  We present a unified classical treatment of partially constrained elastic
rods. Partial constraints often entail singularities in both shapes and
reactions. Our approach encompasses both sleeve and adhesion problems, and
provides simple and unambiguous derivations of counterintuitive results in the
literature. Relationships between reaction forces and moments, geometry, and
adhesion energies follow from the balance of energy during quasistatic motion.
We also relate our approach to the balance of material momentum and the concept
of a driving traction. The theory is generalizable and can be applied to a wide
array of contact, adhesion, gripping, and locomotion problems.
