  We consider the Dirichlet Laplacian in a two-dimensional strip composed of
segments translated along a straight line with respect to a rotation angle with
velocity diverging at infinity. We show that this model exhibits a "raise of
dimension" at infinity leading to an essential spectrum determined by an
asymptotic three-dimensional tube of annular cross-section. If the
cross-section of the asymptotic tube is a disk, we also prove the existence of
discrete eigenvalues below the essential spectrum.
