Abstract
In geometric design, rotation minimizing frames of space curves are used for sweep surface modeling. We give a detailed discussion of these motions within the framework of spherical kinematics. In addition we discuss their approximation by rational spline motions. The results are applied to the automatic generation of robot motions from CAD data and to the construction of sweeping surfaces.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bottema, O., and Roth, B. (1979), Theoretical kinematics, North-Holland, Amsterdam.
Farouki, R.T., and Sakkalis, T. (1994), Pythagorean-hodograph space curves, Adv. in Comput. Math., vol. 2, pp. 41–66.
Horsch, Th., and Jüttler, B. (1998), Cartesian spline interpolation for industrial robots, Comput.-Aided. Design, in press.
Jüttler, B., and Wagner, M.G. (1996), Computer Aided Design with Spatial Rational B-Spline Motions, ASME J. of Mech. Design, vol. 118, pp. 193–201.
Klok, F. (1986), Two moving coordinate frames for sweeping along a 3D trajectory, Comput. Aided Geom. Design, vol. 3, pp. 217–229.
Müller, H.R. (1962), Sphärische Kinematik, Deutscher Verlag der Wissenschaften, Berlin.
Nutbourne, A.W., and Martin, R.R. (1988), Differential Geometry Applied to Curve and Surface Design. Vol. 1: Foundations, Ellis Horwood Ltd., Chichester.
Pottmann, H., and Wagner, M.G. (1998), Contributions to Motion Based Surface Design, manuscript.
Wagner, M.G., and Ravani, B. (1997), Curves with Rational Frenet-Serret motion, Comput. Aided Geom. Design, vol. 15, pp. 79–101.
Wang, W., and Joe, B. (1997), Robust computation of the rotation minimizing frame for sweep surface modeling, Comput.-Aided Design, vol. 29, pp. 379–391.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Jüttler, B. (1998). Rotation Minimizing Spherical Motions. In: Lenarčič, J., Husty, M.L. (eds) Advances in Robot Kinematics: Analysis and Control. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9064-8_42
Download citation
DOI: https://doi.org/10.1007/978-94-015-9064-8_42
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5066-3
Online ISBN: 978-94-015-9064-8
eBook Packages: Springer Book Archive