A Generalized Definition of Jacobian Matrix for Mechatronical Systems

Manipulator kinetostatic performances are usually i nvestigated considering only the geometrical structure of the r obot, neglecting the effect of the drive system. In some circumstances this approach may leads to errors and mistakes. This may happen if the actuators are not identical o each other or when the employed transmission ratio are not ide nt cal and/or not constant. The paper introduces the so called “Generalized Jac obi n Matrix” obtained identifying an appropriate matrix, generally diagonal, defined in order to: 1. properly weigh the different contributions of speed and force of each actuator. 2. describe the possible non-homogeneous behaviour of the drive system that depends on the configuration achieved by the robot. Theoretical analysis is supported by examples highl ighting some of the most common mistakes done in the evaluation of a manipulator kinetostatic properties and how they ca n be avoided using the generalized jacobian matrix.