A Family of Kinematically Redundant Planar Parallel Manipulators

Parallel manipulators feature relatively high payload and accuracy capabilities compared to their serial counterparts. However, they suffer from small workspace and low maneuverability. Kinematic redundancy for parallel manipulators can improve both of these characteristics. This paper presents a family of new kinematically redundant planar parallel manipulators with six actuated-joint degrees of freedom based on a 3-PRRR architecture obtained by adding an active prismatic joint at the base of each limb of the 3-RRR manipulator. First, the inverse displacement of the manipulators is explained, then their reachable and dexterous workspaces are obtained. Comparing the proposed redundant manipulators to the original 3-RRR nonredundant manipulator, both reachable and dexterous workspaces are substantially larger. Next, the Jacobian matrices of the manipulators are derived, and different types of singularities are analyzed and demonstrated. It is shown that the vast majority of singularities can be avoided by using kinematic redundancy.