Kinematic Registration in 3D Using the 2D Reuleaux Method

[+] Author and Article Information
Johannes K. Eberharter

 Am Marienbrunnen 343, A-6290 Mayrhofen, Austriahannes@eberharter.us

Bahram Ravani

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

J. Mech. Des 128(2), 349-355 (Jul 01, 2005) (7 pages) doi:10.1115/1.2159027 History: Received August 27, 2004; Revised July 01, 2005

This paper presents a method for kinematic registration in three dimensions using a classical technique from two-dimensional kinematics, namely the Reuleaux method. In three dimensions the kinematic registration problem involves reconstruction of a spatial displacement from data on a minimum of three homologous points at two finitely separated positions of a rigid body. When more than the minimum number of homologous points are specified or when errors in specification of these points are considered, the problem becomes an over determined approximation problem. A computational geometric method is presented, resulting in a linear solution of the over determined system. The results have applications in robotics, manufacturing, and biomedical imaging. The paper considers the kinematic registration when minimal, over-determined, infinitesimal, and perturbed sets of homologous point data are given.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 6

A geometrical interpretation using line geometry

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Figure 7

Example 1: rotation vector

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Figure 8

Example 1: registration

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Figure 9

Example 2: rotation vector

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Figure 10

Example 2: registration

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Figure 11

Bisecting linear line complex

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Figure 12

The linear line complex of path normals

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Figure 1

Reuleaux’s method

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Figure 2

Midpoints Mi and their projections Mip with intersection point I

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Figure 3

Decomposition of helical velocity vectors

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Figure 4

Points Pi and their projections Pip, velocity vectors vi and their projections vip with intersection point I

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Figure 5

Vectors and their relations




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