Rotation double prisms steered by noncircular gear pairs to scan specified nonlinear trajectories

Anhu Li; Yang Zhang; Xingsheng Liu; Wanli Yi

doi:10.1364/AO.58.000283

Applied Optics
Vol. 58,
Issue 2,
pp. 283-290
(2019)
•https://doi.org/10.1364/AO.58.000283

Rotation double prisms steered by noncircular gear pairs to scan specified nonlinear trajectories

Anhu Li, Yang Zhang, Xingsheng Liu, and Wanli Yi

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Anhu Li, Yang Zhang, Xingsheng Liu, and Wanli Yi, "Rotation double prisms steered by noncircular gear pairs to scan specified nonlinear trajectories," Appl. Opt. 58, 283-290 (2019)

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Abstract

In order to scan some specified nonlinear motion trajectories with high accuracy, simple control process, and good stability, we propose a method to design the drive mechanism of the rotation double-prism scanner, which can transfer the nonlinear motor control to the profile design of corresponding noncircular gear pairs. Given a nonlinear target trajectory, this method can successfully change the complicated nonlinear motion of the motor to the more operative uniform rotation. The simulation and experiment results show that the tracking error is less than 0.981 mm in the distance of 500 mm between the actual tracking trajectory and the original one. The proposed drive mechanical setup offers a perfect alternative to the nonlinear control design of the rotation double-prism scanner.

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	Optimal Polynomial Order		RMSE		R-square
Number	Prism 1	Prism 2	Prism 1	Prism 2	Prism 1	Prism 2
1	13	13	$2.65 \times 10^{- 5}$	$5.84 \times 10^{- 8}$	1.000	1.000
2	9	8	$1.62 \times 10^{- 5}$	$1.71 \times 10^{- 6}$	1.000	1.000
3	7	6	$2.58 \times 10^{- 5}$	$3.55 \times 10^{- 6}$	1.000	1.000
4	5	6	$1.40 \times 10^{- 5}$	$3.40 \times 10^{- 5}$	1.000	0.999
5	5	5	$9.70 \times 10^{- 5}$	$3.04 \times 10^{- 4}$	1.000	0.999
6	5	5	$1.99 \times 10^{- 4}$	$3.91 \times 10^{- 4}$	1.000	0.999
7	5	5	$8.03 \times 10^{- 4}$	$3.64 \times 10^{- 4}$	0.999	0.999
8	4	4	$6.90 \times 10^{- 4}$	$4.66 \times 10^{- 4}$	0.999	0.999
9	4	4	$5.39 \times 10^{- 4}$	$1.54 \times 10^{- 4}$	0.999	0.999
10	4	4	$2.13 \times 10^{- 4}$	$1.95 \times 10^{- 4}$	1.000	0.999
11	4	4	$1.83 \times 10^{- 4}$	$1.00 \times 10^{- 3}$	1.000	0.999
12	4	4	$1.74 \times 10^{- 3}$	$3.23 \times 10^{- 3}$	0.999	0.999

Symbol	Quantity	Value
$m$	Module	2.5 mm
$z_{c}$	Number of tooth	20
$α$	Pressure angle	20°
$h_{a}^{*}$	Addendum coefficient	1
$c^{*}$	Tip clearance coefficient	0.25
$b$	Tooth width	40 mm
$r_{3}$	Radius of pitch circle	25 mm

	$a / mm$	$S_{1} / mm$	$S_{2} / mm$	$z_{1}$	$z_{2}$
Prism 1	150.5	612.202	306.004	78.0	39.0
Prism 2	150.5	612.487	306.257	78.0	39.0

	Method	Maximum $ϵ / (°)$	Minimum $ϵ / (°)$	Average $ϵ / (°)$
Prism 1	Simulation	0.020912	−0.013793	0.007722
Prism 1	Experiment	0.270314	−0.943197	−0.417644
Prism 2	Simulation	0.018816	−0.028588	−0.001118
Prism 2	Experiment	0.293216	−0.366000	0.030296

Method	Maximum Deviation Value (mm)	Average Deviation Value (mm)
Simulation	0.550	0.128
Experiment	0.981	0.447

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Applied Optics