Optimum force balancing with mass distribution and a single elastic element for a five-bar parallel manipulator

This paper deals with optimum force balancing of a planar parallel manipulator, articulated with revolute joints, by properly distributing link masses, and connecting only one spring between its two coupler links. After conducting the static force analysis of the mechanism, the force balancing is formulated as an optimisation problem such that a sum-squared values of bearing forces is minimized throughout an operation range of the manipulator, provided that a set of balancing constraints consisting of balancing conditions, the sizes of some inertial and geometric parameters are satisfied. Optimisation results indicate that the proposed optimisation approach is systematic, versatile and easy to implement for the optimum balancing of the parallel manipulator and other more general parallel manipulators. This work contributes to previously published work from the point of view of being a step towards optimum design of parallel manipulators, which is currently lacking in the literature.