Dynamic modeling of planar closed-chain robotic manipulators in flight and impact phases

This paper presents a systematic procedure for the dynamic modeling of a closed-chain robotic system in both the flight and impact phases. In the proposed approach, first, a planar closed-chain system constructed of n rigid links and n+1 revolute joints is virtually converted to an open kinematic chain. Then, a recursive algorithm based on the Gibbs-Appell principle is applied to reduce the computational load of the developed model, which contains finite constraints. The normal impact phase of this closed-chain robotic system, which includes impulsive constraints, is modeled based on the Newton's kinematic impact law. Finally, computer simulations of a hexagonal closed-chain robotic system in both the flight and impact phases are carried out. This work is actually an extension of the previous investigation of the authors, which was restricted to the study of an open kinematic chain. So, in order to avoid duplication, only the necessary modifications in converting open kinematic chains to closed-chain robotic manipulators are presented here. To the best of our knowledge, this is the first time that a combination of finite and impulsive constraints in a closed-chain mechanical system has been recursively formulated. Since experimental verification of the proposed model is not easy to achieve in this case and no well-defined benchmark problems could be found to validate the model, the findings of this work are compared with the results obtained by simulating the same system in the “Working Model” computer software.