Bipolar planetary nebulae (BPNe) offer a unique opportunity to test models that aim to reproduce the PNe morphologies. In particular, kinematic studies of BPNe allow a reconstruction of the 3D structure of the nebula, otherwise hidden in imaging studies. With this aim in mind we have obtained long-slit echelle spectra of a sample of PNe which cover the full range of observed bipolar morphologies, from elliptical to highly collimated. The analysis of our kinematical data reveals equatorial expansion velocities in the low to medium range (3 to 16 km s-1), while the polar expansion velocities range from 18 to 100 km s-1. We find that the kinematics of the PN K 3-46 can only be explained by a decrease in the expansion velocity with time. The kinematical ages, calculated by using distances estimated from Galactic rotation curves, when available, or by using statistical values, show that the BPNe in our sample - even those which show non-extreme collimation - appear to be young. We have compared our results with the latest theoretical models of BPN formation, and find good agreement between the observed expansion velocities and the numerical models that use magnetic fields coupled with stellar rotation as the collimation mechanism.