  The Penrose transform between twistors and the phase space of massless
particles is generalized from the massless case to an assortment of other
particle dynamical systems, including special examples of massless or massive
particles, relativistic or non-relativistic, interacting or non-interacting, in
flat space or curved spaces. Our unified construction involves always the
\it{same} twistor Z^A with only four complex degrees of freedom and subject to
the \it{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 displayed by the fact that they all share the same twistor
description. Our single twistor approach seems to be rather different and
strikingly economical construction of twistors compared to other past
approaches that introduced multiple twistors to represent some similar but far
more limited set of particle phase space systems.
