The existing industrial parts feeders move the parts through a sequence of mechanical filters that reject parts in unwanted orientations. In this paper we develop a new setup that uses a different vibratory mechanism to systematically manipulate parts, by actively orienting and localizing them. The idea is to generate and change dynamic modes for a plate by varying the applied frequency of oscillation. Depending on the node shapes of the plate for these frequencies, the position and orientation of the parts can be controlled. We develop an analysis of the underlying dynamics, and show that it can be used to predict the behavior of objects placed on the vibrating plate. Using this analysis, we propose that the applied frequencies can be automatically sequenced to obtain a "sensorless" strategy for manipulating a given object.

We model and analyze three dimensional rigid body impact with Coulomb friction and Poisson restitution. The differential equations that describe the progress and outcome of the impact induce a flow in the tangent velocity space which defines the qualitatively different sliding behavior that can occur. We show that the flow patterns depend only on the inertial parameters at the point of contact. We associate each of the possible flow patterns with a distinct region in a three dimensional parameter space. By examining the mass parameters and the initial conditions, we can determine the corresponding flow pattern and the possible outcomes of the impact. The equations of motion cannot be solved in a closed form, but by analyzing the flow at the point of sticking, we can avoid instabilities in the numerical integration of the equations.>