No abstract

The vibratory bowl feeder is the oldest and still most common approach to the automated feeding (orienting) of industrial parts. In this paper we consider a class of vibratory bowl filters that can be described by removing polygonal sections from the track; we refer to this class of filters as traps.For an n-sided polygonal part and an m-sided polygonal trap, we give an O(n 2 m log n) algorithm to decide whether the part in a specific orientation will safely move across the trap or will fall through the trap and thus be filtered out. For an n-sided convex polygonal part and m-sided convex polygonal trap, this bound is improved to O((n + m) log n).Furthermore, we show how to design various trap shapes, ranging from simple traps to general polygons which will filter out all but one of the different stable orientations of a given part. Although the run times of our design algorithms are exponential in the number of trap parameters, many industrial part feeders use few-parameter traps (balconies, canyons, slots); in these cases the running times of our algorithms range from linear to low degree polynomial.

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