Dynamics and control of a planar manipulator with elastic links

A linearized model of a planar manipulator with two elastic links is derived. The elastic deflections are developed as a Rayleigh-Ritz series of the cantilevered modes of a uniform beam. The mass matrix is obtained by using the concept of partial velocities. It is shown for a typical example that the free vibration frequencies of the Iinearized model move by less than 4% as the elbow joint angle is varied. On the other hand, the vibration frequencies of the arm with locked joints are a strong function of the elbow angle. The lowest locked-joints frequency represents the maximum control bandwith attainable when a classical PD compensator is used for each joint.