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A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

Bandyopadhyay, S and Ghosal, A and Ravani, B (2002) A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions. In: Mechanics of Structures and Machines, 30 (3). pp. 279-307.

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Official URL: http://www.tandfonline.com/doi/abs/10.1081/SME-120...

Abstract

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Taylor and Francis Group.
Keywords: Instantaneous kinematics;Dual vector;Dual matrix;Geodesic
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 04 Aug 2011 06:12
Last Modified: 04 Aug 2011 06:12
URI: http://eprints.iisc.ernet.in/id/eprint/38933

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