Abstract: The internal forces play an important role in the stable grasping of three-fingered robot hand. Under the condition of fixed-point contact models with friction between the fingertips and the object surface, it is necessary for the three internal forces to lie in relative frictional sectors of contact points and intersect at a point within concurrent polygon. As a result, the research on optimized algorithm for internal force should be made on the basis of concurrent polygon existence. Based on the analysis of the geometrical characteristics of contact positions on the object surface, the existence condition of the frictional sectors is established. The angle between inner normal vector and relative inner normal vector of each contact point should be smaller than friction cone angle. By means of studying the relative location relationships between the frictional sector borderlines and their intersections, the existence condition of the concurrent polygon for the three internal forces is presented. All intersections of any two frictional sectors are not less than one lying in absolute inner of the third frictional sector or not less than three lying on the borderlines of the third frictional sector. At last, a general algorithm for judging the existence of concurrent polygon is founded, by which the self-balancing internal forces can be determined and used to regulate the fingertip manipulating forces. An example is given to illustrate the validity of the algorithm.

Key words: Concurrent polygon, Existence judgment, Frictional sector, Internal force, Three-fingered hand