Minimal trap design

This paper addresses the issue of trap design for sensorless automated assembly. First, we present a simple algorithm that determines in O(nm α(nm) log(nm)) time whether an n-sided polygonal part will fall through an m-sided polygonal trap. We then introduce the notion of a minimal trap for a polygonal part, and develop an algorithm to design a family of minimal feeders built from these traps. The algorithm runs in O(kn^3+ε) time, where k is the number of stable orientations of P. Moreover, it is complete in the sense that we can always find a feeder, provided that one exists that rejects and supports the appropriate poses of the part.