  We present a systematic procedure to obtain singular solutions of the
constant quantum Yang-Baxter equation in arbitrary dimension. This approach,
inspired in the Lie (super)algebra structure, is explicitly applied to the
particular case of (graded) contractions of the orthogonal real algebra
${\mathfrak{so}}(N+1)$. In this way we show that "classical" contraction
parameters which appear in the commutation relations of the contracted Lie
algebras, become quantum deformation parameters, arising as entries of the
resulting quantum $R$-matrices.
