Expression of dual euler parameters using the dual rodrigues partameters and their application to the screw transformation

Gürsoy A. E., Karakiliç I.

Mathematical and Computational Applications, vol.16, no.3, pp.680-689, 2011 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 3
  • Publication Date: 2011
  • Journal Name: Mathematical and Computational Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.680-689
  • Keywords: Dual euler parameters, Kinematics, Screw transformation, Study mapping
  • Dokuz Eylül University Affiliated: Yes

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 R3 (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 R3 [8]. The dual Euler parameters are used in defining the screw transformation in R 3 [8], but originally in this paper these parameters are constructed from the Rodrigues and the dual Rodrigues parameters [15]. © Association for Scientific Research.