Abstract: When a multi-fingered hand grasps an object, the ways to grasp it stably are infinite, and thus an optimal grasp planning is necessary to find the relatively optimized grasp points on object for achieving the objective of the given grasping and manipulating task. For this, we first define several grasp indices to evaluate the quality of each feasible grasp. Since the physical meanings of the defined grasp indices are different from each other, it is not easy to combine those indices to identify the optimal grasping. Thus, we propose a new generalized grasping performance index to represent all of the grasp indices as one measure based on a non-dimensionalizing technique. Next, by using the proposed grasping performance index, we try to determine the optimal grasp points for multi-fingered hands performing contact tasks. Through task-based simulation studies, we discuss the feasibility of each grasp index as the grasp polygons and then, we show that the trend of the proposed optimal grasp planning is coincident to the physical sense of human grasping. Furthermore, some experimental results showing the task specific performances are incorporated to corroborate the effectiveness of the proposed optimal grasp planning algorithms.