  We propose Lagrangian formulations of a three-particles translation invariant
$N=4$ superconformal mechanics based on the standard and twisted $(1,4,3)$
supermultiplets. We show that in the appropriate set of coordinates, in which
the bosonic kinetic terms for each of the two cases take conformally-flat
forms, the corresponding models produce just similar physical systems with the
flipped angular part of bosonic potential $U(x)\rightarrow 1/U(x)$. This
flipping looks so simple only being written in the "angle" variable, while in
the standard variables it looks more complicated to preserve the superconformal
symmetry. We demonstrate at both the superfield and the component level, how
familiar $N=4$ supersymmetric 3-particles models, including $3-Calogero$, ${\it
BC_2}$ and ${\it G_2}$ ones, can be constructed with twisted supermultiplets.
We also present some new explicit examples of 3-dimensional superconformal
mechanics.
