An alternative method for the optimum dynamic balancing of the four-bar mechanism

Abstract

This article presents the optimum dynamic balancing of the four-bar mechanism, in particular the crank-rocker, by the addition of counterweights. This is done by imposing as little restrictive as possible constraints on the counterweights parameters. First the general analytical equations of motion of the crankrocker four-bar mechanism are obtained, using natural coordinates. This model allows expressing the dynamic equations of the mechanism just in terms of the mass, as opposed to the need of using also the moment of inertia, and the coordinates of the center of gravity of the counterweights, that are used as optimization variables. This implies that no particular counterweight shape is assumed in advance. The only constraints imposed on these optimization variables are that masses must be non-negative. As a novelty, the most influencing variables in the optimization are identified using a global sensitivity analysis based on polynomial chaos. This allows to impose different constraints an also to reduce the total number of optimization variables without affecting the global results. The results obtained are validated by simulations, and compared to those expressed in representative papers obtained by other authors.