The goal of assembly sequencing is to plan a feasible series of operat
ions to construct a product from its individual parts. Previous resear
ch has investigated assembly sequencing under the assumption that part
s have nominal geometry. This paper considers the case where parts hav
e toleranced geometry. Its main contribution is an efficient procedure
that decides if a product admits an assembly sequence with infinite t
ranslations (i.e. translations that can be extended arbitrarily far al
ong 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 pro
posed which generates assembly sequences that are feasible only for so
me values of the toleranced dimensions. If this procedure produces no
such sequence, then no instance of the product is assemblable. These t
wo procedures are described for 2D assemblies made of polygonial parts
and for 3D assemblies made of polyhedral parts. So far, only the firs
t has been implemented (for the planar case). This work assumes a simp
le, but non-trivial tolerance language that falls short of capturing a
ll 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.