Balancing of shaking forces and shaking moments for planar mechanisms using the equimomental systems

A general mathematical formulation of optimization problem for balancing of planar mechanisms is presented in this paper. The inertia properties of mechanisms are represented by dynamically equivalent systems, referred as equimomental systems, of point-masses to identify design variables and formulate constraints. A set of three equimomental point-masses for each link is proposed. In order to determine the shaking forces and the shaking moments, the dynamic equations of motion for mechanisms are formulated systematically in the parameters related to the equimomental point-masses. The formulation leads to an optimization scheme for the mass distribution to improve the dynamic performances of mechanisms. The method is illustrated with two examples. Balancing of combined shaking force and shaking moment shows a significant improvement in the dynamic performances compared to that of the original mechanisms.