On the dynamics of multi-closed-chain robotic mechanisms

Here, a recursive technique based on the Gibbs–Appell (G–A) and the Newton’s impact formulas for dynamic modeling of multi-closed-loop mechanisms has been presented. Each closed loop of the said mechanisms comprises an arbitrary number of rigid links. The challenges encountered in the present research are the following: (1) the relatively large number of the dependent generalized coordinates, (2) how to deal with the holonomic constraints that govern each closed loop in the mentioned mechanisms, (3) dealing with the end effectors of these systems in a way that does not cause any restriction in the recursive method presented, and (4) considering the dynamic coupling between the loops of such linkages. In this article, all these challenges have been responded through the presented dynamic equations and graphical figures. Although the stated equations are valid for all types of linkages belonging to this class of robotic systems, a 4RRR mechanism has been selected as the case study in this work. This research is concluded by simulating the movements of the abovementioned mechanism in the impact and non-impact phases and validating the responses of the system by means of the work and energy principles. •The mathematical modeling of the multi-closed-chain robotic mechanisms has been presented.•The Gibbs–Appell formulation and the Newton’s impact law in recursive form have been used.•An algorithm to detect the exact moments of impact has been proposed.•To divide the mentioned mechanism into several closed loops, a systematic method has been applied.•Presenting a criterion for validating the simulation results.