Kinematics and Accuracy Analysis of Parallel Bidirectional Deflection Platform
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摘要: 本文提出一种新型并联驱动双向偏转平台。动平台通过在空间中呈正十字交错且同心的两个分支结构与底座相连接，该平台可以在X、Y两个方向上实现大角度偏转；建立了该平台的运动学方程，得出了Jacobian矩阵；对平台做了运动学仿真分析，对比了仿真结果与理论计算结果，验证了平台设计的可行性与运动的准确性；给出了平台所有的源误差，根据误差独立作用原理对不同类型的源误差分别采用蒙特卡洛法、瞬时臂法和全微分法做了误差分析、计算，得出了各局部误差。按照误差综合方法的均方法对各局部误差做了误差综合，得出了平台分别绕X、Y轴方向上的最大运动误差。
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关键词:
- 双向偏转平台 /
- Jacobian矩阵 /
- 运动学仿真 /
- 精度分析
Abstract: A new parallel drive bidirectional deflection platform is proposed. The movable platform is connected to the base with the two cross-branched and concentric two-branch structures in the space, and the platform can realize the large-angle deflection in both X and Y directions. The kinematics equation of the platform was established and the Jacobian matrix was obtained. The kinematics simulation analysis of the platform was carried out, and the simulation results and calculation results were compared so as to verify the feasibility of the platform design and the accuracy of the motion. All the source errors of the platform are given. According to the error independent action principle, Monte Carlo method, the instantaneous arm method and the total differential method are used to analyze and calculate the error of different types of source errors respectively. The local errors are obtained. According to the average method of the error synthesis method, the error of each local error is integrated, and the maximum motion error of the platform around the X and Y axes is obtained. -
表 2 平台位置仿真值与理论计算值
(°) t(s) α β 理论值 仿真值 θ1 θ2 θ1 θ2 1
3
5
7
90.8
3.6
10
18
260.8
3.6
10
18
261.2800
11.5427
32.4835
60.3590
91.15702.5440
22.8960
63.6070
114.4800
165.36001.2814
11.5421
32.4842
60.3581
91.15512.5432
22.8972
63.6090
114.4831
165.3631
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表 3 平台速度仿真值与理论计算值
(°/s) t(s) α β 理论值 仿真值 θ′1 θ′2 θ′1 θ′2 1
3
5
7
90.8
2.4
4.0
4.0
4.00.8
2.4
4.0
4.0
4.02.5602
7.7254
13.3768
14.5968
16.23585.0880
15.2640
25.4400
25.4400
25.44002.5622
7.7238
13.3778
14.5976
16.23425.0820
15.2720
25.4380
25.4380
25.4380
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表 4 误差源及性质
轴线 误差名称 误差类型 误差性质 X轴 主动齿轮2制造误差
大驱动拱制造误差
主动齿轮2与电机2轴安装偏心产生的误差
X轴齿轮传动误差制造误差
制造误差
装配误差
制造与装配误差随机误差
随机误差
随机误差
随机误差Y轴 主动齿轮1制造误差
小驱动拱制造误差
主动齿轮1与电机1轴安装偏心产生的误差
Y轴齿轮传动误差
滑伸副配合间隙产生的误差
动平台绕X轴偏转对其绕Y轴偏转的耦合误差制造误差
制造误差
装配误差
制造与装配误差
制造与装配误差
原理误差随机误差
随机误差
随机误差
随机误差
随机误差
系统误差
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表 5 各齿轮误差参数
齿轮 Fp F′i f′i e1 e2 e3 z1 29 41.699 2 12.699 2 4 10 0 z2 29 67.100 1 18.100 1 4.5 10 5 z3 49 41.699 2 12.699 2 4 10 0 z4 64 79.834 8 15.834 8 4.5 10 5
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