The planetary hypothesis of solar cycle is an old idea by which the planetary gravity acting on the Sun might have a non-negligible effect on the solar magnetic cycle. The advance of this hypothesis is based on phenomenological correlations between dynamical parameters of the Sun's movement around the barycenter of the Solar System and sunspots time series. In addition, several authors have proposed, using different methodologies that the first Grand Minima (GM) event of the new millennium is coming or has already begun. We present new fully three dimensional N-body simulations of the solar inertial motion (SIM) around the barycentre of the solar system in order to perform a phenomenological comparison between relevant SIM dynamical parameters and the occurrences of the last GM events (i.e., Maunder and Dalton). Our fundamental result is that the Sun acceleration decomposed in a co-orbital reference system shows a very particular behaviour that is common to Maunder minimum, Dalton minimum and the maximum of cycle 22 (around 1990), before the present prolonged minimum. We discuss our results in terms of a dynamical characterization of GM with relation to Sun dynamics and possible implications for a new GM event.