Abstract
A totally new probabilistic method is introduced which can be used to obtain a global map of the distribution of the velocity and force transmission characteristics of robotic manipulators. The method yields the global distributions of volumes of the velocity and force ellipsoids, the eigenvectors, the eigenvalues, and the condition numbers. It utilizes the most basic definition of the properties of the mapping functions between the joint coordinates and the Cartesian (task) coordinates. The method is extremely simple, numerical in nature, and readily implementable on a computer. It requires very simple and limited analytical formulations. No inverse calculations are involved. The method furnishes a very simple and effective tool for solving a number of synthesis, performance evaluation, and task planning problems. In Part II of this paper, the method is utilized for optimal positioning of task spaces within workspaces of manipulators. Several examples are presented.
