The Kinematic Invariants in Testing Error Motion of Machine Tool Linear Axes

摘要

A discrete kinematic geometry (DKG) approach is proposed in this paper to deal with the kinematic behavior of testing a machine tool linear axis when geometry errors are taken into consideration. An apparatus is set up in connection with a newly acquired 6D high-precision measurement instrument to investigate the actual motion of a worktable (three translations and three rotations) using the proposed model and the measurement data. The invariants for the evaluation of the discrete error motions, especially the spherical image curve and the directrix (Wang and Wang in Kinematic differential geometry and saddle synthesis of linkages. Wiley, Singapore, 2015, 1) are analyzed and compared with the ideal curves, which produce some remarkable global invariants of the erroneous motion of the work-table like the spherical envelope circle error surface and the directrix error space. Three test cases are presented to illustrate how the DKG approach is used to evaluate the accuracy of a machine tool linear axis in a comprehensive and systematical way.