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基于共形几何代数的空间并联机构位置正解

黄昔光 黄旭

黄昔光, 黄旭. 基于共形几何代数的空间并联机构位置正解[J]. 北京航空航天大学学报, 2017, 43(12): 2377-2381. doi: 10.13700/j.bh.1001-5965.2016.0917
引用本文: 黄昔光, 黄旭. 基于共形几何代数的空间并联机构位置正解[J]. 北京航空航天大学学报, 2017, 43(12): 2377-2381. doi: 10.13700/j.bh.1001-5965.2016.0917
HUANG Xiguang, HUANG Xu. Direct kinematics of a spatial parallel mechanism based on conformal geometric algebra[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(12): 2377-2381. doi: 10.13700/j.bh.1001-5965.2016.0917(in Chinese)
Citation: HUANG Xiguang, HUANG Xu. Direct kinematics of a spatial parallel mechanism based on conformal geometric algebra[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(12): 2377-2381. doi: 10.13700/j.bh.1001-5965.2016.0917(in Chinese)

基于共形几何代数的空间并联机构位置正解

doi: 10.13700/j.bh.1001-5965.2016.0917
基金项目: 

国家自然科学基金 51105003

北京市自然科学基金 3172010

详细信息
    作者简介:

    黄昔光 男, 博士, 副教授, 硕士生导师。主要研究方向:机构学与机器人学

    通讯作者:

    黄昔光, E-mail: marchbupt@126.com

  • 中图分类号: TG112

Direct kinematics of a spatial parallel mechanism based on conformal geometric algebra

Funds: 

National Natural Science Foundation of China 51105003

Beijing Natural Science Foundation 3172010

More Information
  • 摘要:

    将共形几何代数(CGA)引入空间并联机构位置正解中,提出了一种空间3-RPS并联机构位置正解新算法。以任意一条支链轴线与静平台平面的夹角为待求变量,基于点的CGA表达方法建立了该支链与动平台连接的铰接点关于待求变量的数学表达式;通过2次构造2个空间球和1个平面的外积,分别获得动平台其余2个铰接点的点对;利用距离公式,只需简单的平方运算可直接推导出该问题关于待求变量的一元16次输入输出方程,进而获得了该机构的全部16组解析解,无增无漏。该方法没有繁琐的坐标变换和矩阵计算,以及复杂的多元高次非线性方程组消元求解。通过数字实例计算表明,求解过程较清晰地揭示出机构运动的几何特点,几何直观性好。

     

  • 图 1  一种空间3-RPS并联机构

    Figure 1.  A spatial 3-RPS parallel mechanism

    表  1  CGA中几何元素的表达式

    Table  1.   Expression of geometric elements in CGA

    几何元素 表达式1 (IPNS) 表达式2 (OPNS)
    P=X+X2e/2+e0
    S=Pr2e/2 S*=X1X2X3X4
    平面 π=n+te π*=X1X2X3e
    Z=S1S2 Z*=X1X2X3
    直线 l=π1π2 l*=X1X2e
    点对 PP=S1S2S3 P*P=X1X2
    下载: 导出CSV

    表  2  位置正解6组实数解

    Table  2.   Six sets of real solutions for direct kinematics

    组号 P1 P2 P3
    1 (0, 4.115, -0.840) (-1.320, 3.795, 0.628) (0.650, 3.545, 0.386)
    2 (0, 4.909, 1.051) (-1.491, 3.616, 0.727) (0.455, 3.710, 0.273)
    3 (0, 3.688, -1.376) (1.456, 5.000, -0.975) (0.150, 3.929, 0.097)
    4 (0, 4.833, 0.719) (1.234, 4.991, -0.847) (0.668, 3.529, 0.399)
    5 (0, 3.566, -1.505) (1.240, 4.991, -0.850) (-0.548, 4.281, -0.306)
    6 (0, 4.861, 0.830) (1.153, 4.984, -0.799) (-0.693, 4.331, -0.390)
    下载: 导出CSV
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出版历程
  • 收稿日期:  2016-12-06
  • 录用日期:  2017-03-06
  • 刊出日期:  2017-12-20

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