平面运动链拓扑胚图与拓扑图的统一综合及其计算机实现

发布时间：2018-07-10 09:19

本文选题：平面运动链 + 胚图综合　；参考：《燕山大学》2011年硕士论文

【摘要】：机构的结构类型综合在机械创新设计中处于基础地位,它不仅可以对已经存在的机构结构进行优化,使其更加合理,而且更重要的是可以发明、创造出新型机构。拓扑胚图与拓扑图在表示机构拓扑结构时各有优势,基于给定平面运动链的构件数和自由度,构造出统一的数学模型,然后综合其不含同构的拓扑胚图以及不含同构和消极子链的拓扑图,最后将综合结果通过开发的软件以图形的形式呈现出来,具有非常重要的理论和实际意义。本文首先简述了平面运动链的拓扑图以及拓扑胚图的相关定义,介绍了图形的同构和消极子链的概念及其判别过程中用到的边环路基础知识。然后提出了综合拓扑胚图的数学模型及其求解算法,并将拓扑图的同构判别原理经过改进,成功的运用到胚图的同构判别过程中,通过求解综合方程组并且将得到的解集进行同构判别和可分离判别,生成了不含同构的特征邻接矩阵,进而将其转化为非可分离的规范周长拓扑胚图。基于拓扑胚图,运用一定的规则将2度点插入到胚图中,然后经过同构判别和消极子链判别就可以得到胚图对应的拓扑图。通过循环运算,生成了给定构件分类数组对应的所有拓扑图。本文改进了同构判别和消极子链判别的方法,使计算时间明显缩短,平均综合时间缩短近2秒,并且综合的运动链的构件数也大大增加,由原来的16杆增加到20杆。运用Visual C++6.0软件开发平台,基于上述理论开发了一套综合的软件。该软件只需输入构件数和自由度数,就可以综合其对应的所有运动链的拓扑胚图和拓扑图。作者运用此软件已经综合出来18杆以内所有自由度以及20杆以内部分自由度的不可分离的拓扑胚图,并且综合出来了15杆以内所有自由度以18杆以内部分自由度的不可分离的拓扑图。
[Abstract]:The structure type synthesis of the mechanism is in the basic position in the mechanical innovation design. It can not only optimize the existing structure, make it more reasonable, but also be more important to invent and create a new type of mechanism. The topology embryo map and topological graph have advantages in expressing the structure of the mechanism, based on a given plane motion chain. The number of components and the degree of freedom, construct a unified mathematical model, and then synthesize its unisomorphic topological embryo map and topological graph without isomorphism and negative subchain. Finally, the comprehensive results are presented in the form of the software developed in the form of graphics, which has very important theoretical and practical significance.
In this paper, the topological graph of plane motion chain and the definition of topological embryo map are briefly introduced. The concept of the isomorphism and negative subchain of the graph and the basic knowledge of the boundary loop are introduced. Then the mathematical model of the comprehensive topological embryo graph and its solving algorithm are put forward, and the principle of the isomorphism discrimination of the topological graph is improved. It is successfully applied to the isomorphic discriminant process of the embryo map. By solving the integrated equation set and the isomorphic discrimination and separation discrimination, the isomorphic feature adjacency matrix is generated, and then it is converted into a non separable normalized topological embryo map of the circumference.
Based on topological embryo map, the 2 degree point is inserted into the embryo map with certain rules, and then the topological graph corresponding to the embryo map can be obtained through the isomorphism discrimination and the negative subchain discrimination. Through the cyclic operation, all the topological graphs of the classified array of given components are generated. The time is obviously shortened, the average synthesis time is shortened by nearly 2 seconds, and the number of components of the integrated kinematic chain is also greatly increased, from the original 16 bar to 20 rods.
Using the Visual C++6.0 software development platform, a set of integrated software is developed on the basis of the above theory. The software only needs to input the number of components and the degree of freedom, and the topology and topology map of all the corresponding kinematic chains can be synthesized. The author uses this software to integrate 18 poles with all freedom within and within 20 bars within part of freedom. The topological graph of the degree of separation can be separated, and the non separable topological graph of all degrees of freedom within 15 rods with 18 degrees of freedom is synthesized.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH112

【引证文献】