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
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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)
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Not optimized and optimized somen motion using the Chaikin algorithm (The darkblue lines represent the motion with optimized projection)




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