  We reproduce the expansion velocity--radius ($V_{\rm{exp}}$--$R_{\rm{n}}$)
relation in planetary nebulae by considering a simple dynamical model, in order
to investigate the dynamical evolution and formation of planetary nebulae. In
our model, the planetary nebula is formed and evolving by interaction of a fast
wind from the central star with a slow wind from its progenitor, the AGB star.
In particular, taking account of the mass loss history of the AGB star makes us
succeed in the reproduction of the observed $V_{\rm{exp}}$-$R_{\rm{n}}$
sequence. As a result, examining the ensemble of the observational and
theoretical evolution models of PNe, we find that if the AGB star pulsates and
its mass loss rate changes with time (from $\sim 10^{-6.4}M_{\odot}$ yr$^{-1}$
to $\sim 10^{-5}M_{\odot}$ yr$^{-1}$), the model agrees with the observations.
In terms of observation, we suggest that there are few planetary nebulae with
larger expansion velocity and smaller radius because the evolutionary
time-scale of such nebulae is so short and the size of nebulae is so compact
that it is difficult for us to observe them.
