  We present a description of singular horizontal curves of a totally
nonholonomic analytic distribution in term of the projections of the orbits of
some isotropic subanalytic singular distribution defined on the nonzero
annihilator of the initial distribution in the cotangent bundle. As a
by-product of our first result, we obtain, under an additional assumption on
the constructed subanalytic singular distribution, a proof of the minimal rank
Sard conjecture in the analytic case. It establishes that from a given point
the set of points accessible through singular horizontal curves of minimal
rank, which corresponds to the rank of the distribution, has Lebesgue measure
zero.
