  We combine and extend the work of Alexander & Antman \cite{alexander.82} and
Fuller \cite{fuller.71,fuller.78} to give a framework within which precise
definitions can be given of topological and geometrical quantities
characterising the contortion of open rods undergoing large deformations under
end loading. We use these definitions to examine the extension of known results
for closed rods to open rods. In particular, we formulate the analogue of the
celebrated formula $Lk=Tw+Wr$ (link equals twist plus writhe) for open rods and
propose an end rotation, through which the applied end moment does work, in the
form of an integral over the length of the rod. The results serve to promote
the variational analysis of boundary-value problems for rods undergoing large
deformations.
