Shaking force and shaking moment balancing of mechanisms: A historical review with new examples

This paper deals with the solutions of the problem of the shaking force and shaking moment balancing of planar mechanisms by different methods based on the generation of the movements of counterweights. Some special cases are examined, such as balancing methods based on the copying properties of pantograph systems that carry the counter-weights (formed by gears or by toothed-belt transmissions). The pantograph system executes a movement exactly opposite to the movement of the total center of the movable link masses. Such a solution provides the conditions for dynamic balancing with a relatively small increase of the total mass of the movable links. The methods are illustrated by many examples.