Positioning and orienting a class of symmetric parts using a combination of a unit-radial and a constant force fields

Part positioning and orientation is a key issue in manufacturing. Extensive recent work has investigated a series of force fields for part positioning and orientation. Typically, a strategy that brings a part to a unique equilibrium consists of several force fields that are employed in sequence. Bohringer and Donald conjectured a few years ago that the combination of a unit radial field with a constant field would give rise to a unique equilibrium. Such a field is extremely interesting as it positions and orients parts without the need of sensing or a clock. We (2000) have proved this conjecture for nonsymmetric parts. In this paper, we focus our attention on symmetric parts and show that some of them can be uniquely positioned and oriented using the same field. Our work further explores the capabilities and limits of force fields and provides additional evidence that force fields are a powerful tool for parts manipulation.