| A systematic way of applying Lagrange's equation and the modal expansion approach to derive the dynamic model of an n-link flexible robotic manipulator, or an n-link manipulator containing both rigid and flexible links, has been developed. The formulation is based on Hamilton's principle and the modal analysis method. The dynamic models for both a single-link flexible manipulator and a two-link flexible manipulator have been developed. The stability analysis for a single-link flexible manipulator and a two-link flexible manipulator also have been completed. The results show that phase plane portraits of the vibration states and the tip deflections are limit cycles near the equilibrium points. The phase plane portraits of the joint movement are limit cycles near some equilibrium points and are saddle points near other equilibrium points. A tip position controller for the single-link flexible manipulator that minimizes the tip position tracking error and the beam vibration with and without control signal and state constraints is also designed. The steepest descent method is employed to design a controller that does not require measurement of the vibration modes of the system. |
