A General and Numerically Efficient Framework to Design Sector-Type and Cylindrical Counterweights for Balancing of Planar Linkages

This paper extends previous work concerning convex reformulations of counterweight balancing by developing a general and numerically efficient design framework for counterweight balancing of arbitrarily complex planar linkages. At the numerical core of the framework is an iterative procedure, in which successively solving three convex optimization problems yields practical counterweight shapes in typically less than 1 CPU s. Several types of counterweights can be handled. The iterative procedure allows minimizing and/or constraining shaking force, shaking moment, driving torque, and bearing forces. Numerical experiments demonstrate the numerical superiority (in terms of computation time and balancing result) of the presented framework compared to existing approaches.