This article discusses and explains the Hamiltonian formulation for a class of simple gauge
invariant mechanical systems consisting of point masses and idealized rods. The study of these
models may be helpful to advanced undergraduate or graduate students in theoretical physics to
understand, in a familiar context, some concepts relevant to the study of classical and quantum
field theories. We use a geometric approach to derive the Hamiltonian formulation for the model
considered in the paper: four equal masses connected by six ideal rods. We obtain and discuss the
meaning of several important elements, in particular, the constraints and the Hamiltonian vector
fields that define the dynamics of the system, the constraint manifold, gauge symmetries, gauge
orbits, gauge fixing, and the reduced phase space.