  We perform an analysis of angular distributions in semileptonic decays of
charmed baryons $B_1^{(\prime)}\to B_2^{(\prime)}(\to
B_3^{(\prime)}B_4^{(\prime)})\ell^+\nu_{\ell}$, where the
$B_1=(\Lambda_c^+,\Xi_c^{(0,+)})$ are the SU(3)-antitriplet baryons and
$B_1'=\Omega_c^-$ is an SU(3) sextet. We will firstly derive analytic
expressions for angular distributions using helicity amplitude technique. Based
on the lattice QCD results for $\Lambda_c^+\to\Lambda$ and $\Xi_c^0\to\Xi^-$
form factors and model calculation of the $\Omega_c^0\to\Omega^-$ transition,
we predict branching fractions: $\mathcal{B}(\Lambda_{c}^{+} \rightarrow p
\pi^{-} e^{+} \nu_{e})=2.48(15)\%$, $\mathcal{B}(\Lambda_{c}^+\rightarrow p
\pi^{-}\mu^{+}\nu_{\mu})=2.50(14)\%$, $\mathcal{B}(\Xi_{c}\rightarrow \Lambda
\pi^{-}e^{+}\nu_{e})=2.40(30)\%$, $\mathcal{B}(\Xi_{c}\rightarrow \Lambda
\pi^{-}\mu^{+}\nu_{\nu})=2.41(30)\%$, $\mathcal{B}(\Omega_{c}\rightarrow
\Lambda K^{-}e^{+}\nu_{e})=0.362(14)\%$, $\mathcal{B}(\Omega_{c}\rightarrow
\Lambda K^{-}\mu^{+}\nu_{\nu})=0.350(14)\%$. Besides, we also predict the
$q^2$-dependence and angular distributions of these processes, in particular
the coefficients for the $\cos n\theta_{\ell}$ ($\cos n\theta_{h}$, $\cos
n\phi$) $(n=0, 1, 2, \cdots)$ terms. This work can provide a theoretical basis
for the ongoing experiments at BESIII, LHCb and BELLE-II.
