Abstract

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 #t 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-speci#c sequence of fence angles #1#. Second, we consider the problem of #xturing convex polygonal parts using a right angle #xture and one clamp #2#. The challenge is to de#ne appropriate tolerance classes and to argue that a solution # a feeding strategy or a #xture # is guaranteed for all parts in the tolerance class. We propose two new parametric tolerance classes. For each, we giveanO#n# time algorithm for testing if an n-sided part is in the class. For feeding we givean O#n 2 # time algorithm to compute the maximum radius of a circular tolerance zone around eachvertex. Numerical experiments provide evi...

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