| Programmable force fields have
been used as an abstraction to represent a whole new class of devices that
have been proposed for part manipulation. The 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 the contact surface of the
part translate and rotate the part. Manipulation plans for these devices
can therefore be considered as strategies for applying a sequence of force
fields to bring parts to some desired configuration. Instances of these
novel devices are currently implemented using microelectromechanical systems
technology, small airjets, vibration, and small motors. Manipulation in
this case is sensorless and nonprehensile and promises to address the handling
of very small or very fragile parts, such as electronics components, that
cannot be handled with conventional pick-and-place robotics techniques.
In this paper, the authors consider the problem of bringing a part to a
stable equilibrium configuration using force fields. The authors study the
combination of a unit radial field with a small constant field. A part placed
on the radial field moves toward the origin of the radial field but cannot
be oriented due to symmetry. Perturbing the radial field with a constant
force field breaks the symmetry and gives rise to a finite number of equilibria.
Under certain conditions, there is a unique stable equilibrium configuration.
For the case in which these conditions are not fulfilled, the authors provide
a comprehensive and unified analysis of the problem that leads to an algorithm
to compute all stable equilibrium configurations. The paper contains a detailed
discussion on how to implement the algorithm for any part. In the analysis,
the authors make extensive use of potential fields. Using the theory of
potential fields, the stable equilibrium configurations of a part are equivalent
to the local minima of a scalar function. The work presented in this paper
leads to the design of a new generation of efficient, open-loop part feeders
that can bring a part to a desired orientation from any initial orientation
without the need of sensing or a clock.