Local Metrics for Rigid Body Displacements

[+] Author and Article Information
Johannes K. Eberharter, Bahram Ravani

Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA 95616

J. Mech. Des 126(5), 805-812 (Oct 28, 2004) (8 pages) doi:10.1115/1.1767816 History: Received August 01, 2003; Revised February 01, 2004; Online October 28, 2004
Copyright © 2004 by ASME
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Grahic Jump Location
A simplistic schematic of the principal hyperbolic shape of Study’s quadric, with its three-dimensional linear subspaces—generators, and the excluded pseudo-generator 3.
Grahic Jump Location
Optimized stereographic projection at the example of a sphere
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New protosoma Q0, minimizing the helical parameter φi
Grahic Jump Location
Definition of the metric with a stereographic projection, and the Euclidean norm, at the example of a sphere
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The metric is not right-invariant
Grahic Jump Location
Without optimization (Qi,i=1,[[ellipsis]]4 are given somen, Q̄0 is the protosoma)
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With optimization (Q0 is the new protosoma after optimization)
Grahic Jump Location
Not optimized and optimized somen motion using the Chaikin algorithm (The darkblue lines represent the motion with optimized projection)




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