  The theory of voltage graphs has become a standard tool in the study graphs
admitting a semiregular group of automorphisms. We introduce the notion of a
cyclic generalised voltage graph to extend the scope of this theory to graphs
admitting a cyclic group of automorphism that may not be semiregular. We use
this new tool to classify all cubic graphs admitting a cyclic group of
automorphisms with at most three vertex-orbits and we characterise
vertextransitivity for each of these classes. In particular, we show that a
cubic vertex-transitive graph admitting a cyclic group of automorphisms with at
most three orbits on vertices either belongs to one of 5 infinite families or
is isomorphic to the well-know Tutte-Coxeter graph.
