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Closed form expressions for the sensitivity of kinematic dexterity measures to posture changing and geometric variations

This paper addresses the sensitivity of dexterity measures w.r.t. the posture of a manipulator, with given design parameters, as well as w.r.t. the manipulator's geometric parameters. These are required for placing a manipulator so to maximize dexterity and for the optimal layout of the link geometry, respectively. Explicit expressions are derived for first and second partial derivatives of dexterity measures w.r.t. to joint angles and w.r.t. geometric link parameters. The latter is obtained using a virtual joint method extending the product of exponentials formula for the forward kinematics. The approach applies to serial and parallel manipulators.