Screw Motion via Matrix Algebra in Three-Dimensional Generalized Space

This paper aims to investigate the screw motion in generalized space. For this purpose, firstly, the change in the screw coordinates is analyzed according to the motion of the reference frames. Moreover, the special cases of this change, such as pure rotation and translation, are discussed. Matrix multiplication and the properties of dual numbers are used to obtain dual orthogonal matrices, which are used to simplify the manipulation of screw motion in generalized space. In addition, the dual angular velocity matrix is calculated and shows that the exponential of this matrix can represent the screw displacement in the generalized space. Finally, to support our results, we give two examples of screw motion, the rotation part of which is elliptical and hyperbolic.

Automated summary

This paper investigates the screw motion in generalized space by analyzing the change in screw coordinates and using dual orthogonal matrices. The exponential of the dual angular velocity matrix is shown to represent screw displacement in generalized space.