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


Department of Mechanical Engineering,Iran University of Science and Technology


In this article, a new systematic method for deriving the dynamic equations of motion
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 33 and 31 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 ecient 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.