Spatial motion interpolation in an image space of so(4)

Proceedings of the ASME Design Engineering Technical Conference

Volumn 2B-1996, Issue , 1996, Pages

  Etzel, Karl R ^a   Michael McCarthy, J ^a  

^a University of California at Irvine   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MACHINE DESIGN;

DUAL QUATERNION; FOUR-DIMENSIONAL SPACE; MECHANICAL SYSTEMS; QUATERNION INTERPOLATION; SMOOTH MOVEMENT; SPATIAL DISPLACEMENT; SPATIAL MECHANISM; SPATIAL MOTIONS;

INTERPOLATION;

EID: 0007625466     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/96-DETC/MECH-1164     Document Type: Conference Paper

References (21)

1. Bottema, O. and Roth, B., 1979 Theoretical Kinematics, Dover Publications, Inc., New York, 558pp
2. Cli-ord, W.K., 1873, "Preliminary Sketch of Biquaternions," In Mathematical papers (edited by R. Tucker), Macmillan, London, 1882, 658pp
3. Coxeter, H.S.M., 1957, Non-Euclidean Geometry, 3rd ed., University of Toronto Press, Toronto, 309pp
4. Curtis, M.L., 1984, Matrix Groups, Springer-Verlag, New York, NY
5. deCasteljau, F., 1963 "Outillage m-ethodes calcul.", Andr-e Citröen Automobiles SA, Paris
6. Etzel, K.R., and McCarthy, J.M., 1995 "A Metric on Spatial Displacements Using Biquaternions on SO(4)", IEEE Robotics and Automation Conference, Minneapolis, MN, April 1996
7. Etzel, K. R., 1996, Biquaternion Theory and Applications to Spatial Kinematics, M.S. Thesis, University of California at Irvine
8. Ge, Q. J., 1994, "On the Matrix Algebra Realization of the Theory of Biquaternions," Proc. of the 1994 ASME Mechanisms Conference, DE-Vol.70:425-432
9. Ge, Q. J. and Ravani, B., 1994 "Geometric Construction of B-ezier Motions", Journal of Mechanical Design, 116:749-755
10. Gerald, C. F. and Wheatley, P. O., 1989 Applied Numerical Analysis, Addison-Wesley Publishing Company, Reading, MA, 679pp
11. Hamilton, W. R., 1860, Elements of Quaternions, Dublin. Repreinted by Chelsea Pub., New York, 1969
12. Johnstone, J. and Williams, J., 1995 "Rational Control of Orientation for Animation", Proceedings of Graphics Interface, pp. 179-186
13. Juttler, B., 1994, "Visualization of Moving Objects Usinf Dual Quaternion Curves", Computers & Graphics, Vol. 18, pp. 315-326
14. McCarthy, J. M., 1983, "Planar and Spatial Rigid Motion as Special Cases of Spherical and 3-Spherical Motion," Journal of Mech., Trans., and Auto. in Design, 105(3):569-575
15. McCarthy, J.M., 1990, An Introduction to Theoretical Kinematics, MIT Press, Cambridge, MA, 130pp
16. Park, F.C and Ravani, B., 1995, "B-ezier Curves on Riemannian Manifolds and Lie Groups with Kinematics Applications", Proc. of the 1994 ASME Mechanisms Conference, DE-Vol.70:15-20
17. Paul, R., 1981, Robot Manipulators, MIT Press, Cambridge, MA
18. Pletinckx, D., 1989 "Quaternion Calculus as a Basic Tool in Computer Graphics," The Visual Computer, Vol. 5, pp.2-13
19. Ravani, B. and Roth, B., 1984 "Mappings of Spatial kinematics", ASME Journal of Mech., Trans., and Auto.in Design, 106:341-347, September 1984
20. Shoemake, K., 1985 "Animating Rotation with Quaternion Curves", ACM Siggraph, Vol. 19, Number 3, pp. 245-254
21. Study, E., Die Geometrie der Dynamen, Leipzig, 1903, 437 pp