Modeling a class of multilink manipulators with the last link flexible

Dynamic equations are derived for a class of multilink manipulators with the last link flexible. The manipulators have three degrees of freedom and are moved by three actuators. This class includes the elbow manipulator and the five-bar-linkage manipulator. Some reasonable assumptions that simplify the dynamic equations for control purposes are described, and the simplified dynamic equations are then presented. It is shown that, for pick-and-place operations, a rigid-body robot controller and a single flexible link controller may be combined to control the manipulator in a straightforward manner