Abstract
This paper deals with smooth motion interpolation. Recently, a direct construction algorithm was developed for generating rigid body motions with second order geometric continuity (G 2). The present paper shows how the G 2 spline motion can be used to fulfill the task of motion interpolation by solving the problem of inverse design for the G 2 spline motion. The results are useful for computer graphics, mechanical systems animation, and Cartesian trajectory generation for robot manipulators.
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References
Ahlberg, J., E. Nilson, and J. Walsh, 1967. The Theory of Splines and their Applications. Academic Press.
Arnold, V.I., 1979. Mathematical Methods of Classical Mechanics,Springer-Verlag.
Boehm, W., 1985. Curvature continuous curves and surfaces, Computer Aided Geometric Design, 2: 313–323.
Bottema, O. and B. Roth, 1990. Theoretical Kinematics. Reprinted Dover Pub.
deBoor, C., 1978. A Practical Guide to Splines. Springer-Verlag.
Dimentberg, F.M., 1965, The Screw Calculus and its Application in Mechanics. Translated and reproduced by the Clearinghouse for Federal Scientific and Techinical Information, Springfield, VA. Document No. FTD–HT–23–1632–67.
Farin, G., 1993. Curves and Surfaces for Computer Aided Geometric Design. 3rd ed., Academic Press, San Diego, 334 pp.
Ge, Q.J., and B. Ravani, 1994a. Computer aided geometric design of motion interpolants, to appear in ASME J. of Mechanical Design.
Ge, Q.J., and B. Ravani, 1994b. Geometric construction of Bézier Type Motions, to appear in ASME J. of Mechanical Design.
Ge, Q.J., and B. Ravani, 1993. Computational geometry and motion approximation. In Computational Kinematics, J. Angeles (eds.), Kluwer Academic Publ., Boston, p 229–238.
Latombe, J.-C., 1991. Robot Motion Planning, Kluwer Academic Publ., Boston.
McCarthy, J.M., and B. Ravani. 1986, Differential kinematics of spherical and spatial motions using kinematic mapping. ASME J. of Appl. Mech., 53: 15–22.
McCarthy, J.M., 1990. Introduction to Theoretical Kinematics,MIT Press.
Pletinckx, D., 1989. Quaternion calculus as a basic tool in computer graphics. The Visual Computer, 5: 2–13.
Ravani, B., and B. Roth, 1984. Mappings of spatial kinematics. ASME J. of Mech., Transmissions., and Auto. in Design. 106(3):341–347.
Shoemake, K., 1985. Animating rotation with quaternion curves. ACM Siggraph, 19 (3): 245–254.
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© 1994 Springer Science+Business Media Dordrecht
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Ge, Q.J. (1994). An Inverse Design Algorithm for a G 2 Interpolating Spline Motion. In: Lenarčič, J., Ravani, B. (eds) Advances in Robot Kinematics and Computational Geometry. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8348-0_8
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DOI: https://doi.org/10.1007/978-94-015-8348-0_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4434-1
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