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Redundant robotic manipulators under kinematic control may exhibit unpredictable behaviors at the joint level. When the end effector describes a closed trajectory, the joint angles may not return to their initial values. Likewise, final configuration in the joint space may depend on the trajectory that is followed by the end effector. In this paper, a complete parameterization of holonomic redundancy resolution techniques that avoid these problems is proposed. The flexibility of the proposed approach is discussed. In particular, it is shown that the selection of the redundancy resolution criterion is totally decoupled from the implementation of a closed-loop inverse kinematics (CLIK) algorithm. Any user-defined redundancy resolution criterion can, thus, be enforced. Potentialities of this new methodology are experimentally verified on an industrial robot in a case study where functional redundancy occurs and is applied in simulation on a 7-degree-of-freedom (7-DOF) anthropomorphic manipulator.