From line geometry to spatial dynamics

One of the most elegant mathematical tools in the motion analysis of multibody systems is the dual vector algebra. Not only the mathematical relationships between the rotational motion and the translational motion of a system may be concisely formulated in the dual vector space, but they also have a simple geometrical representation. This article presents an analysis of the dual vector algebra and its geometric realization. An immediate application of this analysis is the composition of two most relevant quantities in dynamics of multibody systems, the dual velocity and the dual force. It is shown that this composition is not only coordinate free but it is also referential free