Flexibility of Bricards planar linkages and other structures via resultants and computer algebra

Evangelos A. Coutsias; Robert H. Lewis

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Flexibility of Bricards planar linkages and other structures via resultants and computer algebra

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arxiv 1408.6247 v1 pith:FWIFWTBD submitted 2014-08-26 math.MG

Robert H. Lewis , Evangelos A. Coutsias This is my paper

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keywords flexibilitybricardcomputerresultantssoftwarestructuresworkalgebra

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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.

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