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The design of a four-axis wrist with a skewed pitch axis is described. The skew-axis design increases the joint travel over traditional gimballed configurations while the excess degree of freedom can be used to avoid singularities. A generalized inverse kinematics procedure locally minimizes the joint velocities for a given tool orientation while steering the wrist away from singular regions and mechanical hard stops. The singularity surfaces are mapped in 3D-space, and simulations are used to illustrate the operation of the wrist. Hardware integration and testing of the wrist on the new dexterous manipulator for the Ranger Telerobotic Shuttle Experiment are also discussed.