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In this study, we derive a translation vector of manipulating force polytope. The translation vector is derived a function of velocity and acceleration of extended task space. A dynamic manipulability ellipsoid that is performance index is known to translate by joint velocity [12]. We derived the extended task space constructed by task space and internal motion space, and discovered the dynamic manipulability polytope translate by velocity on the extended task space [13]. However, the effect to the manipulating force polytope by velocity on the extended task space is unclear, because external force by contact doesn't consider. In this paper, we discover that the translation vector of the manipulating force polytope becomes a function of acceleration and tensor production of velocity on the extended task space. The manipulating force polytope spanned on an extended force space constructed by a hand force and a force that cause internal motion. Furthermore, we establish that the manipulating force polytope and the manipulating force ellipsoid indicate to same characteristics by showing the manipulating force polytope is circumscribed to the manipulating force ellipsoid. By the results of this paper, we expect to improve force control performance and to improve collision detection performance on a cooperating robot.

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In this research, we examine about acceleration coupling with velocity on extended operational space of a kinetic redundant manipulator. The coupling with velocity appears as a translating a dynamic manipulability polyhedron. The extended operational space is consisted of operational space and redundant space. Redundant space is null space of operational space that is spanned by column vectors of the Jacobi matrix. We clarify translating the dynamic manipulability polyhedron by deriving basis vectors of translating vector and vertex vectors of dynamic manipulability polyhedron that are independent of velocity on the extended operational space. Appropriateness of the translation of dynamic manipulability polyhedron is confirmed by calculating the dynamic manipulability polyhedron with various velocities on simulation.

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