Finger position computation for 3-dimensional equilibrium grasps

Finger position computation for 3-dimensional equilibrium grasps is discussed. The grasp object is a polyhedron and each finger pushes the face of the object within a given polygonal region. It is shown that in a planar grasp the moment equilibrium equation can be made linear by replacing each real finger by a pair of virtual fingers fixed at the vertices of the region. Using such virtual fingers in 3-D grasps, nonlinear constraints still remain, but they exhibit the same properties as the integer requirement in an integer programming problem. An algorithm based on the branch and bound method is proposed. The cases where two fingers push the same region and where the finger contact used is a soft finger contact are discussed