An efficient method to find the dynamic balancing conditions of mechanisms: Planar systems

In this work a novel and general method to find the dynamic balancing conditions, based on the use of Natural Coordinates, is introduced. The method is efficient and very easy to automate, and can be used to obtain the shaking force and the shaking moment balancing conditions for the linkages in the plane and can be extended for linkages in space, although at this time is presented only for planar systems. These conditions can be interpreted and used for the design of dynamic balanced linkages. The application of the method is demonstrated here by finding the force and moment balancing conditions of a general four-bar mechanism that, although simple, can serve as a didactic example to evaluate the method. The resulting conditions are used to the effective design of reactionless linkages with counterweights and counter-inertias.