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A Novel Approach to Algebraic Fitting of a Pencil of Quadrics for Planar 4R Motion Synthesis

[+] Author Affiliations
Q. J. Ge, Ping Zhao, Anurag Purwar, Xiangyun Li

Stony Brook University, Stony Brook, NY

Paper No. DETC2012-71190, pp. 1587-1596; 10 pages
doi:10.1115/DETC2012-71190
From:
  • ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B
  • Chicago, Illinois, USA, August 12–15, 2012
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4503-5
  • Copyright © 2012 by ASME

abstract

The use of the image space of planar displacements for planar motion approximation is a well studied subject. While the constraint manifolds associated with planar four-bar linkages are algebraic, geometric (or normal) distances have been used as default metric for least-squares fitting of these algebraic manifolds. This paper studies the problem of using algebraic distance for least-squares fitting of quadrics defining the constraint manifolds associated with Planar 4R mechanisms. It shows that the problem can be solved by fitting a pencil of quadrics with linear coefficients to a set of image points of a given one dimensional set of displacements. This linear formulation leads to a simple and fast algorithm for kinematic synthesis in the image space.

Copyright © 2012 by ASME
Topics: Fittings , Algebra

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