A systematic formulation of dynamic equations for robot manipulators with elastic links

Although a variety of formulation schemes for the dynamic equations of robot manipulators with rigid links can be found in the literature, an efficient method of the formulation for robot manipulators with elastic links is not well known. Accordingly, this work presents the derivation of the equations of motion for application to mechanical manipulators with elastic links. The formulation is conducted analytically using Hamilton's principle. The resultant equations consist of the terms of inertial, Coriolis, centrifugal, gravitational, and exerted forces. They are expressed in terms of a set of independent generalized coordinates. In contrast to conventional variational approaches, the present method provides an efficient and systematic way for obtaining the compact symbolic equations of flexible manipulator systems. Two examples are presented to illustrate the proposed methodology. Firstly, a three-link flexible manipulator with three revolute joints is studied. A flexible manipulator consisting of a prismatic joint and a discrete mass is the second model.