  We study simple branched coverings of degree d of the 2- and 3- dimensional
sphere branched over oriented links. We demonstrate how to use braid charts to
develop embeddings of these into $S^k \times D^2$ for $k=2,3 when $d=2,3$. This
is an initial part of our study and represents the manuscript submitted to the
RIMS workshop at Intelligence of Low Dimensional Topology.
