TABLE OF CONTENTS Jingliang Chen, University of California at Berkeley, USA
Ken Goldberg, University of California at Berkeley, USA
Mark H. Overmars, University of Utrecht, The Netherlands
Dan Halperin, Tel Aviv University, Isreal
Karl F B hringer, University of California at Berkeley, USA
Yan Zhuang, University of California at Berkeley, USA
Parts are not ideal. Designers and machinists cope with variation in part shape by specifying tolerance zones around a nominal part geometry: all parts that fit within the zone form a tolerance class. In this paper we consider the issue of shape tolerance in two contexts. First, we consider the problem of feeding (orienting) convex polygonal parts on a conveyor belt with a part-specific sequence of fence angles [4]. Second, we consider the problem of fixturing convex polygonal parts using a right angle fixture and one clamp [15]. The challenge is to define appropriate tolerance classes and to argue that a solution - a feeding strategy or a fixture - is guaranteed for all parts in the tolerance class.
We propose two new parametric tolerance classes. For each, we give an O(n) time algorithm for testing if an n-sided part is in the class. For feeding we give an O(n 2) time algorithm to compute the maximum radius of a circular tolerance zone around each vertex. Numerical experiments provide evidence that this bound is tight. For fixturing we give an O(1) time algorithm to compute the maximum dimensions of rectangular tolerance zones. We implemented both algorithms and...
