This paper presents a vectorial parameterization of motion that generalizes the vectorial parameterization of rotation. The Pl¨ucker coordinates of an arbitrary material line of a rigid body subjected to a screw motion are shown to transform by the action of a motion tensor. The proposed vectorial parameterization completely describes an arbitrary motion by means of two vectors that constitute an eigenvector of the motion tensor associated with its positive unit eigenvalue. The first vector is conveniently selected as the vectorial parameterization of rotation, and the second is related to the displacement of a point of the rigid body. A complete description of motion is presented in terms of a generic vectorial parameterization. Relevant formulæ for specific parameterizations of this class can then be easily obtained. More details are given for three parameterizations that present desirable properties: the Euler, Cayley-Gibbs-Rodrigues, and Wiener-Milenkovic motion parameters.

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