The orbital motion of non-contact double-lined spectroscopic binaries (SB2s), with periods of a few tens of days to several years, holds unique, accurate information on individual stellar masses, which only long-term monitoring can unlock. The combination of radial velocity measurements from high-resolution spectrographs and astrometric measurements from high-precision interferometers allows the derivation of SB2 component masses down to the percent precision. Since 2010, we have observed a large sample of SB2s with the SOPHIE spectrograph at the Observatoire de Haute-Provence, aiming at the derivation of orbital elements with sufficient accuracy to obtain masses of components with relative errors as low as 1 per cent when the astrometric measurements of the Gaia satellite are taken into account. In this paper, we present the results from 6 yr of observations of 14 SB2 systems with periods ranging from 33 to 4185 days. Using the TODMOR algorithm, we computed radial velocities from the spectra and then derived the orbital elements of these binary systems. The minimum masses of the 28 stellar components are then obtained with an average sample accuracy of 1.0+/-0.2 per cent. Combining the radial velocities with existing interferometric measurements, we derived the masses of the primary and secondary components of HIP 61100, HIP 95995 and HIP 101382 with relative errors for components (A,B) of, respectively, (2.0, 1.7) per cent, (3.7, 3.7) per cent and (0.2, 0.1) per cent. Using the CESAM2K stellar evolution code, we constrained the initial He abundance, age and metallicity for HIP 61100 and HIP 95995.