Motion Equations Proper for Forward Dynamics of Robotic Manipulator with Flexible Links by Using Recursive Gibbs-Appell Formulation

In this article, a new systematic method for deriving the dynamic equations of motion for exible robotic manipulators is developed by using the Gibbs-Appell assumed modes method. The proposed method can be applied to the dynamic simulation and control system design of exible robotic manipulators. In the proposed method, the link de ection is described by a truncated modal expansion. All the mathematical operations are done by only 3 3 and 3 1 matrices. Also, all dynamic expressions of a link are expressed in the same link local coordinate system. Based on the developed formulation, an algorithm is proposed that recursively and systematically derives the equation of motion, then this method is compared with the recursive Lagrangian method. As shown, this method is computationally simpler and more e cient and it reduces a large amount of computational complexity. Finally, a computational simulation for a manipulator with two elastic links is presented to verify the proposed method.