Geometric Characterization of the Planar Multi-Finger Equilibrium Grasps

Multi-finger equilibrium grasps form the basic building block for synthesizing secure grasps by robot hands. This letter describes a catalog of the 2-D equilibrium grasps. The letter reviews graphical techniques for synthesizing two and three-finger equilibrium grasps, then describes new techniques for identifying and synthesizing four-finger equilibrium grasps as well as higher number-of-finger grasps. For each of these grasps, the letter describes special geometric properties associated with frictionless and frictional contacts. The letter establishes that every 2-D equilibrium grasp can be realized by two or three finger forces that rely on friction effects, or by four finger forces that need not rely on friction effects. The four finger forces can be realized along the grasped object contact normals and are thus maximally robust with respect to uncertainty in the amount of friction at the contacts. Examples illustrate the techniques and a simple experiment demonstrates the ability of four-finger grasps to align their forces towards the contact normals while maintaining an equilibrium grasp. Analogous properties of the 3-D equilibrium grasps are also summarized.