(3):361–367

    Article  Google Scholar 

  22. Tsai L-W (2000) Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work. ASME J Mech Des 122(1):3–9

    Article  Google Scholar 

  23. Pang H, Shahinpoor M (1994) Inverse dynamics of a parallel manipulator. J Robot Syst 11(8):693–702

    Article  MATH  Google Scholar 

  24. Bhattacharya S, Nenchv DN, Uchiyama M (1998) A recursive formula for the inverse of the inertia matrix of a parallel manipulator. Mech Mach Theory 33(7):957–964

    Article  MATH  Google Scholar 

  25. Zanganeh KE, Sinatra R, Angeles J (1997) Kinematics and dynamics of a six-degree-of-freedom parallel manipulator with revolute legs. Robotica 15(4):385–394

    Article  Google Scholar 

  26. Ross A, Xi F, Mechefske C (2001) Varying topology of a reconfigurable parallel kinematic machine. In: Proceedings of the 1st CIRP International Conference on Agile, Reconfigurable Manufacturing, Ann Arbor, Michigan, May 2001

  27. Zhang D, Mechefske C, Xi F (2001) Stiffness analysis of reconfigurable parallel mechanisms with prismatic actuators. In: Proceedings of the 1st CIRP International Conference on Agile, Reconfigurable Manufacturing, Ann Arbor, Michigan, May 2001

  28. Xi F (2001) A comparison study on Hexapods with fixed-length legs. Int J Mach Tools Manuf 41(12):1735–1748

    Article  Google Scholar 

  29. Tsai L-W (1999) Robot analysis: the mechanics of serial and parallel manipulators. Wiley, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Z. M. Bi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bi, Z.M., Lang, S.Y.T. & Verner, M. Dynamic modeling and validation of a tripod-based machine tool. Int J Adv Manuf Technol 37, 410–421 (2008). https://doi.org/10.1007/s00170-007-0980-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-007-0980-5

Keywords