Determination of dynamic accuracy of manipulation systems of robots with elastic hinges

Abstract

Two mathematical models for determining the dynamic accuracy of manipulation systems of robots with elastic hinges are considered. Mathematical models are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical models make it possible to determine the elastic deviations of manipulation systems of robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. One model is the exact implementation of the Lagrange method and makes it possible to determine the total elastic deviation of the manipulation system from the programmed motion trajectory. Another mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by two models are compared to the example of a three-link manipulation system. The considered models can be used when performing investigations of the mathematical accuracy of the manipulation systems of robots.