  We present near-IR K-band intermediate-dispersion spatially-resolved
spectroscopic observations of a limited sample of bipolar planetary nebulae
(PNe). The spectra have been used to determine the excitation mechanism of the
H2 molecule using standard line ratios diagnostics. The H2 molecule is
predominantly shock-excited in bipolar PNe with broad equatorial rings, whereas
bipolar PNe with narrow equatorial waists present either UV excitation at their
cores (e.g., Hb 12) or shock-excitation at their bipolar lobes (e.g., M1-92).
The shock-excitation among bipolar PNe with ring is found to be correlated with
emission in the H2 1-0 S(1) line brighter than Br{\gamma}. We have extended
this investigation to other PNe with available near-IR spectroscopic
observations. This confirms that bipolar PNe with equatorial rings are in
average brighter in H2 than in Br{\gamma} and show dominant shock excitation.
