In anticipation of the Gaia astrometric mission, a sample of spectroscopic
binaries is being observed since 2010 with the Sophie spectrograph at the
Haute--Provence Observatory. Our aim is to derive the orbital elements of
double-lined spectroscopic binaries (SB2s) with an accuracy sufficient to
finally obtain the masses of the components with relative errors as small as 1
% when combined with Gaia astrometric measurements. In order to validate the
masses derived from Gaia, interferometric observations are obtained for three
SB2s in our sample with F-K components: HIP 14157, HIP 20601 and HIP 117186.
The masses of the six stellar components are derived. Due to its edge-on
orientation, HIP 14157 is probably an eclipsing binary. We note that almost all
the derived masses are a few percent larger than the expectations from the
standard spectral-type-mass calibration and mass-luminosity relation. Our
calculation also leads to accurate parallaxes for the three binaries, and the
Hipparcos parallaxes are confirmed.Comment: 10 pages, 3 figures, accepted by MNRA