A Finite Element/Lagrange Approach to Modeling Lightweight Flexible Manipulators

This paper presents a finite element/Lagrangian approach for the mathematical modeling of lightweight flexible manipulators. Each link of the manipulator is treated as an assemblage of a finite number of elements for each of which kinetic and potential energies are derived. These elemental kinetic and potential energies are then suitably combined to derive the dynamic model for the system. It is contended that satisfactory modeling and analysis of the manipulator dynamics can lead to the use of advanced control techniques to solve some of the problems associated with the flexure of otherwise attractive lightweight manipulator arms. Detailed model development and simulation results for the case of a two-link manipulator system are presented.