Skip to main content
SpringerLink
Log in

A comprehensive study on the free vibration of machine tools’ hexapod table

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

Abstract

Prior knowledge of the free-vibration responses of a hexapod is strongly needed to avoid resonance occurring in the prevailing complicated machining situations. A comprehensive study has been conducted by the authors on the free vibration of machine tools’ hexapod table, taking account of the whole kinematic chains. The results have been compared with those obtained from the vibration equations of the moving platform. The second approach entailing fewer equations can yield sufficiently accurate results for vibrations occurring in horizontal planes. The theoretical and finite element method (FEM) results exhibit similar trends of changes and are close to each other. The discrepancies between the results arise mainly from the rotational modes of vibration occurring in vertical planes, which are attributable to the dynamic nature of contact models. A hexapod table possesses distinct vibration modes, including linear vibrations in horizontal planes prevailing in lower modes and rotational vibration in higher modes.

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. Dasgupta B, Mruthyunjaya TS (2000) The Stewart platform manipulator: a review. Mech Mach Theory 35:15–40

    Article  MathSciNet  Google Scholar 

  2. Lin H, McInroy JE (2006) Disturbance attenuation in precise hexapod pointing using positive force feedback. Control Eng Prac 14:1377–1386

    Article  Google Scholar 

  3. Hanieh AA (2003) Active isolation and damping of vibration via Stewart platform. PhD thesis, Active Structure Laboratory, ULB University, Brussels, Belgium

  4. Ren G, Lu Q, Hu N, Nan R, Peng B (2004) On vibration control with Stewart parallel mechanism. Mechatronics 14:1–13

    Article  Google Scholar 

  5. Dasgupta B, Mruthyunjaya TS (1998) Closed-form dynamic equations of the general Stewart platform through the Newton-Euler approach. Mech Mach Theory 33(7):993–1012

    Article  MathSciNet  Google Scholar 

  6. Dasgupta B, Mruthyunjaya TS (1998) A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator. Mech Mach Theory 33(8):1135–1152

    MATH  MathSciNet  Google Scholar 

  7. Ivan J, Baiges V (1996) Dynamic modeling of parallel manipulators. PhD dissertation, Graduate School, University of Florida

  8. Lebret G, Liu K, Lewis FL (1993) Dynamic analysis and control of a Stewart platform manipulator. J Robot Syst 10(5):629–655

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  10. Dohner JL, Kwan CM, Regerlbrugge ME (1996) Active chatter suppression in an octahedral hexapod milling machine: a design study. Proc SPIE 2721:316–325

    Article  Google Scholar 

  11. Kim HS (1999) Design and control of Stewart platform based machine tool. PhD dissertation, Graduate School, Yonsei University, South Korea

  12. Harib K, Srinivasan K (2003) Kinematic and dynamic analysis of Stewart platform-based machine too structures. Robotica 21:541–554

    Article  Google Scholar 

  13. Mahboubkhah M, Nategh MJ, Esmaeilzade Khadem S (2007) Vibration analysis of machine tool’s hexapod table. Int J Adv Manuf Technol DOI 10.1007/s00170-007-1183-9

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Tarbiat Modares University, Jalal Al-Ahmad Boulevard, P.O. Box 14115-143, Tehran, Iran

    M. Mahboubkhah, M. J. Nategh & S. Esmaeilzadeh Khadem

Authors
  1. M. Mahboubkhah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. J. Nategh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Esmaeilzadeh Khadem
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. J. Nategh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mahboubkhah, M., Nategh, M.J. & Esmaeilzadeh Khadem, S. A comprehensive study on the free vibration of machine tools’ hexapod table. Int J Adv Manuf Technol 40, 1239–1251 (2009). https://doi.org/10.1007/s00170-008-1433-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-008-1433-5

Keywords

Search

Navigation