  We investigate the processes $e^+e^-$ annihilating to $J/\psi\pi\pi$,
$\psi^\prime\pi\pi$ and $h_c\pi\pi$. The coupled-channel effects induced by the
couplings between the widely accepted $D$-wave charmonium $\psi(4160)$ and
$D_1D$, $D_1D^*$ and $D_2D^*$ charmed meson pairs in the $S$-wave state with
couplings given by heavy quark spin symmetry are analyzed. The line shapes show
the presence of cusps that result from the singularities of the rescattering
loops, which could be helpful in understanding the nature of $Y(4260)$,
$Y(4360)$, $Z_c(3900)$/$Z_c(3885)$ and $Z_c(4020)$/$Z_c(4025)$.
