On the Number of Equilibrium Placements of Mass Distributions in Elliptic Potential Fields

Recent papers have demonstrated the use of force elds for mechanical part orientation. The force eld is realized on a plane on which the part is placed. The forces exerted on the part's contact surface translate and rotate the part to an equilibrium orientation. Part manipulation by force elds is very attractive since it requires no sensing. We describe force elds that result from elliptic potentials and induce only 2 stable equilibrium orientations for most parts. The proposed elds represent a considerable improvement over previously developed force elds which produced O(n) equilibria for polygonal parts with n vertices. The successful realization of these force elds could signi cantly a ect part manipulation in industrial automation.