MEGA 2007 Effective Methods in Algebraic Geometry Strobl, Austria, June 25th - 29th http://www.ricam.oeaw.ac.at/mega2007

Abstract

Title	Static balancing of parallel mechanisms
Keywords
Abstract	The design of statically balanced mechanisms consists of deriving a set of constraints between kinematic and static parameters such that the center of mass remains fixed for any configuration of the mechanism. Such structures have several practical applications, including the elimination of vibrations which improved both precision and performance. Using the four-bar mechanism as an example, we formulate the kinematic constraints between the angles and the static balancing constraints as algebraic equations over real and complex variables. This reduces to the problem of the factorization of Laurent polynomials which can be solved using Newton polytopes and Minkowsi sums. Finally, we determine necessary and sufficient conditions for statically balanced four-bar mechanisms.

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