Necessary and sufficient number of fingers for capturing pyramidal-like objects

This paper discusses how many fingers are necessary and sufficient for capturing a pyramidal-like object placed on a table under the gravitational field. Allowing that the contact friction is small enough to ensure that any direct grasp may fail in achieving an equilibrium grasp, we prove that a planar two-fingered hand are necessary and sufficient for achieving the task for an idealized 2D triangle object placed vertically on a table. We also consider 3D pyramidal-like objects, and prove that a spatial two-fingered hand are necessary and sufficient for achieving the task