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Flexibility of Bricard’s linkages and other structures via resultants and computer algebra

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  • Lewis, Robert H.
  • Coutsias, Evangelos A.

Abstract

Flexibility of structures is extremely important for chemistry and robotics. Following our earlier work, we study flexibility using polynomial equations, resultants, and a symbolic algorithm of our creation that analyzes the resultant. We show that the software solves a classic arrangement of quadrilaterals in the plane due to Bricard. We fill in several gaps in Bricard’s work and discover new flexible arrangements that he was apparently unaware of. This provides strong evidence for the maturity of the software, and is a wonderful example of mathematical discovery via computer assisted experiment.

Suggested Citation

  • Lewis, Robert H. & Coutsias, Evangelos A., 2016. "Flexibility of Bricard’s linkages and other structures via resultants and computer algebra," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 125(C), pages 152-167.
    • Handle: RePEc:eee:matcom:v:125:y:2016:i:c:p:152-167
    DOI: 10.1016/j.matcom.2014.11.002
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    References listed on IDEAS

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    1. Lewis, Robert H., 2008. "Heuristics to accelerate the Dixon resultant," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 400-407.
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