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TitleDynamic balancing of planar mechanisms using toric geometry
Author(s) Clément M. Gosselin, Brian Moore, Josef Schicho
TypeArticle in Journal
AbstractA mechanism is statically balanced if for any motion, it does not apply forces on the base. Moreover, if it does not apply torques on the base, the mechanism is said to be dynamically balanced. In this paper, a new method for determining the complete set of dynamically balanced planar four-bar mechanisms is presented. Using complex variables to model the kinematics of the mechanism, the static and 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 tools from toric geometry including toric polynomial division, necessary and sufficient conditions for static and dynamic balancing of planar four-bar mechanisms are derived.
KeywordsStatic balancing, Dynamic balancing, Planar four-bar mechanism, Toric geometry, Newton polygon, Minkowski sum
URL http://www.sciencedirect.com/science/article/pii/S0747717109000285
JournalJournal of Symbolic Computation
Pages1346 - 1358
NoteEffective Methods in Algebraic Geometry
Translation No
Refereed No