Qualitative Study of a Robot Arm as a Hamiltonian System

A double pendulum subject to external torques is used as a model to study the stability of a planar manipulator with two links and two rotational driven joints. The hamiltonian equations of motion and the fixed points (stationary solutions) in phase space are determined. Under suitable conditions, the presence of constant torques does not change the number of fixed points, and preserves the topology of orbits in their linear neighborhoods; two equivalent invariant manifolds are observed, each corresponding to a saddle-center fixed point.