基于优化支链矩阵的运动链拓扑图自动绘制

doi:10.3969/j.issn.1004-132X.2026.08.014

摘要/Abstract

摘要：

提出了一种基于优化排列的支链矩阵进行运动链拓扑图连线绘制的新方法。利用树状结构图描述运动链结构信息，根据各构件及复铰的连接关系分离出各支链，生成支链矩阵。运用支链间的亲密度概念和对应的图的交叉判定定理进行支链矩阵的行排列优化，获得无交叉或最少交叉的优化支链矩阵。在此基础上，通过删除重复元素、调整元素位置、新增列和元素平移等操作，生成无交叉或最少交叉的双色拓扑图。案例分析和对比结果表明，所提绘制方法规则简单、环路信息清晰，能有效解决线条交叉问题，并可直接在优化支链矩阵的基础上生成运动链拓扑图。

关键词: 拓扑图绘制, 优化支链矩阵, 亲密度, 交叉判定

Abstract:

This paper presents a novel method for the automatic plotting of kinematic chain topological graphs， based on an optimally arranged branch-chain matrix. The structural information of a kinematic chain is first represented using a dendrogram. Branch chains are then extracted according to the connectivity of components and multiple joints， forming a branch-chain matrix. To minimize or eliminate crossings in the final graph， the row order of this matrix is optimized using the concept of intimacy between branch chains and the corresponding crossover-determination theorem， yielding an optimized branch-chain matrix with no or minimal crossings. Subsequently， a bicolored topological graph with minimal or no crossings is generated through a series of operations， including deletion of duplicate elements， element repositioning， insertion of new columns， and element translation. Case studies and comparative analyses demonstrate that the proposed method provides clear procedural rules and preserves distinct loop information. The method effectively resolves line-crossing issues and enables direct generation of topological graphs from the optimized branch-chain matrix.

Key words: topological graph sketching, optimized branch-chain matrix, intimacy, crossover determination

中图分类号:

TH112

薛钰, 孙亮波, 张博厚, 周华西, 王晓艺. 基于优化支链矩阵的运动链拓扑图自动绘制[J]. 中国机械工程, 2026, 37(8): 1947-1955.

XUE Yu, SUN Liangbo, ZHANG Bohou, ZHOU Huaxi, WANG Xiaoyi. Automatic Sketching of Kinematic Chain Topology Graphs Based on Optimized Branch-chain Matrices[J]. China Mechanical Engineering, 2026, 37(8): 1947-1955.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2026.08.014

https://www.cmemo.org.cn/CN/Y2026/V37/I8/1947

图/表 8

图1 11杆运动链1的结构图和树状结构图

Fig.1 Structure graph and dendrogram graph of the 11-bar kinematic chain 1

图2 运动链1无交叉的树状结构图

Fig.2 Non-crossing dendrogram graph of kinematic chain 1

图3 主链位置变化

Fig.3 Plot of the changes in the position of the main chain

图4 运动链1的拓扑图

Fig.4 Topological graph of kinematic chain 1

图5 拓扑图绘制流程图

Fig.5 Flowchart for topological graph sketching

图6 14杆运动链2的结构图和树状结构图

Fig.6 Structural graph and dendrogram graph of the 14-bar kinematic chain 2

图7 优化支链矩阵 M14的删除调整过程

Fig.7 Deletion and adjustment process for optimized branched-chain matrix M14

图8 运动链2的拓扑图

Fig.8 Topological graph of kinematic chain 2

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