• Optics and Precision Engineering
  • Vol. 31, Issue 22, 3289 (2023)
Guanbin GAO, Pei XIE, Fei LIU*, and Jing NA
Author Affiliations
  • Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming650500, China
  • show less
    DOI: 10.37188/OPE.20233122.3289 Cite this Article
    Guanbin GAO, Pei XIE, Fei LIU, Jing NA. Residual modelling and compensation for articulated arm coordinate measuring machines based on compound calibration and extreme learning machine[J]. Optics and Precision Engineering, 2023, 31(22): 3289 Copy Citation Text show less
    7-DoF articulated arm coordinate measuring machine
    Fig. 1. 7-DoF articulated arm coordinate measuring machine
    Coordinate systems of the AACMM
    Fig. 2. Coordinate systems of the AACMM
    Flow chart of compound calibration method
    Fig. 3. Flow chart of compound calibration method
    Track of the 4th joint in the measurement space
    Fig. 4. Track of the 4th joint in the measurement space
    Diagram of measuring swing angle ω
    Fig. 5. Diagram of measuring swing angle ω
    Diagram of the position and radius of the configuration circle
    Fig. 6. Diagram of the position and radius of the configuration circle
    Effect of first joint on residual value
    Fig. 7. Effect of first joint on residual value
    Circular track formed by probe in moving space
    Fig. 8. Circular track formed by probe in moving space
    Impacts of probe circle on residual value
    Fig. 9. Impacts of probe circle on residual value
    Relationship between configuration parameters and residuals
    Fig. 10. Relationship between configuration parameters and residuals
    Relationship of the elevation angle, swing angle and residual
    Fig. 11. Relationship of the elevation angle, swing angle and residual
    Relationship of the length, swing angle and residual
    Fig. 12. Relationship of the length, swing angle and residual
    Relationship between swing angle and rotation angle and residuals in X and Y-directions
    Fig. 13. Relationship between swing angle and rotation angle and residuals in X and Y-directions
    Residual compensation model based on ELM
    Fig. 14. Residual compensation model based on ELM
    Training process of ELM
    Fig. 15. Training process of ELM
    Calibration compensation software
    Fig. 16. Calibration compensation software
    Error distribution before calibration
    Fig. 17. Error distribution before calibration
    Error distribution after calibration
    Fig. 18. Error distribution after calibration
    Comparison of kinematic calibration effects
    Fig. 19. Comparison of kinematic calibration effects
    Residual compensation results
    Fig. 20. Residual compensation results
    Residual compensation effect of different fitting algorithms
    Fig. 21. Residual compensation effect of different fitting algorithms
    Compensation effect of different residual compensation models
    Fig. 22. Compensation effect of different residual compensation models
    Measurement results of standard gauge
    Fig. 23. Measurement results of standard gauge

    No. of joints

    i

    Linkage length

    ai-1/mm

    Linkage offset

    di/mm

    Torsion angle

    αi-1/rad

    Joint zero offset

    θi0/rad

    lx=0,ly=0,lz=0(mm)
    1421551.570 80
    24201.570 80
    3-28600-1.570 80
    4-280-1.570 80
    5286001.570 80
    6-300-1.570 80
    7023000
    Table 1. Nominal value of kinematic parameter

    No. of joints

    i

    Linkage length

    ai-1/mm

    Linkage offset

    di/mm

    Torsion angle

    αi-1/rad

    Joint zero offset

    θi0/rad

    Δlx=-0.004 mm,Δly=-0.184 mm,Δlz=0.158 mm
    142.682156.8611.570 90.037 0
    242.6630.9251.567 8-0.013 0
    3-28.776596.025-1.569 00.048 8
    4-29.2561.119-1.572 20.020 5
    528.837 6597.2491.570 70.103 6
    6-28.980-1.717-1.559 40.000 9
    70.006 0227.133-0.087 30.007 0
    Table 2. D-H parameter of the AACMM after identification
    MaximumAverageStandard deviation
    Before calibration49.36826.49812.348
    After calibration0.0540.0210.009
    Table 3. Compound kinematic calibration results

    Single point

    calibration

    Compound

    calibration

    Average0.0310.023
    Standard deviation0.0180.011
    Maximum0.0980.061
    RP0.0840.055
    Table 4. Comparison of kinematic calibration effects

    Before

    compensation

    After compensation
    Average0.0240.017
    Standard deviation0.0110.005
    Maximum0.0570.028
    RP0.0570.032
    Table 5. Residual compensation results

    Before

    compensation

    MCCM-ELM

    MCCM-

    BP

    Average0.0230.0140.016
    Standard deviation0.0110.0070.009
    Maximum0.0610.0440.051
    RP0.0550.0350.043
    Table 6. Comparison of residual compensation effects of different fitting algorithms

    Before

    compensation

    MCCM-ELM

    FJCM-

    ELM

    Average0.0230.0140.023
    Standard deviation0.0110.0070.010
    Maximum0.0610.0440.057
    RP0.0550.0350.053
    Table 7. Comparison of compensation effects of different residual compensation models

    Before

    compensation

    After

    compensation

    Average0.0330.021
    Standard deviation0.0370.019
    Maximum0.1370.074
    Table 8. Measurement results of standard gauge
    Guanbin GAO, Pei XIE, Fei LIU, Jing NA. Residual modelling and compensation for articulated arm coordinate measuring machines based on compound calibration and extreme learning machine[J]. Optics and Precision Engineering, 2023, 31(22): 3289
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