Manipulability ellipsoids are effective tools to perform task space analysis of robotic manipulators in terms of velocities, accelerations and forces at the end effector. A new definition of dynamic manipulability ellipsoid for redundant manipulators is proposed which leads to more correct results in evaluating manipulator capabilities in terms of task-space accelerations. The case of manipulators in singular configurations is also analyzed. A case study is presented to illustrate the correctness of the proposed approach for an "easy-to understand" planar arm.