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A Task Driven Approach to the Synthesis of Spherical 4R Linkages Using Algebraic Fitting Method

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

Stony Brook University, Stony Brook, NY

Paper No. DETC2013-13179, pp. V06AT07A062; 10 pages
doi:10.1115/DETC2013-13179
From:
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6A: 37th Mechanisms and Robotics Conference
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5593-5
  • Copyright © 2013 by ASME

abstract

This paper studies the problem of spherical 4R motion approximation from the viewpoint of extraction of circular geometric constraints from a given set of spherical displacements. This paper extends our planar 4R linkage synthesis work to the spherical case. By utilizing kinematic mapping and quaternions, we map spherical displacements into points and the workspace constraints of the coupler into intersection of algebraic quadrics (called constraint manifold), respectively, in the image space of displacements. The problem of synthesizing a spherical 4R linkage is reduced to finding a pencil of quadrics that best fit the given image points in the least squares sense. Additional constraints on the pencil identify the quadrics that represent a spherical circular constraint. The geometric parameters of the quadrics encode information about the linkage parameters which are readily computed to obtain a spherical 4R linkage that best navigates through the given displacements. The result is an efficient and largely linear method for spherical four-bar motion generation problem.

Copyright © 2013 by ASME
Topics: Linkages , Fittings

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