A Reproduction Lissajous Figure Machine

2018 ◽  
Vol 56 (7) ◽  
pp. 428-429 ◽  
Author(s):  
John A. Daffron ◽  
Thomas B. Greenslade
Keyword(s):  
Lissajous Figure

scholarly journals Analysis of the Subdivision Errors of Photoelectric Angle Encoders and Improvement of the Tracking Precision of a Telescope Control System

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 2998 ◽  
Author(s):  
Jiawei Yu ◽  
Qiang Wang ◽  
Guozhong Zhou ◽  
Dong He ◽  
Yunxia Xia ◽  
...  
Keyword(s):  
Error Compensation ◽  
Phase Error ◽  
Tracking Error ◽  
Great Influence ◽  
Measuring Error ◽  
Distribution Law ◽  
Lissajous Figure ◽  
Amplitude Error ◽  
Noise Error ◽  
Angle Encoder

Photoelectric angle encoders, working as position sensors, have a great influence on the accuracy and stability of telescope control systems (TCS). In order to improve the tracking precision of TCS, a method based on subdivision error compensation for photoelectric angle encoders is proposed. First, a mathematical analysis of six types of subdivision errors (DC error, phase error, amplitude error, harmonic error, noise error, and quantization error) is presented, which is different from the previously used analysis based on the Lissajous figure method. In fact, we believe that a mathematical method is more efficient than the figure method for the expression of subdivision errors. Then, the distribution law and period length of each subdivision error are analyzed. Finally, an error compensation algorithm is presented. In a real TCS, the elevation jittering phenomenon occurs, which indicates that compensating for the amplitude error is necessary. A feed-forward loop is then introduced into the TCS, which is position loop- and velocity loop-closed, leading to a decrease of the tracking error by nearly 54.6%, from 2.31” to 1.05”, with a leading speed of 0.25°/s, and by 40.5%, from 3.01” to 1.79”, with a leading speed of 1°/s. This method can realize real-time compensation and improve the ability of TCS without any change of the hardware. In addition, independently of the environment and the kind of control strategy used, this method can also improve the tracking precision presumably because it compensates the measuring error inside the photoelectric angle encoder.

scholarly journals Research and Application of Mathematical Model of Transmission Grating Signal Lissajous Figure

2018 ◽  
Vol 232 ◽  
pp. 03046
Author(s):  
Luqing Hu ◽  
Xianqing Lei ◽  
Xiaoyi Wang ◽  
Yadong Zhang ◽  
Xiaolin Zuo
Keyword(s):  
Mathematical Model ◽  
Measurement System ◽  
Electrical Signal ◽  
Two Phase ◽  
Lissajous Figure ◽  
Transmission Grating ◽  
Straight Line ◽  
Voltage Signal ◽  
Working Principle ◽  
Grating Pair

In this paper, the working principle of the grating measurement system is combined with the Fourier analysis method of Moiré fringe to establish the mathematical model of the grating signal Lissajous figure to know the quality of the grating signal intuitively. The Mathematica numerical analysis software is used to obtain the graphics of the model, and the correctness of the relationship between the parameters of the grating measurement system and the Lissajous figure equation of the grating signal is verified. The influence of the grating pair angle α on the output voltage signal and Lissajous figure of the grating measurement system is studied. The results show that the intensity of the two-phase output electrical signal decreases gradually with the increase of the deviation of the angle α of the grating pair, but the equal-amplitude of the two-phase output electrical signal does not change; Meanwhile, the shape of the grating signal Lissajous figure gradually changes from the ideal circle to the non-ideal ellipse, until a straight line with a strip slope of 135° is formed.

A Method for Measuring Combined Stress of Small Bore Piping Around Weld in Field Using Strain Gauge Holder

2020 ◽  
Author(s):  
Tsunemichi Takahama
Keyword(s):  
Strain Gauge ◽  
Strain Gauges ◽  
Piping System ◽  
Torsional Stress ◽  
3D Display ◽  
Combined Stress ◽  
Dynamic Stresses ◽  
Lissajous Figure ◽  
Bending Stresses ◽  
Fatigue Evaluation

Abstract This paper proposes using the strain gauge holder which has 12 elements of strain gauge in order to measure the 2 directional bending stresses and the torsional stress synchronously around the weld in small bore piping. The paper also provides the actual measured dynamic stresses around the welds in real fields including combined stress by the strain gauge holder. The measured stresses are shown on a time axis, on a frequency axis, on an X-Y display like Lissajous figure, and on an X-Y-Z 3D display. It was confirmed that the strain gauge holder was able to be installed within 20 minutes, to be used on 180°C piping, and to be reused in real fields because it was not necessary to adhere the strain gauges on the piping. The measured strains obtained by using the strain gauge holder can provide useful information of the piping system to decide whether the reinforcements are necessary, to enhance the accuracy of the design and calculation, and to improve the validity of fatigue evaluation. It is planned in future to develop a methodology of fatigue evaluation based on the measured stresses obtained by using the strain gauge holder.

scholarly journals Perceptual Stability of the Lissajous Figure Is Modulated by the Speed of Illusory Rotation

PLoS ONE ◽  
2016 ◽  
Vol 11 (8) ◽  
pp. e0160772 ◽  
Author(s):  
Veith A. Weilnhammer ◽  
Philipp Sterzer ◽  
Guido Hesselmann
Keyword(s):  
Lissajous Figure ◽  
Perceptual Stability
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