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6PUS并联机构的运动学整机标定

Integral kinematic calibration of 6PUS parallel mechanism
FAN Rui , LI Xi , WANG Dan
School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2015-05-25; Accepted: 2015-08-26; Published online: 2016-05-25 12: 00
Foundation item: National Natural Science Foundation of China (51305013)
Corresponding author. E-mail:wangpick@163.com
Abstract: Firstly, the error Jacobi matrix of 54 parameters including the centers of U-joints and S-joints, the length of each link and the guide's position vectors was derived for the target 6PUS parallel mechanism. And the calibration model was established based on least squares method in MATLAB. The correctness of Jacobi matrix and the validity of the identification method using least squares method can be proved with MATLAB simulation. Secondly, the poses were selected based on orthogonal experiment and the integral mechanism calibration experiment was carried out by a laser tracker. The 54 parameter data were obtained through parameter identification using calibration model in MATLAB based on the calibrated results. Finally, the calibrated consequence can be obtained through error compensation. The results show that after compensation, in one direction, the maximum position error of the target mechanism is 0.030 mm and the maximum angle error is 0.0007 rad, while in three directions, the maximum position error of the target mechanism is 0.046 mm and the maximum angle error is 0.0008 rad. Therefore, we did a significant improvement in kinematic precision by integral mechanism calibration.
Key words: parallel mechanism     least squares method     orthogonal experiment     calibration     kinematic precision

1 误差建模及仿真验证 1.1 6PUS并联机构的结构参数

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 图 1 6PUS并联机构示意图 Fig. 1 Schematic of 6PUS parallel mechanism

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 i aix/mm aiy/mm aiz/mm bix/mm biy/mm biz/mm θi/rad ψi/rad Li/mm 1 95.101 34.200 -53.431 243.448 275.664 104.298 π/3 -2π/3 340 2 -17.932 99.460 -53.431 117.008 348.664 104.298 π/3 -2π/3 340 3 -77.168 65.260 -53.431 -360.456 73.000 104.298 π/3 0 340 4 -77.168 -65.260 -53.431 -360.456 -73.000 104.298 π/3 0 340 5 -17.932 -99.460 -53.431 117.008 -348.664 104.298 π/3 2π/3 340 6 95.101 -34.200 -53.431 243.448 -275.664 104.298 π/3 2π/3 340

1.2 参数误差建模

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δl为支链杆长误差;δc为动平台的位姿误差;dp=[dx dy dz]为动平台沿xyz坐标轴移动位置误差;dω=[dα dβ dγ]为动平台绕xyz坐标轴的姿态角误差;δm中dbi为静平台虎克铰铰链点误差,dai为动平台球铰铰链点误差。

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1.3 算法验证

 编号 x/mm y/mm z/mm α/rad β/rad γ/rad 1 -40 -20 520 0.08 0.2 0.2 2 -20 -10 490 0.05 0.1 0.1 3 0 0 460 0 0 0 4 20 10 430 -0.05 -0.1 -0.1 5 40 20 400 0.08 0.2 0.2

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 图 2 仿真流程图 Fig. 2 Simulation flowchart

 误差对比 假设值 辨识值 差值 δaix/mm 1 1.000 2×10-4 δaix/mm 1 1.000 2×10-4 δaiy/mm -1 -1.000 2×10-4 δaiz/mm 1 1.000 7×10-4 δbix/mm 1 1.000 2×10-4 δbiy/mm -1 -1.000 2×10-4 δbiz/mm 1 1.000 2×10-4 δθi/rad 0.01 0.010 10-6 δψi/rad 0.01 0.010 2×10-6 δLi/mm 1 1.000 4×10-4 注：辨识值为误差的近似值。

2 整机标定实验

 图 3 标定位置 Fig. 3 Locations in calibration

 图 4 外界参考点 Fig. 4 External reference points
 图 5 静平台参考点 Fig. 5 Fix-base reference points

 图 6 固定坐标系的建立 Fig. 6 Establishment of a fixed coordinate
 图 7 连体坐标系的建立 Fig. 7 Establishment of a moving coordinate

 编号 x/mm y/mm z/mm α/rad β/rad γ/rad 1 -50 -50 495 0.15 0.20 0.20 2 -40 -40 490 0.10 0.15 0.15 3 -20 -20 485 0.08 0.10 0.10 4 -10 -10 480 0.05 0.05 0.05 5 0 0 465 0 0 0 6 20 20 460 -0.08 -0.10 -0.10 7 40 40 450 -0.10 -0.15 -0.15 8 50 50 440 -0.15 -0.30 -0.30

 i aix/mm aiy/mm aiz/mm bix/mm biy/mm biz/mm θi/rad ψi/rad Li/mm 1 94.796 34.153 -53.367 239.240 269.024 108.955 1.041 4 -2.096 4 339.816 2 -18.039 99.319 -53.400 112.966 -341.515 108.212 1.040 5 -2.097 1 340.544 3 -77.044 65.261 -53.435 -345.858 -73.462 113.912 1.048 4 0.004 1 340.167 4 -77.079 -65.226 -53.307 -341.796 -72.226 116.785 1.048 4 3.7×10-4 340.785 5 -18.007 -99.142 -53.263 112.938 -340.372 112.367 1.050 5 2.093 0 340.047 6 95.021 -34.090 -53.392 239.279 -268.456 111.576 1.051 1 2.094 7 340.337

 图 8 标定前后的位置误差 Fig. 8 Position errors before and after calibration
 图 9 标定前后的姿态误差 Fig. 9 Angle errors before and after calibration

 序号 Δx/mm Δy/mm Δz/mm Δα/rad Δβ/rad Δγ/rad 理论值 补偿值 理论值 补偿值 理论值 补偿值 理论值 补偿值 理论值 补偿值 理论值 补偿值 5 9.431 3 -0.026 7 1.164 0 0.030 1 18.140 4 -0.021 7 -0.038 2 0.000 3 0.009 9 0.000 1 0.017 7 0.000 7 17 10.422 1 0.009 0 1.779 4 0.005 1 17.618 8 -0.010 7 -0.034 4 0.000 2 -0.013 8 -0.000 6 0.016 1 0.000 4 24 13.328 3 -0.000 1 2.645 8 0.001 2 15.202 9 -0.018 4 -0.035 5 0 -0.012 6 -0.000 4 0.014 1 0.000 6

3 结 论

1) 在MATLAB中采用最小二乘法进行参数辨识,建立了标定模型,通过仿真证明辨识结果误差在10-6以上,说明了标定模型的正确性。

3) 首次提出整机形式标定54结构参数,对比传统的拆分标定实验,整机标定操作简单、标定效果良好。同时,整机标定具有很强的适应性,可针对其他类型的并联机构进行标定，为以后的运动学标定实验提供了一种准确方便的方法。

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#### 文章信息

FAN Rui, LI Xi, WANG Dan
6PUS并联机构的运动学整机标定
Integral kinematic calibration of 6PUS parallel mechanism

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(5): 871-877
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0331