The toppling graph: designing pin sequences for part feeding

We consider a sensorless approach to feeding parts on a conveyor belt using pins (rigid barriers) to topple parts into desired orientations. Given the 2D projection of an n-sided convex polyhedral part, its center of mass, and coefficients of friction, we give an O(n/sup 2/) algorithm to compute the "toppling graph", a new data structure that represents the mechanics of toppling, including rolling and jamming. The toppling graph can be used to identify critical pin heights that permit toppling. We compare pin heights predicted by the graph with physical experiments, and give a complete O(n/sup 3n/) algorithm for designing pin sequences.