Positioning of symmetric and nonsymmetric parts using radial and constant fields: Computation of all equilibrium configurations

Programmable force fields have been used as an abstraction to represent a w hole new class of devices that have been proposed for part manipulation. Th e general idea behind these devices is that a force field is implemented in a plane upon which the part is placed. The forces and torques exerted on t he contact surface of the part translate and rotate the part. Manipulation plans for these devices can therefore be considered as strategies for apply ing a sequence of force fields to bring parts to some desired configuration . Instances of these novel devices are currently implemented using microele ctromechanical systems technology, small airjets, vibration, and small moto rs. Manipulation in this case is sensorless and nonprehensile and promises to address the handling of ver) small or very fragile parts, such as electr onics components, that cannot be handled with conventional pick-and-place r obotics techniques. In this paper; the authors consider the problem of brin ging a part to a stable equilibrium configuration using force fields. The a uthors study the combination of a unit radial field with a small constant f ield. A part placed on the radial field moves toward the origin of the radi al field but cannot be oriented due to symmetry. Perturbing the radial fiel d with a constant force field breaks the symmetry and gives rise to a finit e number of equilibria. Under certain conditions, there is a unique stable equilibrium configuration. For the case in which these conditions are not f ulfilled, the authors provide a comprehensive and unified analysis of the p roblem that leads to an algorithm to compute all stable equilibrium configu rations. The paper contains a detailed discussion on how to implement the a lgorithm for any part. In the analysis, the authors make extensive use of p otential fields. Using the theory of potential fields, the stable equilibri um configurations of apart are equivalent to the local minima of a scalar f unction. The work presented in this paper leads to the design of a new gene ration of efficient, open-loop part feeders that can bring a part to a desi red orientation from any initial orientation without the need of sensing or a clock.