  According to Etingof and Varchenko, the classical dynamical Yang-Baxter
equation is a guarantee for the consistency of the Poisson bracket on certain
Poisson-Lie groupoids. Here it is noticed that Dirac reductions of these
Poisson manifolds give rise to a mapping from dynamical r-matrices on a pair
$\L\subset \A$ to those on another pair $\K\subset \A$, where $\K\subset
\L\subset \A$ is a chain of Lie algebras for which $\L$ admits a reductive
decomposition as $\L=\K+\M$. Several known dynamical r-matrices appear
naturally in this setting, and its application provides new r-matrices, too. In
particular, we exhibit a family of r-matrices for which the dynamical variable
lies in the grade zero subalgebra of an extended affine Lie algebra obtained
from a twisted loop algebra based on an arbitrary finite dimensional self-dual
Lie algebra.
