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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2011, 16(3), 680-689; https://doi.org/10.3390/mca16030680

Expression of Dual Euler Parameters Using the Dual Rodrigues Parameters and Their Application to the Screw Transformation

1
Department of Mathematics, Istanbul Technical University, Maslak 34469, Istanbul,Turkey
2
Department of Mathematics, Faculty of Sciences, University of Dokuz Eylül, 35140 Buca, İzmir, Turkey
*
Authors to whom correspondence should be addressed.
Published: 1 December 2011
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Abstract

Dual numbers and dual vectors are widely used in spatial kinematics [3,5- 15,18]. Plücker line coordinates of a straight line can be represented by a dual unit vector located at the dual unit sphere (DUS). By this way, the trajectory of the screw axis of a rigid body in 3 R (the real three space) corresponds to a dual curve on the DUS. This correspondence is done through Study Mapping [8,9]. Conversely a dual curve on DUS obtained from the rotations of the DUS represents a rigid body motion in 3 R [8]. The dual Euler parameters are used in defining the screw transformation in 3 R [8], but originally in this paper these parameters are constructed from the Rodrigues and the dual Rodrigues parameters [15].
Keywords: Kinematics; Study Mapping; Dual Euler Parameters; Screw Transformation Kinematics; Study Mapping; Dual Euler Parameters; Screw Transformation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Gürsoy, A.E.; Karakılıç, İ. Expression of Dual Euler Parameters Using the Dual Rodrigues Parameters and Their Application to the Screw Transformation. Math. Comput. Appl. 2011, 16, 680-689.

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