LIE-ALGEBRAS, MODULES, DUAL QUATERNIONS AND ALGEBRAIC METHODS IN KINEMATICS

A systematic coordinate-free exposition of the different algebraic operations in the set of infinitesimal displacements (screws) and their relations with finite displacements is developed. Six basic operations generate several algebraic structures, in particular Lie algebra and module over the dual number ring endowed with a dual valued inner product. An extension of Veldkamp's theorem (different from the one proposed by Prakash Agrawal) and an intrinsic new definition of dual quaternions are given. The following examples show the efficiency of algebraic methods in the deduction of basic results by very short proofs.