Several results offering insight into the properties of the manipulability measure are presented based on the idea of separating the total manipulability measure into translational and rotational manipulability measures. It is shown that if a manipulator consists of an arm portion with three joints and a spherical wrist portion with three or more revolute joints, the total manipulability measure is given by product of the TMM (translational manipulability measure) in the weak sense of the arm portion and the RMM (rotational manipulation measure) in the weak sense of the wrist portion. Based on this result, it is shown that the singularities of manipulators with spherical wrists can be divided into the arm and wrist singularities. For general serial-link manipulations, the concepts of TMM and RMM in the weak and strong sense are introduced and their relation to the total manipulability measure is discussed.
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