Optimum dynamic balancing of planar parallel manipulators

This paper presents a methodology for optimum dynamic balancing of planar parallel manipulators typified with a variable speed 2 DOF parallel manipulator articulated with revolute joints. The dynamic balancing is formulated as an optimisation problem such that a sum-squared values of bearing forces, driving torques, shaking moment, and the deviation of the angular momentum from its mean value are minimized throughout an operation range of the manipulator, provided that a set of balancing constraints consisting of the shaking force balancing conditions, the sizes of some inertial and geometric parameters are satisfied. Sets of optimisation results corresponding to various combinations of the elements of the objective function are evaluated in order to quantify their influence on the resulting bearing forces, the driving torques, shaking moment and force. The results prove that the proposed optimisation approach can be used to minimize any desired combination of the forces, moments, and torques involved in any parallel mechanism by choosing a suitable set of weighting factors. The method is systematic, versatile and easy to implement for the optimum balancing of the parallel manipulator and more general parallel manipulators.