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In this paper, we propose a novel method for dexterous manipulation planning problem of rotating object with surface of revolution using a robotic multi-fingered hand. This method finds contact point trajectories from contact points between the robotic hand and the object with task-orientated manipulation quality measurement. Based on the defined manipulation quality, the pose for robotic hand relative to object can also be optimized by random sample. Experiments using Schunk anthropomorphic hand with 13 degrees of freedom screwing a light bulb into holder with screw thread demonstrates the feasibility and efficiency of the introduced method.