# Design of a Measurement System for Six-Degree-of-Freedom Geometric Errors of a Linear Guide of a Machine Tool

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## Abstract

**:**

## 1. Introduction

## 2. Structure Layout and Measuring Principle

## 3. Numerical Simulation and Mathematical Model

_{PSD1}= F

_{X}

_{1}(δ

_{x}, δ

_{z}, ε

_{x}, ε

_{y}, ε

_{z}),

_{PSD1}= F

_{Y}

_{1}(δ

_{x}, δ

_{z}, ε

_{x}, ε

_{y}, ε

_{z}),

_{PSD2}= F

_{X2}(δ

_{x}, δ

_{z}, ε

_{x}, ε

_{y}, ε

_{z}),

_{PSD2}= F

_{Y2}(δ

_{x}, δ

_{z}, ε

_{x}, ε

_{y}, ε

_{z}),

_{PSD3}= F

_{X3}(δ

_{x}, δ

_{z}, ε

_{x}, ε

_{y}, ε

_{z}),

_{PSD3}= F

_{Y3}(δ

_{x}, δ

_{z}, ε

_{x}, ε

_{y}, ε

_{z})

_{PSDi}(i = 1, 2, and 3) and Y

_{PSDi}(i = 1, 2, and 3) are the image centroid coordinates of the light spot on PSDi in the X-direction and Y-direction, respectively.

_{PSD1}= Aεy+Bεz+C,

_{PSD1}= Dεx+E,

_{PSD2}= Fεz+G,

_{PSD2}= Hεx+I,

_{PSD3}= Jδx+Kεy+Lεz+M,

_{PSD3}= Nδz+Oεy+Pεx+Q,

## 4. Experimental characterization

## 5. Conclusions

## 6. Patents

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**Simulation results showing variation of light spot positions on PSDs with geometric errors.

**Figure 9.**Verification of the mathematical model: (

**a**) pitch, (

**b**) roll, (

**c**) yaw, (

**d**) horizontal straightness, and (

**e**) vertical straightness, respectively.

**Figure 12.**Measurement results for variation of geometric error with position: (

**a**) pitch, (

**b**) yaw, (

**c**) horizontal straightness, (

**d**) vertical straightness, (

**e**) roll, and (

**f**) positioning errors, respectively.

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**MDPI and ACS Style**

Liu, C.-S.; Lai, J.-J.; Luo, Y.-T. Design of a Measurement System for Six-Degree-of-Freedom Geometric Errors of a Linear Guide of a Machine Tool. *Sensors* **2019**, *19*, 5.
https://doi.org/10.3390/s19010005

**AMA Style**

Liu C-S, Lai J-J, Luo Y-T. Design of a Measurement System for Six-Degree-of-Freedom Geometric Errors of a Linear Guide of a Machine Tool. *Sensors*. 2019; 19(1):5.
https://doi.org/10.3390/s19010005

**Chicago/Turabian Style**

Liu, Chien-Sheng, Jia-Jun Lai, and Yong-Tai Luo. 2019. "Design of a Measurement System for Six-Degree-of-Freedom Geometric Errors of a Linear Guide of a Machine Tool" *Sensors* 19, no. 1: 5.
https://doi.org/10.3390/s19010005