Conclusions. The proposed technique is simple to use and our test shows that it is amenable for deriving astrometry with milliarcsecond accuracy or better, beyond the diffraction limit of the telescope. The technique can be further improved by using simple devices to simultaneously record the spectra with 180 degrees angles. This device together with an optimized data analysis will further reduce the measurement errors. With tachoastrometry, radial velocities and astrometric positions can be measured simultaneously for many double line system binaries in an easy way. The method is not limited to binary stars, but can be applied to any astrophysical configuration in which spectral lines are generated by separate (non-rotational symmetric) regions.