Numerical analysis for optimal posture of circular object grasped with frictions

When grasping an object, friction forces are sometimes utilized effectively. This friction forces allows us to manipulate the object to various directions. Regarding such a grasped object posture, we reported an analysis on the 2D-space grasping with two contact points. Selecting the square sum of the contact forces as an evaluation function of the object posture, we concluded that the optimal posture is the one where the midpoint of two contact points and the center of mass of the object align vertically. In this analysis, however, the friction condition is not taken into account, and thus this result is applied only to the grasp by use of fixtures, not to the one with frictions. In this paper, we aim at extending this result into the grasp with frictions. Especially, we analyze a grasp of circular object in the 2-D space in a numerical manner, and discuss the physical meaning of the optimal posture.