We perform an analysis of angular distributions in semileptonic decays of charmed baryons B_1^{(prime )}rightarrow B_2^{(prime )}(rightarrow 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 the helicity amplitude technique. Based on the lattice quantum chromodynamics (QCD) results for Lambda _c^+rightarrow Lambda and Xi _c^0rightarrow Xi ^- form factors and model calculation of the Omega _c^0rightarrow Omega ^- transition, we predict the branching fractions: {mathcal {B}}(Lambda _{c}^{+} rightarrow Lambda (rightarrow p pi ^{-}) e^{+} nu _{e})=2.48(15)%, {mathcal {B}}(Lambda _{c}^+rightarrow Lambda (rightarrow p pi ^{-})mu ^{+}nu _{mu })=2.50(14)%, {mathcal {B}}(Xi _{c}^0rightarrow Xi ^-(rightarrow Lambda pi ^{-})e^{+}nu _{e})=2.40(30)%, {mathcal {B}}(Xi _{c}^0rightarrow Xi ^-(rightarrow Lambda pi ^{-})mu ^{+}nu _{nu })=2.41(30)%, {mathcal {B}}(Omega _{c}^0rightarrow Omega ^-(rightarrow Lambda K^{-})e^{+}nu _{e})=!0.362(14)%, {mathcal {B}}(Omega _{c}^0rightarrow Omega ^-!(rightarrow Lambda K^{-})mu ^{+!}nu _{nu })=0.350(14)%. We also predict the q^2 dependence and angular distributions of these processes, in particular the coefficients for the cos ntheta _{ell } (cos ntheta _{h}, cos nphi ) (n=0, 1, 2, ldots ) terms. This work can provide a theoretical basis for the ongoing experiments at BESIII, LHCb, and BELLE-II.