Computing tolerance parameters for fixturing and feeding

Fixtures and feeders are important components of automated assembly systems: fixtures accurately hold parts and feeders move parts into alignment. These components can fail when part shape varies. Parametric tolerance classes specify how much variation is allowable. In this paper we consider fixturing convex polygonal parts using right-angle brackets and feeding polygonal parts on conveyor belts using sequences of vertical fences. For both cases, we define new tolerance classes and give algorithms for computing the parameter specifications such that the fixture or feeder will work for all parts in the tolerance class. For fixturing we give an O(1) algorithm to compute the dimensions of rectangular tolerance zones. For feeding we give an O(n(2)) algorithm to compute the radius of the largest allowable tolerance zone around each vertex. For each, we give an O(n) time algorithm for testing if an n-sided part is in the tolerance class.