In manufacturing it is often necessary to orient parts prior to packing or assembly. We say that a planar part ispolygonal if its convex hull is a polygon. We consider the following problem: given a list ofn vertices describing a polygonal part whose initial orientation is unknown, find the shortest sequence of mechanical gripper actions that is guaranteed to orient the part up to symmetry in its convex hull. We show that such a sequence exists for any polygonal part by giving anO[n 2 logn) algorithm for finding the sequence. Since the gripper actions do not require feedback, this result implies that any polygonal part can be orientedwithout sensors.
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Communicated by Bruce Randall Donald.
This report describes research conducted in part while the author was a graduate student supported by NSF Grant DMC-8520475 and NASA-Ames Grant NCC 2-463 at the School of Computer Science at Carnegie Mellon University. The author is currently supported by a grant from the Faculty Research Initiation Fund at the University of Southern California.
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Goldberg, K.Y. Orienting polygonal parts without sensors. Algorithmica 10, 201–225 (1993). https://doi.org/10.1007/BF01891840