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Typical tasks of future service robots involve grasping and manipulating a large variety of objects differing in size and shape. Generating stable grasps on 3D objects is considered to be a hard problem, since many parameters such as hand kinematics, object geometry, material properties and forces have to be taken into account. This results in a high-dimensional space of possible grasps that cannot be searched exhaustively. We believe that the key to find stable grasps in an efficient manner is to use a special representation of the object geometry that can be easily analyzed. In this paper, we present a novel grasp planning method that evaluates local symmetry properties of objects to generate only candidate grasps that are likely to be of good quality. We achieve this by computing the medial axis which represents a 3D object as a union of balls. We analyze the symmetry information contained in the medial axis and use a set of heuristics to generate geometrically and kinematically reasonable candidate grasps. These candidate grasps are tested for force-closure. We present the algorithm and show experimental results on various object models using an anthropomorphic hand of a humanoid robot in simulation.