The motion of a pushed, sliding workpiece

It occurs frequently in robotic applications that a robot manipulates a workpiece which is free to slide on a work surface. Because the pressure distribution supporting the workpiece on the work surface cannot in general be known, the motion of the workpiece cannot be calculated uniquely. Yet despite this indeterminacy, several researchers have shown that sliding motions can be employed to accurately align workpieces without visual or other feedback. Here we find the locus of centers of rotation of a workpiece for all possible pressure distributions. The results allow a quantitative understanding of open-loop robot motions which guarantee the alignment of a workpiece. Several sample problems are solved using the results, including the distance that a flat "fence" or robot finger must push a polygonal workpiece to assure that a facet of the workpiece comes into alignment with the fence.