Singularities of affine equidistants: projections and contacts

Using standard methods for studying singularities of projections and of contacts, we classify the stable singularities of affine $\lambda$-equidistants of $n$-dimensional closed submanifolds of ${\mathbb{R}}^q$, for $q\le 2n$, whenever $(2n,q)$ is a pair of nice dimensions.