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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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 |
|---|---|
| Publication: | Mechanics of Structures and Machines |
| Publisher: | Taylor and Francis Group |
| 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.ac.in/id/eprint/38933 |
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