Simplest geometric example of a nonholonomic constraint is one for the movement of the tangent line along a smooth plane curve. We obtain a better contact with the curve and more interesting constraints if we substitute tangent lines with ÒosculatingÓ algebraic curves of degree $N\gt 1$. My talk is devoted to the vector distributions and sub-Riemannian structures raised from these geometric models, starting from the osculating conics and cubics.