A Numerical Method for the Second-Order Mobility Analysis of Mechanisms

  • Igor Fernández de Bustos
  • Josu Agirrebeitia
  • Rafael Avilés

Abstract

The second order mobility analysis of mechanisms is a complicated problem that can be approached in a direct way via the analysis of the compatibility of the acceleration field. This paper will present a simple, numerical approach to retrieve the restrictions imposed to the movement that are derived from the second order (curvature) restrictions. This algorithm can be easily applied to bi and three dimensional mechanisms and delivers a good degree of efficiency. The results of this analysis can be employed to improve the efficiency of other algorithms which present lack of convergence in the vicinity of singular configurations.

Keywords

Kinematics Mechanism analysis Manipulators 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fernández-Bustos, I. Agirrebeitia, J. Avilés, R. A general procedure for the mobility and singularity analysis of kinematical chains including branch identification. Proceedings of the 12th IFToMM World Congress, Besançon (France), June 18–21, 2007.Google Scholar
  2. 2.
    Altuzarra, O. Pinto, C. Avilés, R. Hernández, A. A practical procedure to analyze singular configurations in closed kinematic chains. IEEE Transactions on Robotics, 20(6) December 2004.Google Scholar
  3. 3.
    Nokelby, S.B. Podhorodeski, R.P. Reprocity-based resolution of velocity degeneracies (singularies) for redundant manipulators. Mechanism and Machine Theory, 36 397–409 2001.Google Scholar
  4. 4.
    Zlatanov, D. Fenton, R.G. Benhabib, B. Identification and classification of the singular configurations of mechanisms. Mechanism and Machine Theory, 33(6) 743–760, 1998.Google Scholar
  5. 5.
    Park, F.C. Kim, J.W. Singularity analysis of closed kinematic chains. Transactions of the ASME Journal of Mechanical Design, 121 32–38, March, 1999.CrossRefGoogle Scholar
  6. 6.
    Karger, A. Singularity analysis of serial robot-manipulators. Transactions of the ASME Journal of Mechanical Design, 118, 1996.Google Scholar
  7. 7.
    Müller, A. Geometric characterization of the configuration space of rigid body mechanisms in regular and singular points. Proceedings of the IDETC/CIE 2005 ASME 2005 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Long Beach, California USA, September 24–28, 2005.Google Scholar
  8. 8.
    Rico, J.M. Gallardo, J. Duffy, J. Screw theory and higher order kinematic analysis of open serial and closed chains. Mechanism and Machine Theory, 34 559–586, 1999.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Igor Fernández de Bustos
    • 1
  • Josu Agirrebeitia
  • Rafael Avilés
  1. 1.Departamento de Ingeniería MecánicaEscuela Superior de Ingenieros de BilbaoSpain

Personalised recommendations