Method for simultaneously and directly measuring all six-DOF motion errors of a rotary axis

Jiakun Li; Qibo Feng; Chuanchen Bao; Bin Zhang

doi:10.3788/COL201917.011203

Journals >Chinese Optics Letters >Volume 17 >Issue 1 >Page 011203 > Article

Chinese Optics Letters
Vol. 17, Issue 1, 011203 (2019)

Method for simultaneously and directly measuring all six-DOF motion errors of a rotary axis

Jiakun Li, Qibo Feng^*, Chuanchen Bao, and Bin Zhang

Author Affiliations

Key Laboratory of Luminescence and Optical Information, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China

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DOI: 10.3788/COL201917.011203 Cite this Article Set citation alerts

Jiakun Li, Qibo Feng, Chuanchen Bao, Bin Zhang. Method for simultaneously and directly measuring all six-DOF motion errors of a rotary axis[J]. Chinese Optics Letters, 2019, 17(1): 011203 Copy Citation Text

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Fig. 1. Schematic of the proposed method.

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Fig. 2. Schematic diagram of the PID closed-loop control.

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Fig. 3. Experimental system.

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Fig. 4. Results of the repeatability experiments for measuring all six-DOF motion errors of an indexing table.

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Fig. 5. Results of the comparison experiments between the auto-collimator and our device for measuring (a) the tilt motion error around the Y axis and (b) the angular positioning error.

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Motion Error	Detector	Expression
$δ_{x} (θ)$	Interferometer	Omitted
$δ_{y} (θ)$	QD1 or QD2	$Δ Y_{QD 1} / 2$ or $Δ Y_{QD 2} / 2$
$δ_{z} (θ)$	QD1 or QD2	$Δ Z_{QD 1} / 2$ or $Δ Z_{QD 2} / 2$
$ε_{x} (θ)$	QD1 and QD2	$(Δ Z_{QD 1} - Δ Z_{QD 2}) / 2 h$
$ε_{y} (θ)$	PSD2	$Δ Z_{PSD 2} / 2 f_{2}$
$ε_{z} (θ)$	PSD2	$Δ Y_{PSD 2} / 2 f_{2} + θ_{ref} - θ$

Table 1. Corresponding Detectors and Expressions for Measuring Each DOF Motion Error of a Rotary Axis

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Errors	Resolution	SDS	MRV
$δ_{x} (θ)$	20 pm	$0.03 μ m$	$3.9 μ m$
$δ_{y} (θ)$	$0.04 μ m$	$0.07 μ m$	$3.0 μ m$
$δ_{z} (θ)$	$0.04 μ m$	$0.04 μ m$	$0.7 μ m$
$ε_{x} (θ)$	0.27 arcsec	0.05 arcsec	2.5 arcsec
$ε_{y} (θ)$	0.26 arcsec	0.17 arcsec	2.4 arcsec
$ε_{z} (θ)$	0.26 arcsec	0.06 arcsec	24.8 arcsec

Table 2. Measurement Resolution, Standard Deviation of Stability (SDS) and Maximum Repeatability Value (MRV)

Jiakun Li, Qibo Feng, Chuanchen Bao, Bin Zhang. Method for simultaneously and directly measuring all six-DOF motion errors of a rotary axis[J]. Chinese Optics Letters, 2019, 17(1): 011203

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