Friction-Induced Velocity Fields for Point Parts Sliding on a Rigid Oscillated Plate

We show that small-amplitude periodic motion of a rigid plate causes point parts on the plate to move as if they are in a position-dependent velocity field. Further, we prove that every periodic plate motion maps to a unique velocity field. By allowing a plate to oscillate with six-degrees-of-freedom, we can create a large family of programmable velocity fields. We examine in detail sinusoidal plate motions that generate fields with either isolated sinks or squeeze lines. These fields can be exploited to perform tasks such as sensorless part orientation.