  We present generalizations of the spin Sutherland systems obtained earlier by
Blom and Langmann and by Polychronakos in two different ways: from SU(n)
Yang--Mills theory on the cylinder and by constraining geodesic motion on the
N-fold direct product of SU(n) with itself, for any N>1. Our systems are in
correspondence with the Dynkin diagram automorphisms of arbitrary connected and
simply connected compact simple Lie groups. We give a finite-dimensional as
well as an infinite-dimensional derivation and shed light on the mechanism
whereby they lead to the same classical integrable systems. The
infinite-dimensional approach, based on twisted current algebras (alias
Yang--Mills with twisted boundary conditions), was inspired by the derivation
of the spinless Sutherland model due to Gorsky and Nekrasov. The
finite-dimensional method relies on Hamiltonian reduction under twisted
conjugations of N-fold direct product groups, linking the quantum mechanics of
the reduced systems to representation theory similarly as was explored
previously in the N=1 case.
