# Multi-Probe Measurement Method for Error Motion of Precision Rotary Stage Based on Reference Plate
## 5 Conclusions  
This paper investigates a novel measurement method for the error motion of the precision rotary stage. Firstly, the conventional three-probe measurement method is examined, establishing that the face error motion, corresponding to the arbitrary probe installation angle, can be expressed as a function of the face error motions along the X and Y axes at the radius \(r\) of the rotary stage. Subsequently, a multi-probe measurement method based on a standard reference plate is proposed, along with principles and methodologies to address harmonic suppression issues during error separation. Finally, an experimental setup is established to verify the proposed error motion measurement method. The results indicate that the multi-probe error separation method successfully separates the form error of the  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Items** & **Reversal** & **SEA** & **Interferometry** & **Multi-Probe** \\ \hline Setup simplicity & Yes & No & No & Yes \\ Measurement accuracy & Yes & Yes & Yes & Yes \\ Measurement repeatability & Yes & Yes & Yes & Yes \\ Low cost & No & No & No & Yes \\ \hline \end{tabular}
\end{table}
Table 2: Comparison between multi-probe method and existing approaches.  
Figure 8: Form error of reference plate. (a) Profile of form error obtained with interferometer. (b) Curve of form error obtained through error separation.  
reference plate from the rotary stage error motion, achieving synchronous measurement accuracy within 4.69%. Consequently, this method can precisely measure the tilt and axial error motion of the rotary stage. The main conclusions of this study can be summarized as follows:  
1. Face error motion can be mathematically modeled as a function of its X-axis and Y-axis components.
2. Probe distribution with prime-numbered angular intervals demonstrates optimal efficacy in eliminating harmonic suppression issues.
3. The reference plate-based multi-probe measurement method enables in situ measurement of tilt and axial error motions, though its inability to simultaneously measure radial error motions presents a limitation.  
The multi-probe measurement method for error motion based on a reference plate demonstrates significant applicability for in situ measurement of precision rotary stages in both machining and metrology equipment. This method introduces a novel paradigm for measuring the error motion of precision rotary stages, effectively advancing precision motion metrology through the following three primary contributions: (1) facilitating real-time decoupling of intrinsic error components, (2) improving metrological traceability, and (3) overcoming the harmonic suppression limitations present in conventional methods.  
Conceptualization, X.Z. and T.Z.; methodology, X.Z. and D.Z.; software, X.Z. and Z.N.; validation, X.Z.; formal analysis, X.Z.; investigation, X.Z.; resources, D.Z.; data curation, X.Z. and T.Z.; writing--original draft, X.Z.; writing--review and editing, L.Z. and D.M.; visualization, X.Z.; supervision, L.Z. and D.M.; project administration, L.Z.; funding acquisition, L.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Jilin Province Science and Technology Development Plan Project of China, Grant No. 20220201044 GX.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
Authors [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] were employed by the company Chang Guang Satellite Technology Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.