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Journal Articles IMA Journal of Mathematical Control and Information Year : 2017

The cross-motion invariant group and its application to kinematics

Abstract

This article presents the cross-motion invariant group—CMI(3)—whose group operation is defined over unit dual quaternions such that rigid motions are cross-motion invariant; that is, the resultant translation does not depend on rotation and vice-versa. We present the main properties of CMI(3) and the differences between this group and the standard group Spin(3) R 3 of unit dual quaternions, as well as the kinematic equations under a sequence of CMI(3) operations. Two numerical examples are presented in order to illustrate the main characteristics of CMI(3).

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Dates and versions

lirmm-01396641 , version 1 (14-11-2016)

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Bruno Vilhena Adorno, Philippe Fraisse. The cross-motion invariant group and its application to kinematics. IMA Journal of Mathematical Control and Information, 2017, 34 (4), pp.1359-1378. ⟨10.1093/imamci/dnw032⟩. ⟨lirmm-01396641⟩
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