Skip to main content

Singularity Distance for Parallel Manipulators of Stewart Gough Type

  • Conference paper
  • First Online:
Advances in Mechanism and Machine Science (IFToMM WC 2019)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 73))

Included in the following conference series:

Abstract

The number of applications of parallel robots, ranging from medical surgery to astronomy, has increased enormously during the last decades due to their advantages of high speed, stiffness, accuracy, load/weight ratio, etc. One of the drawbacks of these parallel robots are their singular configurations, where the manipulator has at least one uncontrollable instantaneous degree of freedom. Furthermore, the actuator forces can become very large, which may result in a breakdown of the mechanism. Therefore singularities have to be avoided. As a consequence the kinematic/robotic community is highly interested in evaluating the singularity closeness, but a geometric meaningful distance measure between a given manipulator configuration and the next singular configuration is still missing. We close this gap for parallel manipulators of Stewart Gough type by introducing such measures. Moreover the favored metric has a clear physical meaning, which is very important for the acceptance of this index by mechanical/constructional engineers.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 429.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 549.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 549.99
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.

Similar content being viewed by others

References

  1. Abbasnejad G, Daniali HM, Kazemi SM (2012) A new approach to determine the maximal singularity-free zone of 3-RPR planar parallel manipulator. Robotica 30(6):1005–1012

    Article  Google Scholar 

  2. Bates DJ, Hauenstein JD, Sommese AJ, Wampler CW (2013) Numerically Solving Polynomial Systems with Bertini. SIAM Books

    Google Scholar 

  3. Chen HY, Pottmann H (1999) Approximation by ruled surfaces. J Comput Appl Math 102(1):143–156

    Article  MathSciNet  Google Scholar 

  4. Husty ML (2009) Non-singular assembly mode change in 3-RPR-parallel manipulators. In: Kecskem´ethy A, Müller A (eds) Computational Kinematics, Springer, pp 51–60

    Google Scholar 

  5. Jiang Q, Gosselin CM (2009) Determination of the maximal singularity-free orientation workspace for the Gough-Stewart platform. Mech Mach Theory 44(6):1281–1293

    Article  Google Scholar 

  6. Kazerounian K, Rastegar J (1992) Object Norms: A Class of Coordinate and Metric Independent Norms for Displacements. In: Kinzel GL (ed) Flexible Mechanisms, Dynamics and Analysis, ASME, pp 271–275

    Google Scholar 

  7. Kilian M, Mitra NJ, Pottmann H (2007) Geometric Modeling in Shape Space. ACM Trans Graph 26(3):64

    Google Scholar 

  8. Li H, Gosselin C, Richard M (2006) Determination of maximal singularity-free zones in the workspace of planar three-degree-of-freedom parallel mechanisms. Mech Mach Theory 41(10):1157–1167

    Article  MathSciNet  Google Scholar 

  9. Li H, Gosselin C, Richard M (2007) Determination of the maximal singularity free zones in the six-dimensional workspace of the general Gough-Stewart platform. Mech Mach Theory 42(4):497–511

    Article  MathSciNet  Google Scholar 

  10. Merlet J-P (1992) Singular Configurations of Parallel Manipulators and Grassmann Geometry. Int J Robot Res 8(5):45–56

    Article  Google Scholar 

  11. Merlet J-P, Gosselin C (2008) Parallel Mechanisms and Robots. In: Siciliano B, Khatib O (eds) Handbook of Robotics, Springer, pp 269–285

    Google Scholar 

  12. Murray RM, Li Z, Sastry SS (1994) A Mathematical Introduction to Robotic Manipulation. CRC Press

    Google Scholar 

  13. Nag A, Reddy V, Agarwal S, Bandyopadhyay S (2016) Identifying singularity-free spheres in the position workspace of semi-regular Stewart platform manipulators. In: Lenarcic J, Merlet J-P (eds) Advances in Robot Kinematics, Springer, pp 421–430

    Google Scholar 

  14. Nawratil G (2009) New Performance Indices for 6-dof UPS and 3-dof RPR Parallel Manipulators. Mech Mach Theory 44(1):208–221

    Article  Google Scholar 

  15. Nawratil G (2017) Point-models for the set of oriented line-elements – a survey. Mech Mach Theory 111:18–134

    Article  Google Scholar 

  16. Park FC (1995) Distance Metrics on the Rigid-Body Motions with Applications to Mechanism Design. ASME J Mech Des 117(1):48–54

    Article  Google Scholar 

  17. Pottmann H, Hofer M, Ravani B (2004) Variational motion design. In: Lenarcic J, Galletti C (eds) On Advances in Robot Kinematics, Kluwer, pp 361–370

    Google Scholar 

  18. Rasoulzadeh A, Nawratil G (2017) Rational Parametrization of Linear Pentapod’s Singularity Variety and the Distance to it. In: Zeghloul S et al (eds) Computational Kinematics, Springer, pp 516–524 (Extended version on arXiv:1701.09107)

    Google Scholar 

  19. Schröcker H-P, Weber MJ (2014) Guaranteed collision detection with toleranced motions. Comput Aided Geom Design 31(7-8):602–612

    Article  MathSciNet  Google Scholar 

  20. ZeinM,Wenger P, Chablat D (2007) Singularity Surfaces andMaximal Singularity- Free Boxes in the Joint Space of Planar 3-RPR Parallel Manipulators. In: Proc of 12th IFToMM World Congress, Besan¸con, France, abs/0705.1409

    Google Scholar 

Download references

Acknowledgments

The author is supported by Grant No. P 30855-N32 of the Austrian Science Fund FWF.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Georg Nawratil .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Nawratil, G. (2019). Singularity Distance for Parallel Manipulators of Stewart Gough Type. In: Uhl, T. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-030-20131-9_26

Download citation

Publish with us

Policies and ethics