Automated fast symbolic modeling of robotic manipulators with compliant links

This paper presents a systematic algorithm for deriving the dynamic equation for a multilink flexible manipulator using the symbolic language MATHEMATICA. The program, developed based on the recursive Lagrangian assumed mode method, is applicable to multilink flexible manipulators. In order to check the validity of the model, results are compared with simulation results of the same system with rigid arm and also finite element approach, and the results are then applied to determining dynamic load carrying capacity for the flexible manipulator. Techniques for overcoming computer memory limitation, simplifying intermediate derivation, omitting negligible term and improving efficiency of equation generation are discussed.