Approximate modeling of robots having elastic links

A method to derive approximate dynamic models is presented, which consists of a system of ordinary differential equations whose order, for a given robot, is related to the desired order of approximation. Such models are obtained by using the Lagrangian approach and by expanding in a limited number of terms the generalized coordinates describing the exact shape of the beams constituting the robot. A procedure is given that allows, if implemented on a computer, the automatic generation of the models. With such a procedure, by using the symbolic language MACSYMA, the models of one- and two-link flexible robots have been developed. Simulation tests to validate the proposed approximate model are included. These tests show that satisfactory results in terms of dynamic behavior of the approximate model are obtainable even with a reduced order of approximation