Skip to main content

Detection and Avoidance of Singularities in Parallel Kinematic Machines

  • Chapter
Robotic Systems for Handling and Assembly

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 67))

Abstract

In this work a geometrical and a physically based method for the detection of singularities are presented, which provide information about the distance of a given position to singularities. The integration of this singularity detection into a robot controller is presented and validated by experimental results. Based on these results a path planning algorithm that avoids singularities is developed. It uses a particle based randomizing scheme for finding a path within the workspace to which a virtual potential field is applied. The HexaII demonstrator of the Collaborative Research Center 562 serves as a validation platform for this algorithm. The singularity avoidance path planner is integrated into the real-time context of the control application RCA562, from which experimental results are presented.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gosselin, C.M., Wang, J.G.: Singularity loci of planar parallel manipulators with revolute actuators. Robotics and Autonomous Systems 21(4), 377–398 (1997)

    Article  Google Scholar 

  2. Huang, Z., Chen, L.H., Li, Y.W.: The singularity principle and property of stewart parallel manipulator. Journal of Robotic Systems 20(4), 163–176 (2003)

    Article  MATH  Google Scholar 

  3. Horin, P.B., Shoham, M.: A class of parallel robots practically free of parallel singularities. Journal of Mechanical Design 130(5) (2008)

    Google Scholar 

  4. Choudhury, P., Ghosal, A.: Singularity and controllability analysis of parallel manipulators and closed-loop mechanisms. Mechanism and Machine Theorie 35(10), 1455–1479 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ball, R.S.: A Treatise on the Theory of Screws. Cambridge University Press, Cambridge (1900)

    Google Scholar 

  6. Hunt, K.H.: Don’t cross-thread the screw. In: Proceedings of a Symposium Commemorating the Legacy, Works, and Life of Sir Robert Stawell Ball upon the 100th Anniversary of A Treatise on the Theory of Screws, pp. 1–36 (2000)

    Google Scholar 

  7. Hunt, K.H.: Kinematic Geometry of Mechanisms. Oxford University Press, New York (1978)

    MATH  Google Scholar 

  8. Poinsot, L.: Sur la composition des moments et la composition des aires. Éc Polyt Paris 6, 182–205 (1806)

    Google Scholar 

  9. Bier, C.: Geometrische und physikalische Analyse von Singularitüten bei Parallelstrukturen. Ph.D. thesis, Fakultät für Maschinenbau, TU Braunschweig, Vulkan-Verlag (2006)

    Google Scholar 

  10. Sciavicco, L., Siciliano, B.: Modeling and Control of Robot Manipulators. Springer, London (2000)

    Google Scholar 

  11. Tsai, L.-W.: Robot Analysis - The Mechanics of Serial and Parallel Manipulators. John Wiley and Sons Inc., New York (1999)

    Google Scholar 

  12. Gosselin, C., Angeles, J.: Singularity analysis of closed-loop kinematic chains. IEEE Transactions on Robotics and Automation 6(3), 281–290 (1990)

    Article  Google Scholar 

  13. Simaan, N., Shoham, M.: Singularity analysis of class of composite serial in-parallel robots. IEEE Transactions on Robotics and Automation 17(3), 301–311 (2001)

    Article  Google Scholar 

  14. Kozak, K., Voglewede, P.A., Ebert-Uphoff, I., Singhose, W.: Concept paper: On the significance of the lowest linearized natural frequency of a parallel manipulator as a performance measure for concurrent design. In: Proceedings of the Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Quebec City (Kanada), pp. 112–118 (2002)

    Google Scholar 

  15. Yoshikawa, T.: Manipulability of robotic mechanisms. The International Journal of Robotics Research 4(2), 3–9 (1985)

    Article  MathSciNet  Google Scholar 

  16. Lee, J., Duffy, J.: The optimum quality index for some spatial in-parallel devices. In: Proceedings of Conference on Recent Advances in Robotics, Miami, USA, pp. 1–19 (1997)

    Google Scholar 

  17. Angeles, J., López-Cajún, C.S.: Kinematic isotropy and conditioning index of serial robotic manipulators. The International Journal of Robotics Research 11(6), 560–571 (1992)

    Article  Google Scholar 

  18. Gosselin, C.: Stiffness mapping for parallel manipulators. Transactions on Robotics and Automation 6(3), 377–382 (1990)

    Article  Google Scholar 

  19. Doty, K.L., Melchiorri, C., Schwartz, E.M., Bonivento, C.: Robot manipulability. IEEE Transactions on Robotics and Automation 11(3), 462–468 (1995)

    Article  Google Scholar 

  20. Duffy, J.: The fallacy of modern hybrid control theory that is based on orthogonal complements of twist and wrench spaces. Journal of Robotic Systems 7(2), 139–144 (1990)

    Article  MathSciNet  Google Scholar 

  21. Lipkin, H., Duffy, J.: Hybrid twist and wrench control for a robot manipulator. Journal of Mechanisms, Transmissions, and Automation in Design 110, 138–144 (1988)

    Article  Google Scholar 

  22. Zanganeh, K.E., Angeles, J.: Kinematic isotropy and optimum design of parallel manipulators. The International Journal of Robotics Research 16(2), 185–197 (1997)

    Article  Google Scholar 

  23. Hesselbach, J., Bier, C., Campos, A., Löwe, H.: Direct kinematic singularity detection of a hexa parallel robot. In: Proceedings of IEEE International Conference of Intelligent Robots and Systems, Edmonton (Kanada), pp. 3249–3254 (2005)

    Google Scholar 

  24. Bier, C., Queiroz, E., Campos, A., Maass, J., Guenther, R.: Direct singularity avoidance strategy for the hexa parallel robot. In: 18th International Congress of Mechanical Engineering (2005)

    Google Scholar 

  25. Maaß, J.: Ein Beitrag zur Steuerungstechnik für parallelkinematische Roboter in der Montage. Ph.D. thesis, Fakultät für Maschinenbau, TU Braunschweig, Vulkan Verlag, 2009 (in german)

    Google Scholar 

  26. Maaß, J., Kolbus, M., Bier, C., Wobbe, F., Schuhmacher, W., Raatz, A., Hesselbach, J.: Advances in motion control for high-performance parallel robots. In: Robotic Systems for Handling and Automation, pp. 285–296 (2008)

    Google Scholar 

  27. Dietrich, F., Maaß, J., Raatz, A., Hesselbach, J.: RCA562: Control Architecture for Parallel Kinematic Robots. In: Schütz, D., Wahl, F.M. (eds.) Robotic Systems for Handling and Assembly. STAR, vol. 67, pp. 315–331. Springer, Heidelberg (2010)

    Google Scholar 

  28. Brueckner, S.: Return from the Ant. Ph.D. thesis, Humboldt-Universitat Berlin (2000)

    Google Scholar 

  29. Hsiao, Y., Chuang, C., Chien, C.: Ant colony optimization for best path planning. In: IEEE International Symposium on Communications and Information Technology, ISCIT 2004, vol. 1 (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Dietrich, F., Maaß, J., Bier, C., Pietsch, I., Raatz, A., Hesselbach, J. (2010). Detection and Avoidance of Singularities in Parallel Kinematic Machines. In: Schütz, D., Wahl, F.M. (eds) Robotic Systems for Handling and Assembly. Springer Tracts in Advanced Robotics, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16785-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16785-0_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16784-3

  • Online ISBN: 978-3-642-16785-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics