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Procedures to determine the principal directions of kinematic performance in serial robots

SUMMARY Assume that the end-effector of a serial mechanism with n-degrees of freedom arrives at the position p0, where it can change arbitrarily the direction of its movement. The physical conditions imply that this change in direction also alters its velocity. The kinematic performance ellipse represents the velocities according to the new direction of the system, and thus solving the problem of which direction will correspond to a maximum or minimum (principal directions) magnitude of the corresponding velocity. In this paper, a new procedure to calculate these principal directions is presented and contrasted with two of the most common procedures employed in the field. All three procedures are considered in some detail, in order to understand their underlying concepts and, therefore, gain a deeper understanding of the physical situation. They are all proved in standard examples.