Geometric Errors Versus Calibration in Manipulators with Less than 6 DOF

Calibration techniques can eliminate geometric error effects on positioning precision of a manipulator only if the real manipulator (that contains the geometric errors) and the ideal manipulator (the one without geometric errors) have the same workspace. In fact, in manipulators with less than six degrees of freedom (dof) some geometric errors may alter the nature of the manipulator workspace making calibration techniques ineffective. This paper demonstrates a statement that provides the conditions that the ideal and real manipulators must satisfy in order for them to have the same workspace. Hence, these conditions can be used to find the geometric parameters whose calibration does not improve the performances of the manipulator (therefore neutralizing the usefulness of their calibration). As a beneficial consequence, suitable values of manufacturing tolerances for different parameters can be chosen, thus reducing manufacturing costs. Finally, examples of application to 3-dof manipulators are given.