Optimum Balancing of Combined Shaking Force, Shaking Moment, and Torque Fluctuations in High-Speed Linkages

This paper presents an analytical and computer-aided procedure on the balancing of high-speed linkages. The method allows for the trade-offs necessary to achieve optimum dynamic response of the linkage in the design stage. These trade-offs involve a balance among the shaking force, the shaking moment, bearing reactions, and input-torque fluctuations by mass distribution of the links or counterweighting the linkage. Analytical mechanics and heuristic optimization techniques have been demonstrated to be useful tools in developing such a trade-off. The first part of this paper concerns the development of an optimality criterion in which an integrated approach is presented using both the Lagrangian and the Newtonian formulations, and consequently, a higher computational efficiency is achieved. Based on this theoretical development, the remainder of the paper focuses on the formulation of an optimization problem for linkage balancing and the solution of the problem by the Heuristic Optimization Technique of Lee and Freudenstein. The theory and computation are illustrated by numerical examples in the case of four-bar linkages.