  A Divide with cusps is the image of a proper generic immersion from finite
intervals and circles into a $2$-disk which allows to have cusps. A divide with
cusps is the generalization of the notion of the divide which is introduced by
A'Campo. From a divide with cusps, we can define the associated link in $S^3$.
In this paper, we give the characterization of the link in $S^3$ which can be
described as the associated link of a divide with cusps. In particular, we
prove that every strongly invertible link and $2$-periodic link can be
described as the link of a divide with cusps.
