  A potential model for the interaction between a charmed baryon ($\Lambda_c$,
$\Sigma_c$, and $\Sigma_c^*$) and the nucleon ($N$) is constructed. The model
contains a long-range meson ($\pi$ and $\sigma$) exchange part and a
short-distance quark exchange part. The quark cluster model is used to evaluate
the short-range repulsion and a monopole type form factor is introduced to the
long-range potential to reflect the extended structure of hadrons. We determine
the cutoff parameters in the form factors by fitting the $NN$ scattering data
with the same approach and we obtain four sets of parameters (a -- d). The most
attractive potential (d) leads to bound $\Lambda_c N$ states with $J^\pi= 0^+$
and $1^+$ once the channel couplings among $\Lambda_c$, $\Sigma_c$ and
$\Sigma_c^*$ are taken into account. One can also investigate many-body
problems with the model. Here, we construct an effective $\Lambda_c N$
one-channel potential with the parameter set (d) and apply it to the 3-body
$\Lambda_c NN$ system. The bound states with $J=1/2$ and $3/2$ are predicted.
