Using an enumeration procedure for connectivity, the theoretically minimum number of actuators is identified for each of six types of point workspace. Robot dexterity is described using the omnidirectional, primary, and dexterous workspaces of a point. It is shown that only two plane workspaces are sufficient to provide all the mechanically achievable workspaces that are dual to the six point workspaces. Several manipulator structures are identified, and these provide equivalent dexterity to that achieved by a spherical wrist with three concurrent, sequentially orthogonal, and fully-rotatable hinge joints.

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