Generic method for deriving the general shaking force balance conditions of parallel manipulators with application to a redundant planar 4-RRR parallel manipulator

摘要

This paper proposes a generic method for derivingudthe general shaking force balance conditions of paralleludmanipulators. Instead of considering the balancing of a paralleludmanipulator link-by-link or leg-by-leg, the architecture isudconsidered altogether.udThe first step is to write the linear momentum of each element.udThe second step is to substitute the derivatives of theudloop equations, by which the general force balance conditionsudare obtained. Subsequently specific kinematic conditions areudinvestigated in order to find advantageous, simple balance solutions.udAs an example, the method is applied to a planar 4-RRR paralleludmanipulator, for which the force balance conditions andudsolutions are discussed and illustrated for each step respectively.udBy including the loop equations, linear relations of theudmotion among mechanism elements lead to an increase of balanceudpossibilities.For specific kinematic conditions, additionaludlinear relations among the motion of mechanism elements mayudbe obtained, resulting in another increase of balance possibilities.udFor the latter, symmetric motion is an important featureudfor which a 4-RRR manipulator is advantageous