Skip to main content
SpringerLink
Log in
Book cover

Advances in Robot Kinematics: Motion in Man and Machine pp 377–384Cite as

Geometric Interpolation by Quartic Rational Spline Motions

  • Conference paper
  • First Online:

  • 3360 Accesses

Abstract

We discuss piecewise rational motions with first order geometric continuity. In addition we describe an interpolation scheme generating rational spline motions of degree four matching given positions which are partially complemented by associated tangent information. As the main advantage of using geometric interpolation, it makes it possible to deal successfully with the unequal distribution of degrees of freedom between the trajectory of the origin and the rotation part of the motion.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Mørken, K., Scherer, K.: A general framework for high-accuracy parametric interpolation. Math. Comp., 66(217), 237–260 (1997).

    Article  MathSciNet  Google Scholar 

  2. de Boor, C., Höllig, K., Sabin, M.: High accuracy geometric Hermite interpolation. Comput. Aided Geom. Design, 4(4), 269–278 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  3. Hoschek, J., Lasser D.: Fundamentals of Computer Aided Geometric Design. AK Peters, Wellesley, MA (1993).

    MATH  Google Scholar 

  4. Schröcker, H.-P., Jüttler, B.: Motion interpolation with Bennett biarcs. In Kecskemethy, A., Müller, A. (Eds.), Proc. Computational Kinematics A. Springer, pp. 101–108 (2009).

    Chapter  Google Scholar 

  5. Bottema, O., Roth, B.: Theoretical Kinematics. Dover (1990).

    MATH  Google Scholar 

  6. Jüttler, B., Wagner, M.G.: Kinematics and animation. In: G. Farin, J. Hoschek, and M.-S. Kim (Eds.), Handbook of Computer Aided Geometric Design, pp. 723–748. Elsevier, Amsterdam (2002).

    Chapter  Google Scholar 

  7. Röschel, O.: Rational motion design – A survey. Comput. Aided Design 30(3), 169–178 (1998).

    Article  MATH  Google Scholar 

  8. Rath, W.: A kinematic mapping for projective and affine motions and some applications. In: Dillen, F. et al. (Eds.), Geometry and topology of submanifolds, VIII. World Scientific, pp. 292–301 (1996).

    Google Scholar 

  9. Horsch, T., Jüttler, B.: Cartesian spline interpolation for industrial robots. Comput. Aided Design, 30, 217–224 (1998).

    Article  MATH  Google Scholar 

  10. Mørken, K.: Parametric interpolation by quadratic polynomials in the plane. In: Mathematical Methods for Curves and Surfaces. Vanderbilt Univ. Press, Nashville, pp. 385–402 (1995).

    Google Scholar 

  11. Kozak, J., Žagar, E.: On geometric interpolation by polynomial curves. SIAM J. Numer. Anal., 42(3), 953–967 (2004).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Geometry, Johannes Kepler University, Linz, Austria

    B. Jüttler

  2. IMFM and FMF, University of Ljubljana, Ljubljana, Slovenia

    M. Krajnc & E. Žagar

Authors
  1. B. Jüttler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Krajnc
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Žagar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Jüttler .

Editor information

Editors and Affiliations

  1. Inst. J. Stefan, University Ljubljana, Ljubljana, Slovenia

    Jadran Lenarcic

  2. , Aerospace and Mechanical Engineering, University of Notre Dame, Fitzpatrick Hall 365, Notre Dame, 46556-5637, USA

    Michael M. Stanisic

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media B.V.

About this paper

Cite this paper

Jüttler, B., Krajnc, M., Žagar, E. (2010). Geometric Interpolation by Quartic Rational Spline Motions. In: Lenarcic, J., Stanisic, M. (eds) Advances in Robot Kinematics: Motion in Man and Machine. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9262-5_40

Download citation

  • DOI: https://doi.org/10.1007/978-90-481-9262-5_40

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9261-8

  • Online ISBN: 978-90-481-9262-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation