A recursive algorithm for dynamics of multiple frictionless impact-contacts in open-loop robotic mechanisms

Abstract

In this paper, the phenomenon of multiple impact-contacts has been dynamically modeled for an open kinematic chain with rigid links and revolute joints. The dynamic equations of the mentioned system have been extracted based on the recursive Gibbs–Appell formulation. The impact-contact phenomenon has been formulated by the regularized method in which the force of impact is a continuous function of the relative penetration and relative velocity of two colliding surfaces with respect to each other. The geometrical specifications and the mechanical properties of colliding surfaces are the two main parameters used in the modeling of viscoelastic contact force models. In this work, a recursive algorithm, which has been developed based on 3 × 3 rotation matrices to reduce the computational load, symbolically derives the motion equations of a multibody system that collides with surrounding surfaces at several points. The system under study includes the non-impact (flight) phase and the impact phase. Going from the flight phase to the impact phase and back, detecting the exact moment of impact, and also solving the differential equations of motion during a very short impact time have their particular challenges and complexities, which are dealt with in this work. In the next step, nine famous contact force models have been compared in order to select the most suitable model for simulation work. Finally, to show the accuracy and the capability of the presented algorithm, the dynamic behavior of an open-chain robotic mechanism consisting of 4 rigid links connected by revolute joints has been simulated and analyzed.