平面含复铰运动链拉普拉斯矩阵描述方法与同构判定  

Laplacian Matrices for Planes Containing Multiple Hinged Kinematic Chains Description and Isomorphism Determination

作　　者：陈诺 孙伟 杨帆行 胡高博 潘宇航 CHEN Nuo;SUN Wei;YANG Fanxing;HU Gaobo;PAN Yuhang(School of Mechinery Automation,Wuhan University of Science and Technology,Wuhan 430081,China)

机构地区：[1]武汉科技大学机械自动化学院,湖北武汉430081

出　　处：《轻工机械》2022年第3期30-35,共6页Light Industry Machinery

基　　金：国家自然科学基金(51875418);湖北省教育厅指导性项目(B2020011)。

摘　　要：为了在运动链构型综合过程中进行同构识别,课题组提出了一种拉普拉斯矩阵方法对平面含有复铰运动链的拓扑结构进行描述以及同构判定。首先,构建了一种拉普拉斯矩阵,利用奇异值分解来确定唯一性;其次,利用SVD分解得到奇异值向量,通过比较不同分量的奇异值向量形成拉普拉斯矩阵,从而判断是否同构来确定矩阵形成的唯一性机制;最后,通过案例进行证明。结果表明该方法具有有效性和高效性。In order to identify isomorphism in the process of kinematic chain configuration synthesis, a Laplacian matrix method was proposed to describe the topological structure of planar kinematic chain with complex hinges and determine the isomorphism. First, a kind of Laplace matrix method was constructed, and the uniqueness of the Laplacian matrix was determined by using singular value decomposition. Secondly, singular value vectors was obtained by SVD decomposition, and the unique mechanism of matrix formation was determined by comparing the singular value vectors of different components to the Laplacian matrix. Finally, results were proved by cases. The results show that the method is effective and efficient.

关 键 词：运动链 同构判定 奇异值向量 拉普拉斯矩阵 

分 类 号：TH122[机械工程—机械设计及理论] TH131.7