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

Abstract

We show that small-amplitude periodic motion of a rigid plate causes point parts in frictional contact with 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 the class of plate motions described by sinusoidal linear and angular accelerations with a single frequency. We hypothesize that this simple class can generate all velocity fields that have constant and linear terms with respect to position, as well as some quadratic fields with respect to position. This set includes fields with isolated sinks and squeeze lines that can be used to perform tasks such as sensorless part orientation. Several of these fields have been verified on our programmable parts-feeding oscillatory device (PPOD). The PPOD is a parallel manipulator similar to a Stewart platform, but with flexures as joints. An iterative learning control algorithm is described that moves the platform with the six-degree-of-freedom periodic motion that creates the desired velocity field.