Empirical evidence suggests a tantalising but unproven link between various indicators of solar activity and the barycentric motion of the Sun. The latter is exemplified by transitions between regular and more disordered motion modulated by the motio
ns of the giant planets, and rare periods of retrograde motion with negative orbital angular momentum. An examination of the barycentric motion of exoplanet host stars, and their stellar activity cycles, has the potential of proving or disproving the Suns motion as an underlying factor in the complex patterns of short- and long-term solar variability indices, by establishing whether such correlations exist in other planetary systems. A variety of complex patterns of barycentric motions of exoplanet host stars is demonstrated, depending on the number, masses and orbits of the planets. Each of the behavioural types proposed to correlate with solar activity are also evident in exoplanet host stars: repetitive patterns influenced by massive multiple planets, epochs of rapid change in orbital angular momentum, and intervals of negative orbital angular momentum. The study provides the basis for independent investigations of the widely-studied but unproven suggestion that the Suns motion is somehow linked to various indicators of solar activity. We show that, because of the nature of their barycentric motions, the host stars HD168443 and HD74156 offer particularly powerful tests of this hypothesis.
