Inverse dynamic equation of motion for flexible link manipulators using recursive gibbs-appell formulation

In this article a new systematic method for deriving the inverse dynamic equations of motion for flexible robot manipulators is developed by using the Gibbs-Appell assumed modes method. In the proposed method, the link deflection is described by a truncated modal expansion. All the mathematical operations are done by only 3times3 matrices or 3times1 vectors. Also all dynamic expressions of a link are expressed in the same link local coordinate system. Based on developed formulation an algorithm is proposed that recursively and systematically derives the inverse dynamic equations of motion. Finally a computational simulation for a manipulator with two elastic links is presented to verify the proposed method.