Optimal Direction of Grasped Object Minimizing Contact Forces

When grasping an object, friction forces are sometimes utilized. Because of this friction forces, the object is manipulable to various direction. In this paper, we discuss which direction is best when contact points, the number of which is two in the 2D-space grasping or three in the 3D one, are assigned. To evaluate the object direction, we focus on the norm of contact forces consisting of the normal forces and friction forces. We conclude that the norm of contact force become minimal when vertical line through the center of mass of the object (i.e., gravitational line) shoots out the midpoint of two contact points in 2D space, while it does the centroid of the contact-point triangles in 3D space