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Kinematic Synthesis of a Watt I Six-Bar Linkage for Body Guidance

  • Mark Plecnik
  • J. Michael McCarthy
  • Charles W. Wampler
Chapter

Abstract

This chapter formulates the synthesis equations for a Watt I six-bar linkage that moves through \(N\) specified task positions. For the maximum number of positions, \(N=8\), the resulting polynomial system consists of 28 equations in 28 unknowns, which can be separated into a nine sets of variables yielding a nine-homogeneous Bezout degree of \(3.43\times 10^{10}\). We verify these synthesis equations by finding isolated solutions via Newton’s method, but a complete solution for \(N=8\) seems beyond the capability of current homotopy solvers. We present a complete solution for \(N=6\) positions with both ground pivots specified.

Keywords

Kinematic synthesis Six-bar linkage 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mark Plecnik
    • 1
  • J. Michael McCarthy
    • 1
  • Charles W. Wampler
    • 2
  1. 1.Robotics and Automation LaboratoryUniversity of CaliforniaIrvineUSA
  2. 2.General Motors R&D CenterWarrenUSA

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