A CMM-Based Method of Control Point Position Calibration for Light Pen Coordinate Measuring System
Abstract
1. Introduction
2. Brief Description of LPCMS
3. Control Point Position Calibration
3.1. Calibration Procedure
3.2. Calibration Method Derivation
3.3. Algorithm Acceleration
3.4. Light Pen Coordinate System Establishement
- Determine the origin of . The first control point is used as the origin. Then a new set of translation vectors is calculated:
- Determine the z-axis of . The fifth to 13th control points are designed to be coplanar. Actually, they are not strictly coplanar because of the machining and installation error. Therefore, a plane is fitted using their new translation vectors . The direction of its unit normal vector, which can be denoted as , is used as the z-axis of .
- Determine the y-axis of . For the same reason, the first to fourth control points are not strictly collinear. They are projected to the plane fitted before. A line is fitted using the coordinates of their projections. The unit direction vector of this line is denoted as . Since the fitted line is in the plane, is satisfied. The direction of can be used as the y-axis of .
- Determining the x-axis of . Given the direction of y-axis and z-axis , the direction of x-axis, which is denoted as , can be determined by the cross product:
- Determining the relative positions of control points with coordinates in . With the origin and axes determined, the coordinates of control points in , which can be denoted as can be calculates as follows:
4. Experiment
4.1. Actual Control Point Position Calibration Experiment
4.2. Simulation Experiment
4.3. Measurement Experiment of LPCMS
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Calibration Method | Advantages | Disadvantages |
---|---|---|
Direct Measurement Method in [10] | Fast calibration speed; Easy operation; No need of calculation | Unable to locate luminous center; Low accuracy |
Structure from Motion Method in [11] | No need of extra equipment; High flexibility; Able to calibrate in real-time | Complicated calculation; Low reliability |
The Proposed Method | High accuracy; Simple calculation process; Able to process tremendous data | High time consumption; Complex calibration procedure |
Control Point Index | |||
---|---|---|---|
1 | −31.343 | −319.578 | 1542.853 |
2 | −130.327 | −317.944 | 1544.784 |
3 | −230.340 | −316.726 | 1546.672 |
4 | −410.261 | −314.924 | 1550.004 |
5 | −571.145 | −309.694 | 1452.690 |
6 | −486.863 | −266.087 | 1451.879 |
7 | −402.882 | −222.740 | 1451.028 |
8 | −318.265 | −179.508 | 1450.131 |
9 | −319.429 | −234.657 | 1449.130 |
10 | −322.394 | −394.058 | 1447.287 |
11 | −323.049 | −449.060 | 1446.452 |
12 | −405.913 | −402.371 | 1448.562 |
13 | −488.814 | −355.599 | 1450.688 |
Control Point Index | |||
---|---|---|---|
1 | 0.000 | 0.000 | 0.000 |
2 | −0.228 | 99.159 | −0.064 |
3 | −0.025 | 199.053 | −0.071 |
4 | 0.730 | 379.013 | −0.024 |
5 | −0.874 | 538.094 | 100.333 |
6 | −45.681 | 454.440 | 100.167 |
7 | −90.222 | 371.082 | 100.043 |
8 | −134.657 | 287.086 | 99.951 |
9 | −79.488 | 287.447 | 100.223 |
10 | 79.949 | 288.113 | 99.950 |
11 | 134.962 | 287.970 | 100.048 |
12 | 89.451 | 371.514 | 100.119 |
13 | 43.858 | 455.096 | 100.176 |
Calibration Index | 1–4 1 | 1–5 | 5–8 | 5–11 | 8–11 | 1–8 | 1–11 |
---|---|---|---|---|---|---|---|
1 | 379.014 | 547.369 | 284.435 | 284.629 | 269.620 | 332.471 | 333.393 |
2 | 379.022 | 547.385 | 284.446 | 284.611 | 269.599 | 332.476 | 333.425 |
3 | 379.012 | 547.355 | 284.461 | 284.603 | 269.625 | 332.483 | 333.420 |
4 | 379.030 | 547.344 | 284.447 | 284.622 | 269.615 | 332.450 | 333.409 |
5 | 379.005 | 547.363 | 284.452 | 284.631 | 269.603 | 332.456 | 333.396 |
6 | 379.024 | 547.359 | 284.458 | 284.615 | 269.621 | 332.464 | 333.433 |
7 | 379.019 | 547.388 | 284.432 | 284.623 | 269.608 | 332.469 | 333.401 |
8 | 379.008 | 547.354 | 284.441 | 284.618 | 269.619 | 332.472 | 333.422 |
9 | 379.027 | 547.376 | 284.459 | 284.607 | 269.618 | 332.456 | 333.411 |
10 | 379.016 | 547.371 | 284.429 | 284.614 | 269.603 | 332.448 | 333.430 |
Ave | 379.018 | 547.366 | 284.446 | 284.617 | 269.613 | 332.465 | 333.414 |
Std | 0.00818 | 0.01408 | 0.01158 | 0.00911 | 0.00909 | 0.01165 | 0.01417 |
Range | 0.025 | 0.044 | 0.032 | 0.028 | 0.026 | 0.035 | 0.040 |
Distance | 100 Gauge | 250 Gauge | 1000 Gauge | Cylinder | ||||
---|---|---|---|---|---|---|---|---|
Ave | Std | Ave | Std | Ave | Std | Ave | Std | |
2 m | 99.994 | 0.0025 | 250.009 | 0.0028 | 999.982 | 0.0062 | 63.502 | 0.0022 |
4 m | 100.002 | 0.0037 | 250.014 | 0.0049 | 999.994 | 0.0133 | 63.507 | 0.0027 |
6 m | 100.006 | 0.0048 | 249.983 | 0.0072 | 1000.015 | 0.0187 | 63.513 | 0.0042 |
8 m | 99.988 | 0.0056 | 250.003 | 0.0123 | 999.989 | 0.0227 | 63.505 | 0.0053 |
10 m | 99.992 | 0.0071 | 250.007 | 0.0158 | 999.979 | 0.0315 | 63.519 | 0.0085 |
Distance | Method in [10] | Method in [11] | Proposed Method | |||
---|---|---|---|---|---|---|
Ave | Std | Ave | Std | Ave | Std | |
2 m | 250.033 | 0.0258 | 250.019 | 0.0121 | 250.009 | 0.0028 |
4 m | 249.976 | 0.0376 | 250.033 | 0.0213 | 250.014 | 0.0049 |
6 m | 249.982 | 0.0627 | 249.975 | 0.0381 | 249.983 | 0.0072 |
8 m | 250.041 | 0.1032 | 250.029 | 0.0419 | 250.003 | 0.0123 |
10 m | 249.963 | 0.1523 | 250.038 | 0.0688 | 250.007 | 0.0158 |
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Wang, S.; Liu, S.; Mao, Q. A CMM-Based Method of Control Point Position Calibration for Light Pen Coordinate Measuring System. Sensors 2020, 20, 5592. https://doi.org/10.3390/s20195592
Wang S, Liu S, Mao Q. A CMM-Based Method of Control Point Position Calibration for Light Pen Coordinate Measuring System. Sensors. 2020; 20(19):5592. https://doi.org/10.3390/s20195592
Chicago/Turabian StyleWang, Sen, Shugui Liu, and Qing Mao. 2020. "A CMM-Based Method of Control Point Position Calibration for Light Pen Coordinate Measuring System" Sensors 20, no. 19: 5592. https://doi.org/10.3390/s20195592
APA StyleWang, S., Liu, S., & Mao, Q. (2020). A CMM-Based Method of Control Point Position Calibration for Light Pen Coordinate Measuring System. Sensors, 20(19), 5592. https://doi.org/10.3390/s20195592