The Dual Rodrigues Parameters

Year 2010, Volume: 2 Issue: 2, 23 - 32, 01.06.2010

İ. Karakılıç

Abstract

The development of Rodrigues parameters in the first half of 19th century has attracted much attention in the field of theoretical kinematics. The importance of the Rodrigues formulae depends on the use of the tangent of the half rotation angle being integrated with the components of the rotation axis. In this paper Rodrigues parameters of the dual spherical motion are obtained, which are called the dual Rodrigues parameters. The dual Rodrigues parameters contain the rotation angle and the distance parameter of the straight lines (the shortest distance between the straight lines) of the corresponding spatial motion

Keywords

Study mapping, Dual spherical motion, Rotation angle, Dual Rodrigues parameters

References

• W. K. Clifford Proc. London Mathematic Society, 4, 1873, p. 381.
• F. M. Dimentberg, The Screw Calculus and its Applications in Mechanics, (Izdat, “Nauka”, Moscow, USSR, 1965) English translation: AD680993, Clearinghouse for Federal and Sciencetific Information, Virginia).
• E. Study, Die Geometrie der Dynamen, Leibzig, 1901.
• W.L. Edge, The Theory of Ruled Surfaces, Cambridge University Press, Cambridge, 1931.
• V. Hlavaty, Differential Line Geometry, P. Nothoft Ltd., Groningen, 1953.
• E. A. weis, Einführong in die Linengeometri und Kinematic, Leipzig, Berlin, 1935.
• K. Zidler Linengeometri mit Anwendungen, 2 volumes, De Gruyter, Berlin, 1902.
• J. M. McCarthy, An Introduction to Theoretical Kinematics, The MIT Press, Cambridge.
• O. Bottema, B. Roth, Theoretical Kinematics, North Holland, Amsterdam, 1979.
• J. M. McCarthy, B. Roth, The Curvature Theory of Line Trajectories in Spatial Kinematics, ASME Journal of Mechanical Design 103, 4, 1981.
• Y. Kirson, Curvature Theory in Space Kinematics, PhD dissertation 140, University of California Berkley, 1975.
• G. R. Veldkamp, On the Use of Dual Numbers, Vectors and Matrices in Instantaneous Spatial Kinematics, Mechanism and Machine Theory 11(2), (1976), 141-156.
• Ö. Köse, C. C. Sarıoğlu, B. Karabey, İ. Karakılıç, Kinematic Differential Geometry of a Rigid Body in Spatial Motion Using Dual Vector Calculus: Part II, Applied Mathematics and Computation 182 (2006) 333-358. [14] H. Potmann, J. Wallner, Computational line geometry, Springer-Verlag , Berlin, 2001.
• I. S. Fischer, Dual-Number Methods in Kinematics, Statics and Dynamics, CRC Press LLC. Florida, 1999.