A new kinematic design of a parallel spherical wrist with actuatorredundancy is presented. A special feature of this parallel manipulator is thearrangement of co-axial actuators which allows unlimited rotation about any axisinside a cone-shaped workspace. A detailed kinematic analysis has shown thatactuator redundancy not only removes singularities but also increases workspacewhile improving dexterity. The structure optimization has been performed with aglobal dexterity criterion. Using a conditioning measure, a comparison with anon-redundant structure of the same type was performed and shows that asignificant improvement in dexterity has been obtained.