This paper is concemed with a manipulatability of redundant manipulators for trajectory tracking and obstacle avoidance using a kinematical redundancy. Possibility of avoiding a collision with obstacles during tracking the desired hand trajectory is discussed with a proposed avoidance matrix， avoidance manipulatabi1ity ellipsoid and avoidance manipu1atability which are defined on each link constructing the manipulator except the top link. A necessary and sufficient condition that the intermediate links can avoid obstacles in the work coordinates is indicated that the dimension of range space of the avoidance matrix and the one of the work space of the manipulator are coincident. That means the avoidance manipukatability ellipsoid is expanded in the work space. And factors which influence the shape of the ellipsoid， the figure of the manipulator， redundant degree， the serial position of the link from the base， and the priority of the avoiding tasks are also analyzed. Finally we show the evaluation of avoidance possibility with the avoidance manipulatability ellipsoid and avoidance manipulatability using numerical examples.
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