This paper treats the three-jointed spherical wrist on which the tool is placed at an angle δ ≠ 0. A two-parameter set of axes is identified for the wrist such that the angular velocities and accelerations at the three joints are within acceptable limits during a 2π-rotation of the end-effector at constant speed about each such axis. This set of axes is compared both to the total set of available axes of full rotation and to the set for which the determinant of the wrist Jacobian is greater than a specified minimum value. For each set of axes, hypothetical substitute-wrists permit the generalization of design conditions for robots with spherical wrists on which δ = 0 to robots with spherical wrists on which δ ≠ 0, and they provide geometrical limits on tool-placement which bound the velocities and accelerations at the wrist joints. Lastly, comments are made about balancing the velocity and acceleration characteristics of the actuators in a spherical wrist.

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