Symbolic Dynamic Balance of the 3-RRR Planar Parallel Manipulator

The balancing of mechanisms consists of eliminating the shaking forces and shaking moments induced by the moving links on the fixed platform by redistributing masses and inertias or adding extra links to the original topology. This work reports symbolic expressions for the dynamic balancing of the 3-RRR in-line planar parallel manipulator. The proposed conditions allow the complete balancing of the linear momentum and the partial balancing of the angular momentum. The method, although it focuses on a particular topology, is easy to follow and can be applied to any planar parallel manipulator regardless of the degrees of freedom or the velocity and acceleration conditions imposed to the generalized coordinates.