Dynamic modeling of closed-chain robotic manipulators in the presence of frictional dynamic forces: A planar case

Abstract

In this paper, the phenomenon of impact-contact in a closed-loop robotic chain has been dynamically modeled. The motion of this system, which comprises rigid links and ideal joints, has two phases. In the flight phase, the system is suspended in the air and moves only under the effect of Earth’s gravity. And in the impact phase, the mentioned robotic mechanism collides with a rough surface. We first present the direct form of dynamic equations for an open chain robotic system in the suspension phase. Then by applying the constraints that originate from the closed topology of the examined kinematic chain, the differential equations of the closed-loop system are obtained for the flight phase. In the impact phase, the contact force model is employed for modeling the impact-contact phenomenon. Although this method of impact modeling is more realistic, it leads to the stiffening of motion equations. In order to solve these equations, a special computational algorithm has been developed in this paper. To achieve more realistic results, the force of friction has also been considered in the collision of system joints with the ground. The dynamic formulations of friction have been used to obtain the friction force. In these models, an additional state variable is added to system variables in order to simulate some of the existing friction phenomena. Another objective of this paper is to present a criterion for selecting the most suitable model for simulating the motion of closed-loop robotic systems in the presence of friction. In this regard, the four dynamic friction force models of Dahl, reset integrator, LuGre, and elasto-plastic have been compared with the two static models of Coulomb and Bengisu & Akay. Although the developed algorithm is able to simulate any closed-loop robotic system that comes into contact with an uneven surface, the simulation of a 5-rigid-link closed-loop mechanism in collision with a rough surface of sinusoidal profile has been presented in this paper.