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].
Highlights
The dual representation of a line is the Plücker vector written as a dual unit vector [9]
When a dual vector xis rotated to the dual vector x in dual unit sphere (DUS), this movement corresponds to a screw transformation in R3
This paper discusses the usage of dual Euler parameters for the transformations of screws in R3 and these parameters are defined in terms of the Rodrigues and the dual Rodrigues parameters
Summary
The dual representation of a line is the Plücker vector written as a dual unit vector [9]. The dual Euler parameters are used for defining the transformation of screws in R3. When a dual vector xis rotated to the dual vector x in DUS, this movement corresponds to a screw transformation in R3. This transformation can be given by the dual Euler parameters. This paper discusses the usage of dual Euler parameters for the transformations of screws in R3 and these parameters are defined in terms of the Rodrigues and the dual Rodrigues parameters. Euler parameters c0 , c 1, c2 , c3 and the corresponding spatial displacement is given by the dual vector w w v
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