Abstract

Dual numbers are introduced by Clifford in the mid-nineteenth century and they are  systematically applied to  kinematics by Study (1903) and Kotelnikov (1895). Any point  on  the dual unit sphere (DUS) corresponds to a straight line in  QUOTE  (real three space), and vice versa. By this way, there is a one to one correspondence between the dual curves on DUS and the one parameter rigid body motions in  QUOTE  . Using Cayley Mapping (McCarthy, 1990) we get a relation between the dual rotation matrices and the dual skew symmetric matrices. In this  paper, this relation is given by the exponential mapping which can be called the dual  exponential mapping.

Keywords: Kinematics, study mapping, cayley mapping, dual exponential mapping.

Abbreviation

DUS, Dual  unit sphere.