一种基于图论理论的大尺度连续变形机构构型综合分析方法  

Comprehensive analysis method for configuration of large-scale continuous deformation mechanisms based on graph theory

作　　者：姚齐水[1,2] 董鹏林 唐嘉昌 夏艳 邱梓潼[1,2] YAO Qishui;DONG Penglin;TANG Jiachang;XIA Yan;QIU Zitong(School of Mechanical Engineering,Hunan University of Technology,Zhuzhou 412007,China;Key Laboratory of High-performance Rolling Bearings in Hunan Province,Zhuzhou 412007,China;China Academy of Launch Vehicle Technology,Beijing 100076,China)

机构地区：[1]湖南工业大学机械工程学院,湖南株洲412007 [2]高性能滚动轴承技术湖南省高校重点实验室,湖南株洲412007 [3]中国运载火箭技术研究院,北京100076

出　　处：《机电工程》2024年第6期1075-1086,共12页Journal of Mechanical & Electrical Engineering

基　　金：国家自然科学(企业发展联合)基金重点资助项目(U20B2028);中国运载火箭技术研究院自研项目(2022AVZS1887);株洲市“小荷”行动专项(202211)。

摘　　要：针对航空航天领域大尺度连续变形机构构型问题,提出了一种基于图论理论的大尺度连续变形机构构型综合分析方法。首先,分析了大尺度连续变形机构的组成与基本功能,获得了满足机构拓扑结构、约束条件的要求,对变形机构运动链进行了分析,得到了符合条件的运动链,并对其进行了数学描述;其次,选择并分析了运动链的拓扑对称性,利用特征数组的方法得到了判别矩阵,对运动链进行了同构判别,从而得到了可行的多种运动链形式;再次,建立了各运动链的拓扑图,通过筛选得到了最终的拓扑图,去掉该拓扑图的各个构件,得到了拓扑变换子图和相对应的邻接矩阵,对拓扑图进行了同构判别,再通过改变机架与移动副的位置得到了满足要求的12种构型,画出了其相应的机构拓扑图和机构简图;最后,考虑了大尺度连续变形机构的整体稳定性,避免了尺寸过大等因素,对大尺度变形机构进行了构型优选,得到了符合要求的多种新构型。研究结果表明:该方法能够将大尺度连续变形机构抽象为图形式,获得了22种构型,可根据机构变形要求的不同,改变优选依据,从而得到符合不同要求的构型。Aiming at the problem of large-scale continuous deformation mechanism configuration in aerospace field,a comprehensive analysis method of large-scale continuous deformation mechanism configuration based on graph theory was proposed.Firstly,the composition and basic functions of large-scale continuous deformation mechanism were analyzed to meet the requirements of the topological structure and constraint conditions of the mechanism.The kinematic chain of the mechanism was analyzed to obtain the conforming kinematic chain and its mathematical description.Secondly,the topological symmetry of the kinematic chain was selected and analyzed,and the discriminant matrix was obtained by using the method of characteristic array,and the isomorphism of the kinematic chain was discriminated,so that various feasible kinematic chain forms were obtained.Thirdly,the topological graph of each motion chain was established,and the final topological graph was obtained through screening.The topological transformation subgraph and the corresponding adjacency matrix were obtained by removing each component of the topological graph,and the isomorphism of the topological graph was judged.Then 12 configurations that meet the requirements were obtained by changing the position of the frame and the moving pair,and the corresponding mechanism topology diagram and mechanism diagram were drawn.Finally,considering the overall stability of the large-scale continuous deformation mechanism and avoiding excessive size and other factors,the configuration of the large-scale deformation mechanism was optimized,and many new configurations that met the requirements were obtained.The research results show that this method can abstract the large-scale continuous deformation mechanism into a graph form and obtain 22 configurations.According to the different deformation requirements of the mechanism,the basis of optimization can be changed,so that the configuration meeting different requirements can be obtained.

关 键 词：大尺度连续变形机构 图论法 构型综合 同构判别 运动链结构拓扑分析 机构变形要求 

分 类 号：TH112[机械工程—机械设计及理论] V22[航空宇航科学与技术—飞行器设计]