Design of a measurement system for simultaneously measuring six-degree-of-freedom geometric errors of a long linear stage

This study designs and characterizes a novel precise measurement system for simultaneously measuring six-degree-of-freedom geometric motion errors of a long linear stage of a machine tool. The proposed measurement system is based on a method combined with the geometrical optics method and laser interferometer method. In contrast to conventional laser interferometers using only the interferometer method, the proposed measurement system can simultaneously measure six-degree-of-freedom geometric motion errors of a long linear stage with lower cost and faster operational time. The proposed measurement system is characterized numerically using commercial software ZEMAX and mathematical modeling established by using a skew-ray tracing method, a homogeneous transformation matrix, and a first-order Taylor series expansion. The proposed measurement system is then verified experimentally using a laboratory-built prototype. The experimental results show that, compared to conventional laser interferometers, the proposed measurement system better achieves the ability to simultaneously measure six-degree-of-freedom geometric errors of a long linear stage (a traveling range of 250 mm).