Design of planar 3-DOF 3-RRR reactionless parallel manipulators

This paper discusses the development of reactionless 3-RRR planar parallel manipulators, which apply no reaction forces or moments to the mounting base during motion. Design equations and techniques are proposed which allow for the dynamic substitution of the mass of the moving platform of a parallel manipulator by three concentrated masses. The dynamic model of the moving platform consequently represents a weightless link with three concentrated masses. This allows for the transformation of the problem of the design of a reactionless manipulator into a problem of balancing pivoted legs carrying concentrated masses. The total angular momentum of the manipulator can be reduced to zero using two approaches: (i) on the basis of counter-rotations and (ii) using an inertia flywheel rotating with a prescribed angular velocity. The suggested solutions are illustrated through computer simulations and the results verified by showing that the manipulator is indeed reactionless, there being no forces or moments transmitted to the base during motion of the moving platform.