  In this paper we investigate locally nilpotent derivations on the polynomial
algebra in three variables over a field of characteristic zero. We introduce an
iterating construction giving all locally nilpotent derivations of rank $2$.
This construction allows to get examples of non-triangularizable locally
nilpotent derivations of rank $2$. We also show that the well-known example of
a locally nilpotent derivation of rank $3$, given by Freudenburg, is a member
of a large family of new examples of rank $3$ locally nilpotent derivations.
Our approach is based on considering all locally nilpotent derivations
commuting with a given one. We obtain a characterization of locally nilpotent
derivations with a given rank in terms of sets of commuting locally nilpotent
derivations.
