Using 2T-physics techniques the Penrose transform between twistors and the phase space of massless particles is generalized to an assortment of other (D=4) particles dynamical systems, including as special examples massless and massive particles, relativistic and non-relativistic, interacting and non-interacting, in flat space and curved spaces. The unified construction involves always the same twistor with only four complex degrees of freedom and subject to the same helicity constraint. Only the twistor to phase space transform differs from one case to another. Hence a unification of diverse particle dynamical systems is exhibited by the fact that all share the same twistor description. Finally, further generalizations to other dimensions and possible applications will be discussed.