Constraining the formation and evolution of multiple systems requires a rigorous characterization of these systems, which is constantly in demand for new methods allowing new detections as well as extending, confirming or supporting already existing observations. The goal of this thesis is to constrain the orbital parameters and dynamical masses of binary systems using data from Hipparcos and Gaia, two astrometric missions of the European Space Agency launched respectively in August 1989 and December 2013. The Hipparcos mission has largely set the basis for the study of astrometric binaries, and being strong of its 24 years gap with Gaia, the Hipparcos data are now experiencing a renewed attention, leading to the search for ways to efficien...