A total solution to kinematic calibration of hexapod machine tools with a minimum number of measurement configurations and superior accuracies

A total solution to the kinematic calibration should encompass various procedures consisting of error modeling, measurement, identification of kinematic parameters and compensation for the errors. A viable solution should further entail a feasible number of measurement configurations while yielding accuracies acceptable to machine tool industries. The existing solutions suffer deficiencies especially with respect to the totality, viability and acceptable accuracies. In an attempt to remedy these deficiencies, the authors of this paper have proposed an optimized method encompassing the whole kinematic calibration procedures. This method has been verified by simulation and experiments and could give considerably superior results compared with the existing achievements. By employing only eleven measurement configurations, the maximum position and orientation errors of the upper platform in the experiments amounted to 0.1 mm and 0.03°, respectively. Much better results have been obtained by simulation, which implies that the accuracies can still further improve if some uncertainties such as backlash and other manufacturing errors usually existing in a laboratory device diminish in its industrial counterpart. In the proposed model, the hexapod workspace was first investigated to find general guidelines for maximum observability. The results were subsequently used in the main identification module. The required number of optimized configurations to achieve acceptable accuracies could thus considerably decrease to a feasible limit. A simple and accurate image processing method has been employed for the spatial measurement of the position and orientation of the moving platform. The identification jacobian matrix was used to evaluate the observability of the measurement configurations and determine optimum number of configurations for minimum identification error. Singular value decomposition and observability indices were used for this purpose. The real values of the kinematic parameters were identified by minimization of a cost function based on Levenberg-Marquardt least-square algorithm. In order to provide clues as to optimally directing the expensive manufacturing time and resources, a comparative study has also been carried out on the degree of influence each kinematic parameter exerts on the final accuracy.