Skip to main content
View expanded cover

International Symposium on Advances in Robot Kinematics

ARK 2018: Advances in Robot Kinematics 2018 pp 179–186Cite as

Analysis of Kinematic Singularities for a Serial Redundant Manipulator with 7 DOF

Part of the Springer Proceedings in Advanced Robotics book series (SPAR,volume 8)

Abstract

In this work, the kinematic singularities of serial manipulators with 7 rotational joints are analyzed and their effects on the possible end effector movement are studied. We obtain the numerical kinematic singularities through algebraic varieties and demonstrate this on the kinematically redundant serial manipulator KUKA LBR iiwa. The algebraic equations for determining the variety are derived by taking the determinant of the 6-by-6 submatrix of the Jacobian matrix of the forward kinematics. By using the primary decomposition, the singularities can be decomposed and classified. Further analysis of the kinematic singularities including the inverse kinematics of the redundant manipulator provide us valuable insights. Firstly, there are kinematic singularities where the inverse kinematics has no effect on the self-motion and cannot be used to avoid obstacles. Secondly, there are kinematic singularities, which lead to a single closed-loop connection with the serial redundant manipulator, so that a kinematotropic mechanism is achieved.

Keywords

  • Kinematotropic mechanism
  • Computational algebraic geometry
  • Primary decomposition

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-93188-3_21
  • Chapter length: 8 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   189.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-93188-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   249.99
Price excludes VAT (USA)
Hardcover Book
USD   249.99
Price excludes VAT (USA)
Learn about institutional subscriptions
Fig. 1.

References

  1. Bongardt, B.: Inverse kinematics of anthropomorphic arms yielding eight coinciding circles. In: Computational Kinematics, pp. 525–534. Springer (2018)

    Google Scholar 

  2. Denavit, J., Hartenberg, R.S.: A kinematic notation for lower-pair mechanisms based on matrices. Trans. ASME J. Appl. Mech. 22, 215–221 (1955)

    MathSciNet  MATH  Google Scholar 

  3. Faria, C., Ferreira, F., Erlhagen, W., Monteiro, S., Bicho, E.: Position-based kinematics for 7-dof serial manipulators with global configuration control, joint limit and singularity avoidance. Mech. Mach. Theory 121, 317–334 (2018)

    CrossRef  Google Scholar 

  4. Galletti, C., Fanghella, P.: Single-loop kinematotropic mechanisms. Mech. Mach. Theory 36(6), 743–761 (2001)

    MathSciNet  CrossRef  Google Scholar 

  5. Hayes, M.J.D., Husty, H., Zsombor-Murray, P.J.: Singular configurations of wrist-partitioned 6R serial robots: a geometric perspective for users. Trans. Can. Soc. Mech. Eng. 26, 41–56 (2002)

    CrossRef  Google Scholar 

  6. Hegedüs, G., Schicho, J., Schröcker, H.-P.: Factorization of rational curves in the study quadric. Mech. Mach. Theory 69, 142–152 (2013)

    CrossRef  Google Scholar 

  7. Manfred, L.H., Pfurner, M., Schröcker, H.-P.: A new and efficient algorithm for the inverse kinematics of a general serial 6R manipulator. Mech. Mach. Theory 42(1), 66–81 (2007)

    MathSciNet  CrossRef  Google Scholar 

  8. Manfred, L.H., Schröcker, H.-P.: Algebraic geometry and kinematics. In: Ioannis, Z.E., Sottile, F., Theobald, T. (eds.) Nonlinear Computational Geometry, The IMA Volumes in Mathematics and its Applications, vol. 151, pp. 85–107. Springer (2010)

    Google Scholar 

  9. Karger, A.: Singularity analysis of serial robot manipulators. ASME J. Mech. Des. 118, 505–525 (1996)

    Google Scholar 

  10. Kong, X., Pfurner, M.: Type synthesis and reconfiguration analysis of a class of variable-dof single-loop mechanisms. Mech. Mach. Theory 85, 116–128 (2015)

    CrossRef  Google Scholar 

  11. Li, Z., Schicho, J.: A technique for deriving equational conditions on the Denavit-Hartenberg parameters of 6R linkages that are necessary for movability. Mech. Mach. Theory 94, 1–8 (2015)

    CrossRef  Google Scholar 

  12. Müller, A., Piipponen, S.: On regular kinematotropies. In: Proceedings of the 14th World Congress in Mechanism and Machine Science, Taipei, Taiwan (2015)

    Google Scholar 

  13. Pfurner, M., Kong, X.: Algebraic analysis of a new variable-dof 7R mechanism. In: New Trends in Mechanism and Machine Science, pp. 71–79. Springer (2017)

    Google Scholar 

  14. Wohlhart, K.; Kinematotropic linkages. In: Recent Advances in Robot Kinematics, pp. 359–368 (1996)

    CrossRef  Google Scholar 

Download references

Acknowledgements

This research was funded by the Austrian Ministry for Transport, Innovation and Technology (BMVIT) within the framework of the sponsorship agreement formed for 2015–2018 under the project RedRobCo.

Author information

Authors and Affiliations

  1. Institute for Robotics and Mechatronics, JOANNEUM RESEARCH, Lakeside B08a, 9020, Klagenfurt, Austria

    Zijia Li, Mathias Brandstötter & Michael Hofbaur

Authors
  1. Zijia Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mathias Brandstötter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Hofbaur
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mathias Brandstötter .

Editor information

Editors and Affiliations

  1. J. Stefan Institute, Ljubljana, Slovenia

    Jadran Lenarcic

  2. Department of Industrial Engineering, University of Bologna, Bologna, Italy

    Prof. Vincenzo Parenti-Castelli

Rights and permissions

Reprints and Permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Li, Z., Brandstötter, M., Hofbaur, M. (2019). Analysis of Kinematic Singularities for a Serial Redundant Manipulator with 7 DOF. In: Lenarcic, J., Parenti-Castelli, V. (eds) Advances in Robot Kinematics 2018. ARK 2018. Springer Proceedings in Advanced Robotics, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-93188-3_21

Download citation