A general mass balancing method for complex planar mechanisms

The 1968 work by Berkof and Lowen provided a new perspective in the balancing of machines by using “linearly independent vectors” for the complete shaking force balancing of simple mechanisms. As logical extensions of their work, methods presented in this paper allow the complete balancing of complex mechanisms for shaking force or shaking moment (which inherently satisfies the shaking force criteria). These methods further allow the satisfaction of user specified non-zero values of the dynamic properties of the mechanism including driving torque, shaking momentum, shaking force, or combinations of these. The formulation provides, by direct non-iterative computation, redistribution of the mass content of the system in the most general sense to enhance the operating smoothness of the total system. These synthesis results are addressable by all designers since their uniform mathematical formulation can be packaged in compact interactive computational programs for all conceivable dynamic properties to be considered for balancing.