Determination of the complete set of statically balanced planar four-bar mechanisms

Brian Moore; C. Gosselin; Josef Schicho

Determination of the complete set of statically balanced planar four-bar mechanisms

Brian Moore, C. Gosselin, Josef Schicho

Research Institute for Symbolic Computation

Research output: Working paper and reports › Research report

Abstract

In this paper, we present a new method to determine the complete set of statically balanced planar four-bar mechanisms. We formulate the kinematic constraints and the static balancing constraints as algebraic equations over real and complex variables. This leads to the problem of factorization of Laurent polynomials which can be solved using Newton polytopes and Minkowski sums. The result of this process is a set of necessary and sufficient conditions for statically balanced four-bar mechanisms.

Original language	English
Place of Publication	Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria
Publisher	SFB F013
Number of pages	16
Publication status	Published - Jul 2007

Publication series

Name	SFB F013 Reports
No.	2007-14

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

Cite this

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abstract = "In this paper, we present a new method to determine the complete set of statically balanced planar four-bar mechanisms. We formulate the kinematic constraints and the static balancing constraints as algebraic equations over real and complex variables. This leads to the problem of factorization of Laurent polynomials which can be solved using Newton polytopes and Minkowski sums. The result of this process is a set of necessary and sufficient conditions for statically balanced four-bar mechanisms.",

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AB - In this paper, we present a new method to determine the complete set of statically balanced planar four-bar mechanisms. We formulate the kinematic constraints and the static balancing constraints as algebraic equations over real and complex variables. This leads to the problem of factorization of Laurent polynomials which can be solved using Newton polytopes and Minkowski sums. The result of this process is a set of necessary and sufficient conditions for statically balanced four-bar mechanisms.

M3 - Research report

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BT - Determination of the complete set of statically balanced planar four-bar mechanisms

PB - SFB F013

CY - Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria

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