Rational Bézier Line-Symmetric Motions

[+] Author and Article Information
Shutian Li

Metalsoft, Inc., 2130 South Yale Street, Santa Ana, CA 92704

Q. J. Ge

Department of Mechanical Engineering, State University of New York, Stony Brook, NY 11794-2300

J. Mech. Des 127(2), 222-226 (Mar 25, 2005) (5 pages) doi:10.1115/1.1798251 History: Received March 19, 2002; Revised March 01, 2004; Online March 25, 2005
Copyright © 2005 by ASME
Topics: Motion
Your Session has timed out. Please sign back in to continue.


Ge, Q. J., and Ravani, B., 1991, “Computer Aided Geometric Design of Motion Interpolants,” ASME Publ. DE-Vol. 3202:33-41, Advances in Design Automation 1991; ASME J. Mech. Des., 116 , pp. 756–762.
Ge,  Q. J., and Ravani,  B., 1994a, “Geometric Construction of Bézier Motions,” ASME J. Mech. Des., 116, pp. 756–762.
Barr,  A., Curin,  B., Gabriel,  S., and Hughes,  J., 1992, “Smooth Interpolation of Orientations With Angular Velocity Constraints Using Quaternions,” Comput. Graphics, 26, pp. 313–320.
Park,  F. C., and Ravani,  B., 1995, “Bézier Curves on Riemannian Manifolds and Lie Groups With Kinematic Applications,” ASME J. Mech. Des., 117, pp. 35–40.
Kim,  K.-S., and Nam,  K.-W., 1995, “Interpolating Solid Orientations With Circular Blending Quaternion Curves,” Comput.-Aided Des., 27, pp. 385–398.
Etzel, K., and McCarthy, J. M., 1996, “Spatial Motion Interpolation in an Image Space of SO(4),” Proc. 1996 ASME Mechanisms Conference, Paper Number 96-DETC/MECH-1164.
Jüttler,  B., and Wagner,  M., 1996, “Computer Aided Design With Spatial Rational B-Spline Motions,” ASME J. Mech. Des., 118, pp. 193–201.
Jüttler,  B., and Wagner,  M., 1999, “Rational Motion-Based Surface Generation,” Comput.-Aided Des., 31, pp. 203–213.
Zefran,  M., and Kumar,  V., 1998, “Rigid Body Motion Interpolation,” Comput.-Aided Des., 30, pp. 179–189.
Srinivasan,  L. N., and Ge,  Q. J., 1996, “Parametrically Continuous and Smooth Motion Interpolation,” ASME J. Mech. Des., 118, pp. 494–498.
Srinivasan,  L., and Ge,  Q. J., 1998, “Fine Tuning of Rational B-Spline Motions,” ASME J. Mech. Des., 120, pp. 46–51.
Röschel,  O., 1998, “Rational Motion Design—A Survey,” Comput.-Aided Des., 30, pp. 169–178.
Ge,  Q. J., and Sirchia,  M., 1999, “Computer Aided Geometric Design of Two-Parameter Freeform Motions,” ASME J. Mech. Des., 121, pp. 502–506.
Ge,  Q. J., and Larochelle,  P., 1999, “Algebraic Motion Approximation With NURBS Motions and Its Application to Spherical Mechanism Synthesis,” ASME J. Mech. Des., 121, pp. 529–532.
Xia,  J., and Ge,  Q. J., 2001, “On the Exact Representation of the Boundary Surfaces of the Swept Volume of a Cylinder Undergoing Rational Bezier and B-Spline Motions,” ASME J. Mech. Des., 123, pp. 261–265.
Study, E., 1903, Die Geometrie der Dynamen, Leipzig.
Klein, F., 1908, Elementary Mathematics From an Advanced Standpoint: Geometry. Translated by E. R. Hedrick and C. A. Noble (1939), Dover, New York.
Krames,  J., 1937, “Zur Aufrechten Ellipsenbewegung des Raumes (Über Symmetrische Schotungen III),” Monatshefte Math. Phys.,46, pp. 38–50.
Yang, A. T., 1964, “Application of Quaternion Algebra and Dual Numbers to the Analysis of Spatial Mechanisms,” Ph.D. dissertation, Columbia University, UMI-No. 64-2803.
Woo,  L., and Freudenstein,  F., 1970, “Application of Line Geometry to Theoretical Kinematics and the Kinematic Analysis of Mechanical Systems,” J. Mech., 5, pp. 417–460.
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North Holland, Amsterdam.
Röschel,  O., 1985, “Rationale Räumliche Zwangläufe Vierter Ordnung,” Sitzungsber. Akad. Wiss. Wien, Math.-Naturwiss. Kl., Abt. 2A, 194, pp. 185–202.
Hunt, K., 1990, Kinematic Geometry of Mechanisms, Oxford University Press, New York.
Ravani,  B., and Wang,  J., 1991, “Computer Aided Geometric Design of Line Constructs,” ASME J. Mech. Des., 113, pp. 363–371.
Ge, Q. J., and Ravani, B., 1998, “Geometric Design of Rational Bezier Line Congruences and Ruled Surfaces Using Line Geometry,” Computing Supplement 13: Geometric Modeling, edited by G. Farin, H. Beiri, G. Brunnett, and T. DeRose, Springer, Berlin, pp. 101–120.
Dooley, J. R., and Ravani, B., 1994, “Geometric Analysis of Spatial Rigid Body Dynamics With Multiple Frictional Contacts,” Advances in Robot Kinematics and Computational Geometry, edited by J. Lenarcic and B. Ravani, Kluwer Academic, Dordrechtt, pp. 71–80.
Sprott, K., and Ravani, B., 1997, “Ruled Surfaces, Lie Groups, and Mesh Generation,” Proc. 1997 Design Automation Conference, Paper no. DETC97/DAC-3996, Sacramento, CA.
Pottmann, H., and Wallner, J., 2001, Computational Line Geometry, Springer, Berlin.
Ge, Q. J., 1996, “Kinematics-Driven Geometric Modeling: A Framework for Simultaneous Tool-Path Generation and Sculptured Surface Design,” Proc. 1996 IEEE Robotics and Automation Conference, Vol. 2, pp. 1819–1824, Minneapolis, MN, April 1996.
Xia, J., and Ge, Q. J., 2000, “Kinematic Approximation of Ruled Surfaces Using NUEBS Motions of a Cylindrical Cutter,” Proc. 2000 ASME Design Automation Conference, Baltimore, MD, Paper No. DETC2000/DAC-14280.
Piegl,  L. A., and Tiller,  W., 2002, “Biarc Approximation of NURBS,” Comput.-Aided Des., 34, pp. 807–814.
McCarthy, J. M., 1990, Introduction to Theoretical Kinematics, MIT Press, Cambridge, MA.
Ball, R., 1900, A Treatise on the Theory of Screws, Cambridge, University, Press Cambridge.
McCarthy,  J. M., 1986, “Dual Orthogonal Matrices in Manipulator Kinematics,” Int. J. Robot. Res., 5, pp. 43–49.
Ravani, B., 1982, “Kinematic Mappings as Applied to Motion Approximation and Mechanism Synthesis,” Ph.D. dissertation, Stanford University.
Struik, D. J., 1961, Lectures On Classical Differential Geometry, 2nd ed., Addison-Wesley, Reading, MA.
Ravani,  B., and Roth,  B., 1984, “Mappings of Spatial Kinematics,” ASME J. Mech., Trans., Automation, Des.,106, pp. 341–347.


Grahic Jump Location
A screw motion as a rational line-symmetric motion of degree 2
Grahic Jump Location
A Bennet motion with a=b=c=1
Grahic Jump Location
A rational line-symmetric motion of degree 4 with its basic surface



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In