Points, Lines, Screws and Planes in Dual Quaternions Kinematics

Quaternions and dual quaternions are interesting elements which are being used to robot kinematics over five decades. They arise from Clifford algebras as many isomorphisms. In this chapter we offer representations to points, vectors, lines, screws and planes in dual quaternions coordinates, allowing a huge possibilities to solve problems, especially robot kinematics. No Clifford algebra is necessary, we will use only quaternions units. The displacement of the given elements are found in terms of dual quaternions algebra. For all these elements we must define the right dual quaternions conjugation and operations to handle with. Also, the principle of transference now is not sufficient, as we will explain into the chapter. Examples are presented to show the applicability of our results.

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