Dynamic analysis of multiple inclined and frictional impact-contacts in multi-branch robotic systems

•The dynamic modeling of multiple inclined impact-contacts in multi-branch robotic systems has been presented.•The G–A formulation, the regularized method, and the friction force model have been used to model the system's equations.•A criterion for choosing the most suitable contact and friction models for attaining realistic results has been presented.•The proposed algorithm deals with the stiffening of differential equations and detecting the exact moments of impact. In this paper, the dynamic behavior of a multi-branch robotic mechanism made up of n rigid links and suspended inside an enclosure with curved walls has been investigated. The system's motion occurs in two stages: the suspension stage and the impact stage. The recursive Gibbs–Appell formulation and the regularized method (which is able to compute the impact forces occurring during a short collision time) have been used to extract the system's motion equations. Furthermore, to increase the accuracy of modeling, a friction force has also been considered at the locations where robot joints collide with enclosure walls. The stiffening of differential equations (which originates from the adoption of the regularized method in modeling the impact-contact phenomenon), the inclined impacts of the robotic system, the precise detection of impact time, and the existence of multiple impacts are some of the fundamental challenges faced during simulation; and the structured algorithm proposed in this article has been able to deal with these challenges quite successfully. Lastly, to show the precision and efficacy of the suggested algorithm, the motion of a 10-link, 4-branch robotic mechanism has been simulated and analyzed using several contact and friction force models.