  Any ruled surface in Euclidean 3-space is described as a curve of unit dual
vectors in the algebra of dual quaternions (=the even Clifford algebra of type
(0,3,1)). Combining this classical framework and Singularity Theory, we
characterize local diffeomorphic types of singular ruled surfaces in terms of
geometric invariants. In particular, using a theorem of G. Ishikawa, we show
that local topological type of singular (non-cylindrical) developable surfaces
is completely determined by vanishing order of the dual torsion, that
generalizes an old result of D. Mond for tangent developables of non-singular
space curves. Our approach would be useful for analysis on singularities
arising in differential line geometry related with several applications such as
robotics, vision theory and architectural geometry.
