  The dibaryon model for $NN$ interaction, which implies the formation of an
intermediate six-quark bag dressed by a $\sigma$-field, is applied to the $3N$
system, where it results in a new three-body force of scalar nature between the
six-quark bag and a third nucleon. A new multicomponent formalism is developed
to describe three-body systems with nonstatic pairwise interactions and
non-nucleonic degrees of freedom. Precise variational calculations of $3N$
bound states are carried out in the dressed-bag model including the new scalar
three-body force. The unified coupling constants and form factors for $2N$ and
$3N$ force operators are used in the present approach, in a sharp contrast to
conventional meson-exchange models. It is shown that this three-body force
gives at least half the $3N$ total binding energy, while the weight of
non-nucleonic components in the $^3$H and $^3$He wavefunctions can exceed 10%.
The new force model provides a very good description of $3N$ bound states with
a reasonable magnitude of the $\sigma NN$ coupling constant. A new Coulomb $3N$
force between the third nucleon and dibaryon is found to be very important for
a correct description of the Coulomb energy and r.m.s. charge radius in $^3$He.
In view of the new results for Coulomb displacement energy obtained here for
A=3 nuclei, an explanation for the long-term Nolen--Schiffer paradox in nuclear
physics is suggested. The role of the charge-symmetry-breaking effects in the
nuclear force is discussed.
