Shape tolerance in feeding and fixturing

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 give an O(n) time algorithm for testing if an n-sided part is in the class. For feeding we give an O(n) 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 xturing we give an O(1) time algorithm to compute the maximum dimensions of rectangular tolerance zones. We implemented both algorithms and report experimental results.