An Innovative Approach to Detect Isomorphism in Planar and Geared Kinematic Chains Using Graph Theory
An Innovative Approach to Detect Isomorphism in Planar and Geared Kinematic Chains Using Graph Theory
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DOI：
10.1115/1.4037628
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发表时间：
2017-12
影响因子：
3.3
通讯作者：
V. V. Kamesh-V.;K. M. Rao;Annambhotla Balaji Srinivasa Rao
中科院分区：
文献类型：
--
作者：
V. V. Kamesh-V.;K. M. Rao;Annambhotla Balaji Srinivasa Rao
平面和齿轮运动链的同构检测是多年来一个有趣的领域。只有当同构问题得到有效解决时，平面运动链和齿轮运动链的枚举才变得容易。许多研究人员提出了基于拓扑特征或一些编码的算法，这些算法需要大量的计算和比较。本文以图论为基础，提出了一种新的、简单的同构链消去算法，利用该算法可以很容易地消除同构链，而不需要进行繁琐的计算或比较。在图论的基础上，提出了网距的新概念，作为评价平面运动链同构和GKCs同构的量化指标。将该算法完全应用于九连杆两自由度不同运动链上，并给出了计算结果。以8杆1自由度、10杆1自由度、12杆1自由度和15杆4自由度为例对算法进行了测试。该算法还在四个六连杆1自由度GKC上进行了测试，以检测同构。所得结果与已有文献基本一致。[DOI：10.1115/1.4037628]
Detection of isomorphism in planar and geared kinematic chains (GKCs) is an interesting area since many years. Enumeration of planar and geared kinematic chains becomes easy only when isomorphism problem is resolved effectively. Many researchers proposed algorithms based on topological characteristics or some coding which need lot of computations and comparisons. In this paper, a novel and simple algorithm is proposed based on graph theory by which elimination of isomorphic chains can be done very easily without any tedious calculations or comparisons. A new concept “Net distance” is proposed based on the graph theory to be a quantitative measure to assess isomorphism in planar kinematic chains (PKCs) as well as GKCs. The proposed algorithm is applied on nine-link two-degrees-of-freedom (DOF) distinct kinematic chains completely and the results are presented. Algorithm is tested on examples from eight-link 1-DOF, ten-link 1-DOF, 12-link 1-DOF, and 15link 4-DOF PKCs. The algorithm is also tested on four, six-link 1-DOF GKCs to detect isomorphism. All the results are in agreement with the existing literature. [DOI: 10.1115/1.4037628]