Assembly sequencing with toleranced parts

The goal of assembly sequencing is to plan a feasible series of operations to construct a product from its individual parts. Previous research has investigated assembly sequencing under the assumption that parts have nominal geometry. This paper considers the case where parts have toleranced geometry. Its main contribution is an efficient procedure that decides if a product admits an assembly sequence with infinite translations (i.e. translations that can be extended arbitrarily far along a fixed direction), that is feasible for all possible instances of the components within the specified tolerances. If the product admits one such sequence, the procedure can also generate it. For the cases where there exists no such assembly sequence, another procedure is proposed which generates assembly sequences that are feasible only for some values of the toleranced dimensions. If this procedure produces no such sequence, then no instance of the product is assemblable. These two procedures are described for 2D assemblies made of polygonial parts and for 3D assemblies made of polyhedral parts. So far, only the first has been implemented (for the planar case). This work assumes a simple, but non-trivial tolerance language that falls short of capturing all imperfections of a manufacturing process. In particular, it assumes that faces and edges have perfect relative orientations. Thus, it is only one step towards dealing with tolerances in assembly sequencing.