On the Metrics of Rigid Body Displacements for Infinite and Finite Bodies

[+] Author and Article Information
J. M. R. Martinez

Departamento de Ingeniería Mecánica, Instituto Tecnológico de Celaya Av. Tecnológico 2002, 38000 Celaya, Gto. México

J. Duffy

Center for Intelligent Machines and Robotics, Department of Mechanical Engineering, University of Florida, Gainesville, FL 32611

J. Mech. Des 117(1), 41-47 (Mar 01, 1995) (7 pages) doi:10.1115/1.2826115 History: Received August 01, 1993; Revised July 01, 1994; Online January 25, 2008


This paper presents a critical analysis of the metric of rigid body displacements obtained from the so-called kinematic mapping. It is shown that this metric is not suitable for finite rigid bodies. The paper also addresses the metrics obtained for the planar group, as it can be regarded as a subgroup of the group of all rigid body displacements, which is denoted here as the Euclidean group. Finally, the paper proposes some metrics for the set of spatial and planar displacements for a finite rigid body, undergoing a finite displacement.

Copyright © 1995 by The American Society of Mechanical Engineers
Topics: Displacement
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