This enzyme interconverts L-rhamnose and L-rhamnulose. In some species, including E. coli, this is the first step in rhamnose catabolism. Sequential steps are catalyzed by rhamnulose kinase (rhaB), then rhamnulose-1-phosphate aldolase (rhaD) to yield glycerone phosphate and (S)-lactaldehyde. Characterization of this family is based on members in E. coli and Salmonella. [Energy metabolism, Sugars]