An application of natural matrices to the dynamic balance problem of planar parallel manipulators

Abstract This paper introduces a simplified matrix method for balancing forces and moments in planar parallel manipulators. The method resorts to Newton’s second law and the concept of angular momentum vector, yet it is not necessary to perform the velocity and acceleration analyses, tasks that were normally unavoidable in seminal contributions. With the introduction of natural matrices, the proposed balancing method is independent of the time and the trajectory generated by the moving links of parallel manipulators. The effectiveness of the method is exemplified by balancing two planar parallel manipulators.