The optimal grasping point of the object varies depending on the shape of the object, such as the weight, the material, the grasping contact with the robot hand, and the grasping force. In order to derive the optimal grasping points for each object by a three fingered robot hand, optimal point and posture have been derived based on the geometry of the object and the hand using the artificial neural network. The optimal grasping cost function has been derived by constructing the cost function based on the probability density function of the normal distribution. Considering the characteristics of the object and the robot hand, the optimum height and width have been set to grasp the object by the robot hand. The resultant force between the contact area of the robot finger and the object has been estimated from the grasping force of the robot finger and the gravitational force of the object. In addition to these, the geometrical and gravitational center points of the object have been considered in obtaining the optimum grasping position of the robot finger and the object using the artificial neural network. To show the effectiveness of the proposed algorithm, the friction cone for the stable grasping operation has been modeled through the grasping experiments.