Three-Degree-of-Freedom Measurement Method Based on Plane Normal Vector

Guoming Fang; Qi Peng; Haotong Ma; Shan Qiao; Jiang Bian; Feng Chen; Xincheng Liu; Yufeng Tan; Bi He; Li Dong

doi:10.3788/LOP55.111201

Laser & Optoelectronics Progress, Volume. 55, Issue 11, 111201(2018)

Three-Degree-of-Freedom Measurement Method Based on Plane Normal Vector

Guoming Fang^1,2,3、**, Qi Peng^1,2、*, Haotong Ma^1,2, Shan Qiao^1,2,3, Jiang Bian², Feng Chen^1,2,3, Xincheng Liu^1,2,3, Yufeng Tan^1,2,3, Bi He^1,2,3, and Li Dong^1,2,3

Author Affiliations

¹ Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China

² Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China

³ University of Chinese Academy of Sciences, Beijing 100049, China

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Figures & Tables(10)

Fig. 1. Schematic of 3-DOF measurement principle

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Fig. 2. Error analysis. (a) Position error; (b) parallelism error

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Fig. 3. Angle values after 3-DOF simulation. (a) Angle α; (b) angle γ

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Fig. 4. Displacement values after 3-DOF simulation

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Fig. 5. Experimental device. (a) Schematic; (b) physical map

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Fig. 6. Experimental results of angle. (a) Angle α in 2-DOF experiment; (b) real-time waveform of γ in 2-DOF experiment; (c) angle α in 3-DOF experiment; (d) angle γ in 3-DOF experiment

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Fig. 7. Experimental results of displacement. (a) 2-DOF experiment; (b) 3-DOF experiment

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Table 1. Analysis results of angle α0
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Table 1. Analysis results of angle α0
Variable -b c α
Ranges >0 >0 arcsin (s)
<0 >0 π-arcsin (|s|)
<0 <0 π+arcsin (|s|)
>0 <0 -arcsin (|s|)
>0 =0 0
<0 =0 π
=0 >0 π/2
=0 <0 -π/2

Table 2. Fixed difference value removal of angle α
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Table 2. Fixed difference value removal of angle α
Variable α |α| Results ofangle α
Determinationcondition <0 >1 α+π
>0 >1 α-π
Others α

Table 3. Positional deviations of measuring points in simulation process
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Table 3. Positional deviations of measuring points in simulation process
Point Positionaldeviation /μm Parallelism /(″)
X Z Vertical Horizontal
A 1.00 3.00 71.28 77.76
B 4.00 1.50 -71.28 58.32
C 2.20 1.80 84.24 -51.84

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Guoming Fang, Qi Peng, Haotong Ma, Shan Qiao, Jiang Bian, Feng Chen, Xincheng Liu, Yufeng Tan, Bi He, Li Dong. Three-Degree-of-Freedom Measurement Method Based on Plane Normal Vector[J]. Laser & Optoelectronics Progress, 2018, 55(11): 111201

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