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一种运动链拓扑对称性识别方法

吴昌军 邓涛 许辉 张露

吴昌军,邓涛,许辉, 等. 一种运动链拓扑对称性识别方法[J]. 机械科学与技术,2022,41(4):523-529 doi: 10.13433/j.cnki.1003-8728.20200384
引用本文: 吴昌军,邓涛,许辉, 等. 一种运动链拓扑对称性识别方法[J]. 机械科学与技术,2022,41(4):523-529 doi: 10.13433/j.cnki.1003-8728.20200384
WU Changjun, DENG Tao, XU Hui, ZHANG Lu. A Method for Recognizing Topological Symmetry of Kinematic Chain[J]. Mechanical Science and Technology for Aerospace Engineering, 2022, 41(4): 523-529. doi: 10.13433/j.cnki.1003-8728.20200384
Citation: WU Changjun, DENG Tao, XU Hui, ZHANG Lu. A Method for Recognizing Topological Symmetry of Kinematic Chain[J]. Mechanical Science and Technology for Aerospace Engineering, 2022, 41(4): 523-529. doi: 10.13433/j.cnki.1003-8728.20200384

一种运动链拓扑对称性识别方法

doi: 10.13433/j.cnki.1003-8728.20200384
基金项目: 重庆市教委科学技术研究重点项目(KJZD-K202000701)与重庆市技术创新与应用发展专项重点项目(cstc2019jscx-fxydX0028)
详细信息
    作者简介:

    吴昌军(1997−),硕士研究生,研究方向为机电复合传动系统,759654145@qq.com

    通讯作者:

    邓涛,教授,硕士生导师, d82t722@cqjtu.edu.cn

  • 中图分类号: TH112

A Method for Recognizing Topological Symmetry of Kinematic Chain

  • 摘要: 运动链拓扑对称性需要识别以减少机械装置新构型的备选方案,提高机械结构设计的效率。本文基于连杆邻接矩阵提出了一种新的运动链拓扑对称性识别方法。首先以连杆邻接矩阵为已知量导出汉明矩阵,计算汉明矩阵的平方阵与连杆邻接矩阵的立方阵,其次将上述平方阵与立方阵求积得积矩阵且将此积矩阵各行中的元素按降序排列得积矩阵行序列,最后将序列中各元素与拓扑因子相乘并求和得出运动链的拓扑对称性识别码(Topological symmetry recognition code,TSRC)。若同一拓扑图中两顶点的对称性识别码相同,则它们是对称的,否则是非对称的。通过单铰、复铰运动链和行星轮系的实例证明此方法的有效性,结果表明:此方法简单、高效且便于计算机编程。
  • 图  1  瓦特链及其拓扑图

    图  2  一种复铰运动链及其拓扑图

    图  3  辛普森行星轮系及其拓扑图

    图  4  构件拓扑对称性识别流程

    图  5  瓦特链形成的两种同构机构

    图  6  单铰运动链实例[14]

    图  7  复铰运动链实例

    图  8  行星轮系实例

    表  1  图1各构件的TSRC值

    构件号123456
    TSRC105241003610036105241003610036
    下载: 导出CSV

    表  2  图6a)各构件的TSRC值

    组别TSRC构件组别TSRC构件
    1 118544 2,10 5 144806 4
    2 120996 7 6 145134 8
    3 126096 6 7 147240 3,9
    4 133930 5 8 182290 1
    下载: 导出CSV

    表  3  图6b)各构件的TSRC值

    组别TSRC构件组别TSRC构件
    11141508 61308343
    2122272271409244
    3124384781420529
    41264081091440845
    51298466101695601
    下载: 导出CSV

    表  4  图6a)各构件的连杆邻接串

    构件
    标号
    连杆邻接串
    1 34, 000001311301, (32, 000001212301)×3
    2 50, 000014310001, 40, 000002402101
    3 40, 000012203101, 40, 000002402101, 32, 000001212301
    4 (40, 000002402101)×2, 36, 000000252001
    5 40, 000012203101, 34, 000001311301
    6 50, 000014310001, 36, 000000252001
    7 50, 000014310001, 40, 000002402101
    8 (40, 000002402101)×2, 32, 000001212301
    9 40, 000012203101, 40, 000002402101, 32, 000001212301
    10 50, 000014310001, 40, 000002402101
    下载: 导出CSV

    表  5  图7a)各顶点的TSRC值

    组别TSRC顶点组别TSRC顶点
    185847244 6921122410
    288773467798950405
    3888890668101818003
    489185602913984848
    5920808691013986921
    下载: 导出CSV

    表  6  图7b)各顶点的TSRC值

    组别TSRC顶点组别TSRC顶点
    16942886 48878565,7
    27527364,8 ~ 10511906881,3
    38122402
    下载: 导出CSV

    表  7  图7a)各顶点的CPVS值

    组别SPVS顶点组别SPVS顶点
    1 2826268400000 8 6 26984440000 9,10
    2 2826268222000 1 7 26654420000 7
    3 281087542000 3 8 7754442000 4
    4 28774441000 5 9 7654440000 6
    5 261084441000 2
    下载: 导出CSV

    表  8  图8a)各顶点的TSRC值

    组别TSRC顶点组别TSRC顶点
    133540306,7 342168143,5
    240153482,4451130041
    下载: 导出CSV

    表  9  图8b)各顶点的TSRC值

    组别TSRC顶点组别TSRC顶点
    112262206 415839104
    213608423515983345
    314678462617685541
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-07-19
  • 录用日期:  2021-12-17
  • 网络出版日期:  2022-05-11
  • 刊出日期:  2022-09-05

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