On certain methods of determining the ellipses and ellipsoids of the positioning accuracy of robot manipulators

When analysing the problem of positioning accuracy of robot manipulators it is important to know how large may random deviations of the hand be from the desired position if the joint positioning errors possess a normal distribution. Two simple methods of determining the ellipses and ellipsoids of probability concentration are proposed. One of them consists in finding at first the polygon or polyhedron of the positioning accuracy, and then in finding the ellipse or ellipsoid of the principal axes and second order moments coinciding with those of the polygon or polyhedron, respectively. In the second of the proposed methods a computer generates random Gaussian deviations from the desired joint positions. The calculated numerous positioning errors are forming an elliptical or ellipsoidal pattern demonstrating good agreement with theortically obtained ellipses or ellipsoids of probability concentration.