Error Sensitivity Analysis for Optimal Calibration of Parallel Kinematic Machines

Abstract

In this paper, error sensitivity analysis is discussed for the purpose of optimal calibration of parallel kinematic machines (PKMs). The idea is to find a less error sensitive area in the workspace for calibration. To do so, an error model is developed that takes into consideration all the geometric errors due to imprecision in manufacturing and assembly. Based on this error model, it is shown that the error mapping from the geometric errors to the pose error of the PKM depends on the Jacobian inverse. The Jacobian inverse would introduce spurious errors that would affect the calibration results, if used without proper care. Hence, it is suggested to select the areas in the workspace with smaller condition numbers for calibration. A case study is presented to illustrate the proposed method.

Global Quantitative Sensitivity Analysis and Compensation of Geometric Errors of CNC Machine Tool

“…Huang et al [23] applied matrix differential method to establish the error mapping function and identify the error source affecting the uncompensable pose error; and the results of this investigation were successfully applied in the machine tool's assembly. Xi et al [24] analyzed the sensitivity of the inverse Jacobian matrix for optimal calibration of parallel kinematic machines. The discretetime dynamic inversion compensation method [25] has been proposed based on approximating the unknown functions and unknown backlash by the fuzzy logic systems.…”