Calibration of parallel kinematics machine-tools using small displacement torsors

The accuracy of a machine-tool depends on manufacturing and assembly errors, backlash in the structure and the links, thermal variations, vibrations, and others. The method presented in this paper deals with manufacturing and assembly errors but it can be adapted to other sources of errors. This method uses the concept of Small Displacement Torsors (SDT) to the calibration of parallel kinematics machine-tools. The following hypothesis is made: the defaults of the structure can be modelled by a combination of small displacements of the surfaces in contact. The method consists first of all in modelling each link by a SDT expressed in the local frame of the link (n parameters characterize the defaults of the structure). Then each torsor is written in the frame of the structure where measurements are done. The value of the components of the torsors depends on the pose (position and orientation) of the tool. The relations between the torsors and the tool pose are calculated (N equations connect the parameters to the pose of the tool). Then the pose error is measured in m correctly selected points, so that the n parameters can be identified solving the equation : E=M.D, where E is the vector containing the measured pose errors ; M is the invertible matrix formed with the relations between the torsors and the tool pose ; D is the vector containing the parameters of the torsors. After the identification of vector D, the hypothesis of small displacement must be verified. Finally the pose error of the tool can be calculated in all the working volume. This paper presents the general method based on the Small Displacement Torsors. The links used in machine-tools is modelled by SDT. Then this method is applied to the calibration of the Hita-STT machine-tool, an industrial prototype. The objective is to reach an absolute accuracy of less than 10 microns with a relative accuracy of 5 microns, considering manufacturing and assembly errors in the first calibration phase.