We construct a family of (n + 1)-component links $\mathcal{L}_n$
which are closures of rational 3-string braids
$(\sigma_1^{-1/2}\sigma_2^2)^n$
and show that for n \geq 3 they arise as singular sets of hyperbolic
$\pi-orbifolds$. Moreover, their 2-fold branched coverings are described
by Dehn surgeries.
