Optimal dynamic balancing and shape synthesis of links in planar mechanisms

•A two stage optimization method is proposed for optimum design of planar mechanisms.•The method shows effectiveness of the equimomental point-mass systems.•The shaking force and shaking moment are reduced significantly using the optimization method.•The method provides a design solution for balancing as well as link shapes.•The method demonstrates application of GA as a solver in mechanism balancing and design.

This paper presents a two stage optimization procedure for dynamic balancing of planar mechanisms and finding optimum link shapes. In the first stage, the shaking force and shaking moment are minimized by optimizing mass distribution of links using the equimomental system of point-masses for each link. Then for the optimum inertial parameters of the balanced mechanism, the optimum links shapes are synthesized systematically using closed parametric curve such as cubic B-spline in the second stage. The control points of cubic B-spline curve are taken as the design variables for link shape formation to minimize the percentage error in the resulting link inertia values. The constraints on design variables are defined for both symmetrical and non-symmetrical shapes in the optimization problem formulation. The proposed method of balancing and shape synthesis can be applied to any planar single and multiloop mechanism with revolute as well as prismatic joints. Its effectiveness is demonstrated by applying it to four-bar, five-bar, six-bar and slider-crank mechanisms.