A Method for Isomorphism Recognition of Kinematic Chain based on the Hamming Matrix and Connecting Rod Adjacency Matrix

Changjun Wu; Hui Xu; Tao Deng; Lu Zhang; Xubin Hua

doi:10.16578/j.issn.1004.2539.2021.11.005

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A Method for Isomorphism Recognition of Kinematic Chain based on the Hamming Matrix and Connecting Rod Adjacency Matrix

Theory·Reserach | 更新时间：2022-11-10

- A Method for Isomorphism Recognition of Kinematic Chain based on the Hamming Matrix and Connecting Rod Adjacency Matrix
- Journal of Mechanical Transmission Vol. 45, Issue 11, Pages: 29-33(2021)
- 作者机构：
  
  1.重庆交通大学机电与车辆工程学院，重庆 400074
  2.重庆交通大学航空学院，重庆 400074
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2021.11.005
  CLC：
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吴昌军,许辉,邓涛等.一种基于汉明矩阵和连杆邻接矩阵的运动链同构识别方法[J].机械传动,2021,45(11):29-33.

Wu Changjun,Xu Hui,Deng Tao,et al.A Method for Isomorphism Recognition of Kinematic Chain based on the Hamming Matrix and Connecting Rod Adjacency Matrix[J].Journal of Mechanical Transmission,2021,45(11):29-33.
吴昌军,许辉,邓涛等.一种基于汉明矩阵和连杆邻接矩阵的运动链同构识别方法[J].机械传动,2021,45(11):29-33. DOI： 10.16578/j.issn.1004.2539.2021.11.005.

Wu Changjun,Xu Hui,Deng Tao,et al.A Method for Isomorphism Recognition of Kinematic Chain based on the Hamming Matrix and Connecting Rod Adjacency Matrix[J].Journal of Mechanical Transmission,2021,45(11):29-33. DOI： 10.16578/j.issn.1004.2539.2021.11.005.

摘要

在机械装置的创造性设计中，应淘汰同构运动链，为后续设计减少机构方案，提高机械装置的设计效率。基于汉明矩阵提出了一种新的运动链同构判别方法。首先，从连杆邻接矩阵中导出运动链汉明矩阵；接着，将汉明矩阵的平方阵与连杆邻接矩阵的立方阵求积，得到运动链积矩阵；然后，将积矩阵各行元素以降序排列得积矩阵行序列；最后，将行序列中各元素与本文中所定义的拓扑因子相乘并求总和，得出运动链的同构识别码，即IRC（Isomorphism recognition code）。同构识别码不随构件标号的改变而改变，故若运动链的同构识别码相同，则它们为同构链，否则为异构链。大量实例证明了该方法的有效性。因其简洁、高效且利于计算机执行的特点，故可以考虑将其作为同构筛选的一种新的选择。

Abstract

In the creative design of mechanical devices，the isomorphic kinematic chains should be eliminated to reduce the mechanism scheme for subsequent design and improve the design efficiency of mechanical device. A new method for isomorphism recognition of kinematic chains is proposed based on the Hamming matrix. Firstly，the Hamming matrix of kinematic chains is educed from the link adjacency matrix，then the square matrix of Hamming matrix and the cubic matrix of link adjacency matrix are integrable to obtain the product matrix of kinematic chains. Secondly，the elements of each row in the product matrix are ordered in descending to get the row sequences of the product matrix. Finally，the isomorphism recognition code (IRC) of the kinematic chain is obtained by the sum of the product of the element in the row sequence with the defined topological factor. The isomorphism recognition code does not change with the link labels，so if the isomorphism recognition codes of the kinematic chains are the same，they are isomorphic，otherwise they are not. The effectiveness of this method is proved by a large number of examples. Because of its simplicity，efficiency and convenience for computer execution，it can be considered as a new option for isomorphism screening.

关键词

运动链同构行星轮系汉明矩阵

Keywords

Kinematic chainIsomorphismPlanetary gear trainHamming matrix

references

颜鸿森.机械装置的创造性设计［M］.北京：机械工业出版社，2002：1-209.

YAN Hongsen.Creative design of mechanical devices［M］.Beijing：China Machine Press，2002：1-209.

邓涛，周豪，唐鹏.并联混合动力传动系统结构创新设计研究［J］.汽车工程，2018，40（9）：5-12.

DENG Tao，ZHOU Hao，TANG Peng.Innovative design research on the structure of parallel hybrid powertrain system［J］.Automotive Engineering，2018，40（9）：5-12.

RAO A C.An artificial neural network approach to mechanism kinematic chain isomorphism identification［J］.Mechanism & Machine Theory，1999，37（5）：549-551.

YAN H S，CHIU Y T.On the number synthesis of kinematic chains［J］.Mechanism and Machine Theory，2015，89：128-144.

WOO L S.Type synthesis of plane linkages［J］.Journal of Engineering for Industry，1967，89（1）：159.

UICKER J J，RAICU A.A method for the identification and recognition of equivalence of kinematic chains［J］.Mechanism and Machine Theory，1975，10（5）：375-383.

RAO A C，VARADA R D.Application of the hamming number technique to detect isomorphism among kinematic chains and inversions［J］.Mechanism and Machine Theory，1991，26（1）：55-75.

YAN H S，HUNG C C.Identifying and counting the number of mechanisms from kinematic chains sbject to design constraints［J］.Journal of Mechanical Design，2006，128（5）：1177-1182.

褚金奎，张然，邹炎火.平面机构拓扑结构理论及在机构创新设计中的应用［M］.北京：科学出版社，2017：1-390.

CHU Jinkui，ZHANG Ran，ZOU Yanhuo.Topological structure theory of planar mechanism and its application in innovative design of mechanism［M］.Beijing：Science Press，2017：1-390.

DHARANIPRAGADA V，CHINTADA M.Split hamming String as an isomorphism test for one degree-of-freedom planar simple-jointed kinematic chains containing sliders［J］.Journal of Mechanical Design，2016，138（8）：1-8.

YANG W J，DING H F，LAI X Z，et al.Automatic synthesis of planar simple joint mechanisms with up to 19 links［J］.Mechanical and Machine Theory，2017，113：193-207 .

RAI R K，PUNJABI S.Kinematic chains isomorphism identification using link connectivity number and entropy neglecting tolerance and clearance［J］.Mechanism and Machine Theory，2018，123：40-65.

RAI R K，PUNJABI S.A new algorithm of links labelling for the isomorphism detection of various kinematic chains using binary code［J］.Mechanism and Machine Theory，2019，131：1-32.

YANG W J，DING H F，Andrés Kecskeméthy .Automatic synthesis of plane kinematic chains with prismatic pairs and up to 14 links［J］.Mechanism and Machine Theory，2019，132：236-247.

李安明，孙伟，孔建益，等.含复铰运动链的改进邻接矩阵描述及同构判定［J］.机械科学与技术，2020，39（4）：516-523.

LI Anming，SUN Wei，KONG Jianyi，et al.Improved adjacency matrix description and isomorphism identification of kinematic chain with multiple joints［J］.Mechanical Science and Technology for Aerospace Engineering，2020，39（4）：516-523.

DENG T，XU H，TANG P，et al.A novel algorithm for the isomorphism detection of various kinematic chains using topological index［J］.Mechanism and Machine Theory，2020，146：1-26.

孙伟，孔建益，王兴东，等.基于构件-构件邻接矩阵的含复铰运动链描述与同构判定［J］.机械工程学报，2020，56（3）：41-46.

SUN Wei，KONG Jianyi，WANG Xingdong，et al.Description and isomorphism judgment of the kinematic chain with multiple joints based on link-link adjacency matrix［J］.Chinese Journal of Mechanical Engineering，2020，56（3）：41-46.

SUN L，CUI R J，YE Z Z，et al.Similarity recognition and isomorphism identification of planar kinematic chains［J］.Mechanism and Machine Theory，2020，145：1-30.

丁华锋，黄真.平面机构统一拓扑描述模型的建立及同构判别［J］.机械工程学报，2009，45（3）：99-103.

DING Huafeng，HUANG Zhen.Establishment of uniform topology description model for planar mechanism and identification of isomorphism［J］.Chinese Journal of Mechanical Engineering，2009，45（3）：99-103.

YANG W J，DING H F，ZI B，et al.New graph representation for planetary gear trains［J］.Journal of Mechanical Design，2018，140：5-7.

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