We present new medium resolution kinematic data for a sample of 21 dwarf early-type galaxies (dEs) mainly in the Virgo cluster, obtained with the WHT and INT telescopes at the Roque de los Muchachos Observatory (La Palma, Spain). These data are used to study the origin of the dwarf elliptical galaxy population inhabiting clusters. We confirm that dEs are not dark matter dominated galaxies, at least up to the half-light radius. We also find that the observed galaxies in the outer parts of the cluster are mostly rotationally supported systems with disky morphological shapes. Rotationally supported dEs have rotation curves similar to those of star forming galaxies of similar luminosity and follow the Tully-Fisher relation. This is expected if dE galaxies are the descendant of low luminosity star forming systems which recently entered the cluster environment and lost their gas due to a ram pressure stripping event, quenching their star formation activity and transforming into quiescent systems, but conserving their angular momentum.