The goal of this article is to develop practical descriptions of the relationship between forces and motions in sliding manipu lation. We begin by reviewing the limit surface, a concept from the mechanics of sliding bodies that uses kinematic analysis to find the force and moment required to produce any given sliding motion. Next we provide experimental results showing that the limit surface only approximates the actual force-motion relationship. Then we look at other approximations that can be used to provide a simplified model useful in control, planning, and simulation of manipulation. These approximations include square pyramids, cones, ellipsoids, and ellipsoids with facets removed. Different approximations may be most appropriate, depending on the required computational speed and accuracy and the need to produce conservative results.
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