| The vibratory bowl feeder is
the oldest and still most common approach to the automated feeding (orienting)
of industrial parts. In this paper, the authors consider a class of vibratory
bowl filters that can be described by removing polygonal sections from the
track; this class of filters is referred to as traps. For an n-sided polygonal
part and an m-sided polygonal trap, an O(n2m log n) algorithm is given 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, the authors 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 runtimes of the 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
the algorithms range from linear to low-degree polynomial. |
