This paper describes the development of a novel vision-based grasping system for unknown objects based on range images. We realize a synthesis of the calculated grasp points with a 3D model of a hand prosthesis, which we are using as gripper. We locally find grasp point candidates based on the shape of the object and validate the globally by checking collisions between the gripper and surrounding objects and the table top. Our approach integrates a robust object segmentation and grasp point detection for every object on a table in front of a 7-DOF robot arm. The algorithm analyzes the top surface of every object and outputs the generated grasp points and the required gripper pose to grasp the desired object. Additionally we can calculate the optimal opening angle of the gripper. The first experimental results show that the presented automated grasping system is able to generate successful grasp points for a wide range of different objects.