  Based on axi-symmetric hydrodynamical simulations and 3D reconstructions with
Shape, we investigate the kinematic signatures of deviations from homologous
("Hubble-type") outflows in some typical shapes of planetary nebulae. We find
that, in most situations considered in our simulations, the deviations from a
Hubble-type flow are significant and observable. The deviations are systematic
and a simple parameterization of them considerably improves morpho-kinematical
models of the simulations. We describe such extensions to a homologous
expansion law that capture the global velocity structure of hydrodynamical
axi-symmetric nebulae during their wind-blown phase. It is the size of the
poloidal velocity component that strongly influences the shape of the position
velocity diagrams that are obtained, not so much the variation of the radial
component. The deviations increase with the degree of collimation of the nebula
and they are stronger at intermediate latitudes. We describe potential
deformations which these deviations might produce in 3D reconstructions that
assume "Hubble-type" outflows. The general conclusion is that detailed
morpho-kinematic observations and modeling of planetary nebulae can reveal
whether a nebula is still in a hydrodynamically active stage (windy phase) or
whether it has reached ballistic expansion.
