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

Robert H. Lewis; Evangelos A. Coutsias

doi:10.1016/j.matcom.2014.11.002

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

Robert H. Lewis
, Evangelos A. Coutsias

Applied Mathematics and Statistics

Fordham University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	152-167
Number of pages	16
Journal	Mathematics and Computers in Simulation
Volume	125
DOIs	https://doi.org/10.1016/j.matcom.2014.11.002
State	Published - Jul 2016

Keywords

Computer algebra
Flexible
Quadrilateral
Resultant

Access to Document

10.1016/j.matcom.2014.11.002

Cite this

@article{abf01e2b89c9421abe9bce43c6a4cbbf,

title = "Flexibility of Bricard's linkages and other structures via resultants and computer algebra",

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.",

keywords = "Computer algebra, Flexible, Quadrilateral, Resultant",

author = "Lewis, \{Robert H.\} and Coutsias, \{Evangelos A.\}",

note = "Publisher Copyright: {\textcopyright} 2014 International Association for Mathematics and Computers in Simulation (IMACS).",

year = "2016",

month = jul,

doi = "10.1016/j.matcom.2014.11.002",

language = "English",

volume = "125",

pages = "152--167",

journal = "Mathematics and Computers in Simulation",

issn = "0378-4754",

}

TY - JOUR

T1 - Flexibility of Bricard's linkages and other structures via resultants and computer algebra

AU - Lewis, Robert H.

AU - Coutsias, Evangelos A.

PY - 2016/7

Y1 - 2016/7

N2 - 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.

AB - 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.

KW - Computer algebra

KW - Flexible

KW - Quadrilateral

KW - Resultant

UR - https://www.scopus.com/pages/publications/84914816943

U2 - 10.1016/j.matcom.2014.11.002

DO - 10.1016/j.matcom.2014.11.002

M3 - Article

AN - SCOPUS:84914816943

SN - 0378-4754

VL - 125

SP - 152

EP - 167

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this