  We present a new method for modelling the kinematics of galaxies from
interferometric observations by performing the optimization of the kinematic
model parameters directly in visibility-space instead of the conventional
approach of fitting velocity fields produced with the CLEAN algorithm in
real-space. We demonstrate our method on ALMA observations of $^{12}$CO
(2$-$1), (3$-$2) or (4$-$3) emission lines from an initial sample of 30 massive
850$\mu$m-selected dusty star-forming galaxies with far-infrared luminosities
$\gtrsim$$\,10^{12}\,$L$_{\odot}$ in the redshift range $z \sim\,$1.2$-$4.7.
Using the results from our modelling analysis for the 12 sources with the
highest signal-to-noise emission lines and disk-like kinematics, we conclude
the following: (i) Our sample prefers a CO-to-$H_2$ conversion factor, of
$\alpha_{\rm CO} = 0.92 \pm 0.36$; (ii) These far-infrared luminous galaxies
follow a similar Tully$-$Fisher relation between the circularized velocity,
$V_{\rm circ}$, and baryonic mass, $M_{\rm b}$, as more typical star-forming
samples at high redshift, but extend this relation to much higher masses $-$
showing that these are some of the most massive disk-like galaxies in the
Universe; (iii) Finally, we demonstrate support for an evolutionary link
between massive high-redshift dusty star-forming galaxies and the formation of
local early-type galaxies using the both the distributions of the baryonic and
kinematic masses of these two populations on the $M_{\rm b}\,-\,\sigma$ plane
and their relative space densities.
