  In this article, we take the point of view that the charmed axial-vector
meson $D_{s1}(2460)$ is the conventional $c\bar{s}$ meson and calculate the
strong coupling constant $g_{D_{s1} D^* K}$ in the framework of the light-cone
QCD sum rules approach. The numerical values of strong coupling constants
$g_{D_{s1} D^* K}$ and $g_{D_{s0} D K}$ are very large, and support the
hadronic dressing mechanism. Just like the scalar mesons $f_0(980)$ and
$a_0(980)$, the scalar meson $D_{s0}(2317)$ and axial-vector meson
$D_{s1}(2460)$ may have small $c\bar{s}$ kernels of the typical $c\bar{s}$
meson size, the strong couplings to the hadronic channels (or the virtual
mesons loops) may result in smaller masses than the conventional $c\bar{s}$
mesons in the constituent quark models, and enrich the pure $c\bar{s}$ states
with other components.
