V-type roller linear guides can achieve extremely high motion accuracy through precision design and machining; however, theoretical research and methodologies in this field remain limited. This paper proposes a computational method for estimating the motion errors of V-type roller linear guides and establishes a four-degree-of-freedom error model that accounts for guide rail yaw errors, guide rail pitch errors, variations in roller positions, and the contact states of rollers. The effects of the error wavelength ratio, load, and number of roller rows on the motion error of a single V-type roller linear guide are investigated, and the mechanisms and characteristics of the error averaging effect are analyzed. The motion error characteristics of a double V-type roller linear guide are also discussed. Finally, the proposed model is applied to the development and motion error estimation of a double V-type roller linear guide for a grating ruling engine. The straightness of the carriage in the X and Y directions over a 600 mm travel distance reached 0.62 μm and 0.48 μm, respectively. Furthermore, a high-precision echelle diffraction grating with a wavefront PV of 0.21λ was fabricated. These results further validate the proposed model and provide guidance for the manufacturing error allocation and precision design of V-type roller linear guides.

The error motion of the precision rotary stage, particularly the tilt error motion, significantly influences the accuracy of machining and measuring equipment. Nonetheless, reliable and effective in situ measurement methods for tilt error motion are still limited. Based on the analysis of the conventional three-probe measurement method, this paper proposes a multi-probe measurement method using an ultra-precision reference plate with high-resolution displacement sensors. This method employs principles and methods to avoid harmonic suppression issues through optimal probe designs, enabling simultaneous quantification of tilt and axial error motions via error separation. Error separation techniques can effectively decouple motion errors from artifact form error, making them widely applicable in precision measurement data processing. Experimental validation confirmed that the synchronous measurement error is not greater than 4.69%, consequently affirming the metrological efficacy and reliability of the method. This study provides an effective method for real-time error characterization of rotary stages.

The rotational error motion of precision aerostatic rotary stages substantially affects the accuracy of machining and measuring equipment. A comprehensive and flexible error modeling method is absent. This paper develops an analytical model for the error motion of an aerostatic rotary stage bearing, utilizing linear superposition and spatial force equilibrium principles. The error motion of an orifice-restricted rotary stage is computed using this approach. The impact of bearing manufacturing inaccuracies (e.g., journal roundness, thrust plate profile) and micro-vibrations caused by internal turbulence is analyzed. Finally, the model was validated experimentally using the reversal method. The results indicate that bearing manufacturing errors positively correlate with error motion, and micro-vibration considerably influences errors at the sub-100 nm level. The relative error between the predicted and measured values is less than 15%, confirming the validity and applicability of this modeling and analytical approach. This research enhances error motion analysis methods and offers a novel constructive reference for predicting and optimizing error motion in precision aerostatic rotary stages.