| In this paper we present a
new framework for worst-case toleranced assembly planning of planar mechanical
systems. Unlike most assembly planners, which produce plans for nominal
parts, our framework incorporates the inherent imprecision of the manufacturing
process, which introduces uncertainties in the shape and size of the assembly
parts. It accounts for the uncertainty of the relative part placements in
the assembled state and allows planning for all assembly instances. Our
framework is more general than existing approaches in terms of the part
model, the tolerance specification model, and the type of motions used in
the assembly sequences. We describe efficient algorithms for computing the
sensitivity of part positioning to variations in part geometries, and for
incorporating these computations into the geometric core of existing assembly
planners for nominal parts.We show that the cost of accounting for toleranced
parts in planning is a multiplicative factor which is a polynomial of low
degree in the number of tolerance parameters. Our implementation and experiments
on five assembly models show that tolerancing significantly reduces the
volume of the space of valid motions for assembly sequence planning, and
that for translational motions this reduction depends linearly on the size
of the tolerance intervals.We conclude that geometric computation for assembly
planning with tolerance parts is time efficient and practical. |
