  We present a novel nonperturbative approach for calculating the form factors
of the quark-gluon vertex, in a general covariant gauge. The key ingredient of
this method is the exact all-order relation connecting the conventional
quark-gluon vertex with the corresponding vertex of the background field
method, which is Abelian-like. When this latter relation is combined with the
standard gauge technique, supplemented by a crucial set of transverse Ward
identities, it allows the approximate determination of the nonperturbative
behavior of all twelve form factors comprising the quark-gluon vertex, for
arbitrary values of the momenta. The actual implementation of this procedure is
carried out in the Landau gauge, in order to make contact with the results of
lattice simulations performed in this particular gauge. The most demanding
technical aspect involves the calculation of certain (fully-dressed) auxiliary
three-point functions, using lattice data as input for the gluon propagators
appearing in their diagrammatic expansion. The numerical evaluation of the
relevant form factors in three special kinematical configurations (soft gluon
and quark symmetric limit, zero quark momentum) is carried out in detail,
finding rather good agreement with the available lattice data. Most notably, a
concrete mechanism is proposed for explaining the puzzling divergence of one of
these form factors observed in lattice simulations.
