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Input and output singularities for parallel manipulators

  • S. Vahid AmirinezhadEmail author
  • Peter Donelan
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

We develop a differential-geometric approach to kinematic modelling for manipulators which provides a framework for analysing singularities for forward and inverse kinematics via input and output mappings defined on the manipulator’s configuration space.

Keywords

kinematic constraint mapping configuration space singularities 

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References

  1. 1.
    Amirinezhad, S.V., Donelan, P.: Kinematic constraint maps, C-space singularities and generalised Grashof conditions. In: 2017 IDETC/CIE Conference. ASME (2017)Google Scholar
  2. 2.
    Amirinezhad, S.V., Donelan, P.: Kinematic constraint maps and c-space singularities for planar mechanisms with prismatic joints. In: International Symposium on Advances in Robot Kinematics. pp. 212–220. Springer (2018)Google Scholar
  3. 3.
    Amirinezhad, S.V., Donelan, P., Müller, A.: Transversality and its applications to kinematics. In: International Symposium on Advances in Robot Kinematics. pp. 221–229. Springer (2018)Google Scholar
  4. 4.
    Coxeter, H.S.M.: Introduction to geometry, vol. 136. Wiley New York (1969)Google Scholar
  5. 5.
    Daniali, H.M., Zsombor-Murray, P., Angeles, J.: Singularity analysis of planar parallel manipulators. Mechanism and Machine Theory 30(5), 665–678 (1995)CrossRefGoogle Scholar
  6. 6.
    Gosselin, C., Angeles, J.: Singularity analysis of closed-loop kinematic chains. IEEE Journal of Robotics and Automation 6(3), 281–290 (June 1990)CrossRefGoogle Scholar
  7. 7.
    Krantz, S.G., Parks, H.R.: The implicit function theorem: history, theory, and applications. Springer Science & Business Media (2012)Google Scholar
  8. 8.
    Park, F.C., Kim, J.W.: Manipulability of closed kinematic chains. Journal of Mechanical Design 120, 542–548 (1998)CrossRefGoogle Scholar
  9. 9.
    Piipponen, S., Tuomela, J.: Algebraic analysis of kinematics of multibody systems. Mechanical Sciences 4(1), 33–47 (2013)CrossRefGoogle Scholar
  10. 10.
    Selig, J.M.: Geometric fundamentals of robotics. Springer Science & Business Media (2004)Google Scholar
  11. 11.
    Yang, G., Chen, W., Chen, I.M.: A geometrical method for the singularity analysis of 3-RRR planar parallel robots with different actuation schemes. In: Intelligent Robots and Systems, 2002. IEEE/RSJ International Conference on. vol. 3, pp. 2055–2060. IEEE (2002)Google Scholar
  12. 12.
    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)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Victoria University of WellingtonWellingtonNew Zealand

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