Statics as a Means to Assess the Sensitivity of a Manipulator to Kinematic Parameter Deviations

The paper suggests a new method to determine the dependence of the pose of a manipulator end-effector on the dimensional variations of the manipulator rigid links. Based on the principle of virtual work, the method is applicable to all statically determinate manipulators, i.e., to the manipulators whose joint reactions can be found by resorting to equilibrium equations only. The distinctive feature of the proposed method over the previous ones is the ability to keep the complexity of the kinematic model of the analyzed manipulator to a minimum: no generalized kinematic model is necessary even in case a nominally special-geometry manipulator transforms into a general-geometry manipulator when geometric inaccuracies are taken into account. A numerical example shows application of the proposed method to a case study. Use of the method in kinematic calibration of manipulators is also outlined.