Dynamic balancing of planar mechanisms using toric geometry

Brian Moore; Clement M. Gosselin; Josef Schicho

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arxiv 0711.3742 v1 pith:PALAES2E submitted 2007-11-23 math.AG math.CV

Dynamic balancing of planar mechanisms using toric geometry

Brian Moore , Josef Schicho , Clement M. Gosselin This is my paper

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keywords balancingdynamicplanarvariablesangularcomplexfour-barjoint

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In this paper, a new method to determine the complete set of dynamically balanced planar four-bar mechanims is presented. Using complex variables to model the kinematics of the mechanism, the dynamic balancing constraints are written as algebraic equations over complex variables and joint angular velocities. After elimination of the joint angular velocity variables, the problem is formulated as a problem of factorization of Laurent polynomials. Using toric polynomial division, necessary and sufficient conditions for dynamic balancing of planar four-bar mechanisms are derived.

Dynamic balancing of planar mechanisms using toric geometry

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