基于创新技法的机构拓扑结构若干问题研究
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摘要
机构拓扑结构是机构学研究的直接对象，对其进行描述和分析是机构结构学的基础，对其进行综合是机械产品设计的重要环节。目前，不仅稳定拓扑结构的研究重点已覆盖到非线性、强耦合的广义机构系统，而且变拓扑结构也成为研究热点。然而，在研究内容上，不同拓扑结构的理论研究相对独立，机构拓扑结构本身和相关概念的界线比较模糊，同时，尚未有考虑驱动和机架在内的稳定拓扑和变拓扑结构整体分析模型；此外，工程中迫切需要理论指导的专利资源有效利用在机构综合研究中仍是一个尚未探索的新课题。在研究方法上，直接运用数学方法和力学原理对非数值、非线性、变结构和强耦合机构拓扑系统进行研究，难以全面描述其详细结构信息，对于含有复合铰链和变胞运动副等复杂结构的拓扑系统，分析和综合非常困难，迫切需要改进研究方法，从更广泛的角度寻找解决途径。
本文针对广义化和变结构机构拓扑在描述、分析和综合中存在的上述问题，采用TRIZ理论、公理设计理论、复杂性理论、组合技法、设计目录等多种具有不同优势的创新技法，结合数学方法和力学原理，开展了深入系统的研究。
本文完成主要研究工作如下
（1）针对机构拓扑结构缺乏系统模型、相关概念模糊不确定的问题，从集合论角度，对机构拓扑结构、运动链拓扑结构、变拓扑机构、可重构机构、变胞机构、稳定构态、变拓扑构态和变胞构态等概念提出了严密的数学表达；基于TRIZ物-场分析方法，建立了机构系统物-场模型；运用公理设计理论，对运动副物-场建立了功能域和物理域模型；运用TRIZ标准解找到了理想化模型转化方案；示例表明这些定义和模型可从不同层次对拓扑系统进行有效描述和分析。
（2）针对复合铰运动链拓扑结构强耦合关系难以描述及同构识别困难的问题，按照复合铰链理想化模型转化思路，基于功能独立性公理，引入pin构件对复合铰链进行解耦，建立转化邻接矩阵对含复铰运动链进行描述，并提出了运用其阶数、对角线元素向量、矩阵特征值和特征向量等参数判断运动链拓扑同构关系的新方法，通过实例验证了方法的有效性。
（3）针对变结构、非线性变胞运动副难以全面描述其结构信息的问题，将复杂性概念引入运动副物-场对模型中的“物质”进行描述；基于组合创新技法定义了约束函数，用于广泛描述运动副的性质、类型、级别、自由度、方位、约束的有效性、作用的程度及其变化等诸多信息；按照变胞副理想化模型转化思路，定义了反映运动副蜕化和激活状态的变胞基因，建立了基本运动副变胞模型；基于效应原理，分析了基元变胞的物理实现方式。实例应用验证了这些理论的正确性和有效性。
（4）针对变拓扑机构非数值、非线性构态变化难以分析的问题，提出了机构构态切换的6个充分条件；基于TRIZ冲突问题解决技法，分析了变拓扑机构物-场的物理冲突，提出了利用稳定构态作为内部资源构建变拓扑机构超系统模型—胞源机构的新思路；运用集合论和旋量理论对胞源机构进行了描述和分析，构建了基于运动副约束函数的胞源机构邻接矩阵，建立了6类变胞形式的机构变胞态变胞方程。实例证明了理论的可行性和有效性。
（5）针对面向专利资源进行机构综合创新的新课题进行了研究。基于TRIZ功能裁剪法和设计目录，构建了机构综合再创新程序化过程理论模型，通过实例应用证明了该过程模型在产品开发中的可操作性和实用性。
总之，本文对机构拓扑结构的相关概念进行了严密数学定义，明确了概念之间的关系。运用诸多创新技法，结合数学方法和力学原理，对稳定拓扑和变拓扑机构的概念和系统模型进行了基础研究、对含复合铰链和变胞运动副的拓扑结构描述和分析问题进行了详细研究、对利用专利资源进行机构综合创新设计进行了初步探索。本文研究工作为机构学研究和机械产品创新设计提供了新的理论和方法，具有重要的应用价值。
Topology structure of mechanisms (TSM) reflects the composition and workingprinciple of mechanisms. The description and analysis of TSM lays the foundation ofstructural research of mechanisms, and the synthesis of TSM plays a key role inmechanical products designing. Presently, the key points of research of stable TSMare expended to nonlinear and strong-coupling generalized mechanism systems.Meanwhile, the mechanism with variable topologies (MVT) is becoming the hotresearch area in mechanisms.
Up to now, theory researches of different topology structures are mutuallyindependent in mechanisms, and some concepts related to TSM and their relationshipremain ambiguous. On the other hand, there are few integral analysis models of stableTSM and MVT that take driver and frame into account. The utilizing of patentresources, which is very important for engineering design, is unexplored in the designand synthesizing of mechanisms. As for research methods, it is difficult to applymathematical methods and mechanics principles directly to represent the detailedinformation of TSM system with non-numerical, non-linear, variable structure andstrong-coupling characteristics. Analyzing and synthesizing are extremely difficultfor systems with complex structure, such as multiple joint and metamorphic pair.
This dissertation is focusing on improving research method and solving theseproblems on a broader perspective. Several innovative methods with differentstrengths are adopted in research. These methods combined with mathematicalmethods and mechanics principles are employed to describe, analyze and synthesizegeneralized mechanisms and variable topology mechanisms.
The main works of the dissertation are as follows
(1) In order to build a system model of stable TSM and MVT and explicaterelationships among different TSMs, based on the set theory, the dissertation gives therigorous mathematical definitions of TSM, TSKC, MVT, Reconfigurable Mechanism,Metamorphic Mechanism, etc. Based on the Su-field analysis, the hierarchical modelis established to describe a mechanism system. The functional domain model and thephysical domain model are also built to represent a kinematic pair by applying theAxiomatic Design theory. To improve the ideality of the Su-field models of a multiplejoint and a metamorphic pair, the evolution schemes are created according to standard solutions of TRIZ. The examples indicate that these definitions and models caneffectively describe and analyze TSM at different levels.
(2) To describe the strong coupled relation of the topological structure ofkinematic chains with multiple joint and identify isomorphism, based on thefunctional autonomy principle, the dissertation introduces the Pin-link to decouplemultiple joints according to the evolution scheme of a multiple joint model. Thetransformed adjacency matrix is established to describe kinematic chains withmultiple joints, and a new method for isomorphism identification of planar kinematicchains is proposed by using some characteristic parameters of the converted adjacentmatrix. The application examples show that the converted adjacent matrix couldconveniently represent planar kinematic chains with multiple joints, and the eigenvalues and eigenvectors of the converted adjacent matrix can be used to efficientlyidentify the isomorphism of planar kinematic chains.
(3) In order to completely represent the structural information of a metamorphickinematic pair, the dissertation introduces the complexity into the Su-field model ofkinematic pair to describe the “substance” in the model. By using the combinationmethod, the constraint function is defined to represent the “field” in Su-field model ofkinematic pair, which can be used to describe the properties, type, grade, DOF,direction, constraint efficiency, degree, and their changes. According to the evolutionscheme of a metamorphic pair model, the metamorphic gene is defined to determinewhether a kinematic pair is activated or not while the metamorphic models of basickinematic pairs are constructed to denote the metamorphic directions of a pair. Thephysical implementations of metamorphic gene elements are analyzed based on theeffect principles. The examples show that the theory and the method can be used torepresent and analyze a metamorphic pair effectively.
(4) To analyze the non-numerical and non-linear configuration transformation ofvariable topological mechanisms, the dissertation considers six sufficient conditionsfor configuration switching according to the definition of TSM. Based on TRIZ, thephysical contradictions in the Su-field model of MVT are analyzed and a newapproach to create the metamorphic origin mechanism by using the stableconfigurations as internal resources is proposed. With constraint functions aselements, the adjacent matrix of the metamorphic origin mechanism is built and themetamorphic equations of six kinds of metamorphic forms are established. Theexamples show that the method can analyze the configuration transformation of MVTreasonably.
(5) Focusing on the innovative mechanism synthesis by using of patentresources, based on the function trimming of TRIZ and Catalog Design, thedissertation proposes a patent oriented and competitive patent circumvented processmodel of mechanism synthesis re-innovating. The application example indicates thatthis process model can feasibly direct the mechanism synthesis in the innovativedesign of products.
In summary, the dissertation develops the rigorous mathematical expression toTSM system and clarifies the relationship among different TSMs. By using severalinnovation methods and combining with mathematical methods as well as mechanicalprinciples, the dissertation conducts basic research works on the systematical modelsof stable and variable topological mechanisms. The problems for describing andanalyzing the topological structure with multiple joints and metamorphic kinematicpairs are investigated. A patent oriented and competitive patent circumvented processmodel of mechanism synthesis innovation in product design is proposed. Thisdissertation provides new theories and methods for mechanism research andinnovative design of mechanical products.
本文针对广义化和变结构机构拓扑在描述、分析和综合中存在的上述问题，采用TRIZ理论、公理设计理论、复杂性理论、组合技法、设计目录等多种具有不同优势的创新技法，结合数学方法和力学原理，开展了深入系统的研究。
本文完成主要研究工作如下
（1）针对机构拓扑结构缺乏系统模型、相关概念模糊不确定的问题，从集合论角度，对机构拓扑结构、运动链拓扑结构、变拓扑机构、可重构机构、变胞机构、稳定构态、变拓扑构态和变胞构态等概念提出了严密的数学表达；基于TRIZ物-场分析方法，建立了机构系统物-场模型；运用公理设计理论，对运动副物-场建立了功能域和物理域模型；运用TRIZ标准解找到了理想化模型转化方案；示例表明这些定义和模型可从不同层次对拓扑系统进行有效描述和分析。
（2）针对复合铰运动链拓扑结构强耦合关系难以描述及同构识别困难的问题，按照复合铰链理想化模型转化思路，基于功能独立性公理，引入pin构件对复合铰链进行解耦，建立转化邻接矩阵对含复铰运动链进行描述，并提出了运用其阶数、对角线元素向量、矩阵特征值和特征向量等参数判断运动链拓扑同构关系的新方法，通过实例验证了方法的有效性。
（3）针对变结构、非线性变胞运动副难以全面描述其结构信息的问题，将复杂性概念引入运动副物-场对模型中的“物质”进行描述；基于组合创新技法定义了约束函数，用于广泛描述运动副的性质、类型、级别、自由度、方位、约束的有效性、作用的程度及其变化等诸多信息；按照变胞副理想化模型转化思路，定义了反映运动副蜕化和激活状态的变胞基因，建立了基本运动副变胞模型；基于效应原理，分析了基元变胞的物理实现方式。实例应用验证了这些理论的正确性和有效性。
（4）针对变拓扑机构非数值、非线性构态变化难以分析的问题，提出了机构构态切换的6个充分条件；基于TRIZ冲突问题解决技法，分析了变拓扑机构物-场的物理冲突，提出了利用稳定构态作为内部资源构建变拓扑机构超系统模型—胞源机构的新思路；运用集合论和旋量理论对胞源机构进行了描述和分析，构建了基于运动副约束函数的胞源机构邻接矩阵，建立了6类变胞形式的机构变胞态变胞方程。实例证明了理论的可行性和有效性。
（5）针对面向专利资源进行机构综合创新的新课题进行了研究。基于TRIZ功能裁剪法和设计目录，构建了机构综合再创新程序化过程理论模型，通过实例应用证明了该过程模型在产品开发中的可操作性和实用性。
总之，本文对机构拓扑结构的相关概念进行了严密数学定义，明确了概念之间的关系。运用诸多创新技法，结合数学方法和力学原理，对稳定拓扑和变拓扑机构的概念和系统模型进行了基础研究、对含复合铰链和变胞运动副的拓扑结构描述和分析问题进行了详细研究、对利用专利资源进行机构综合创新设计进行了初步探索。本文研究工作为机构学研究和机械产品创新设计提供了新的理论和方法，具有重要的应用价值。
Topology structure of mechanisms (TSM) reflects the composition and workingprinciple of mechanisms. The description and analysis of TSM lays the foundation ofstructural research of mechanisms, and the synthesis of TSM plays a key role inmechanical products designing. Presently, the key points of research of stable TSMare expended to nonlinear and strong-coupling generalized mechanism systems.Meanwhile, the mechanism with variable topologies (MVT) is becoming the hotresearch area in mechanisms.
Up to now, theory researches of different topology structures are mutuallyindependent in mechanisms, and some concepts related to TSM and their relationshipremain ambiguous. On the other hand, there are few integral analysis models of stableTSM and MVT that take driver and frame into account. The utilizing of patentresources, which is very important for engineering design, is unexplored in the designand synthesizing of mechanisms. As for research methods, it is difficult to applymathematical methods and mechanics principles directly to represent the detailedinformation of TSM system with non-numerical, non-linear, variable structure andstrong-coupling characteristics. Analyzing and synthesizing are extremely difficultfor systems with complex structure, such as multiple joint and metamorphic pair.
This dissertation is focusing on improving research method and solving theseproblems on a broader perspective. Several innovative methods with differentstrengths are adopted in research. These methods combined with mathematicalmethods and mechanics principles are employed to describe, analyze and synthesizegeneralized mechanisms and variable topology mechanisms.
The main works of the dissertation are as follows
(1) In order to build a system model of stable TSM and MVT and explicaterelationships among different TSMs, based on the set theory, the dissertation gives therigorous mathematical definitions of TSM, TSKC, MVT, Reconfigurable Mechanism,Metamorphic Mechanism, etc. Based on the Su-field analysis, the hierarchical modelis established to describe a mechanism system. The functional domain model and thephysical domain model are also built to represent a kinematic pair by applying theAxiomatic Design theory. To improve the ideality of the Su-field models of a multiplejoint and a metamorphic pair, the evolution schemes are created according to standard solutions of TRIZ. The examples indicate that these definitions and models caneffectively describe and analyze TSM at different levels.
(2) To describe the strong coupled relation of the topological structure ofkinematic chains with multiple joint and identify isomorphism, based on thefunctional autonomy principle, the dissertation introduces the Pin-link to decouplemultiple joints according to the evolution scheme of a multiple joint model. Thetransformed adjacency matrix is established to describe kinematic chains withmultiple joints, and a new method for isomorphism identification of planar kinematicchains is proposed by using some characteristic parameters of the converted adjacentmatrix. The application examples show that the converted adjacent matrix couldconveniently represent planar kinematic chains with multiple joints, and the eigenvalues and eigenvectors of the converted adjacent matrix can be used to efficientlyidentify the isomorphism of planar kinematic chains.
(3) In order to completely represent the structural information of a metamorphickinematic pair, the dissertation introduces the complexity into the Su-field model ofkinematic pair to describe the “substance” in the model. By using the combinationmethod, the constraint function is defined to represent the “field” in Su-field model ofkinematic pair, which can be used to describe the properties, type, grade, DOF,direction, constraint efficiency, degree, and their changes. According to the evolutionscheme of a metamorphic pair model, the metamorphic gene is defined to determinewhether a kinematic pair is activated or not while the metamorphic models of basickinematic pairs are constructed to denote the metamorphic directions of a pair. Thephysical implementations of metamorphic gene elements are analyzed based on theeffect principles. The examples show that the theory and the method can be used torepresent and analyze a metamorphic pair effectively.
(4) To analyze the non-numerical and non-linear configuration transformation ofvariable topological mechanisms, the dissertation considers six sufficient conditionsfor configuration switching according to the definition of TSM. Based on TRIZ, thephysical contradictions in the Su-field model of MVT are analyzed and a newapproach to create the metamorphic origin mechanism by using the stableconfigurations as internal resources is proposed. With constraint functions aselements, the adjacent matrix of the metamorphic origin mechanism is built and themetamorphic equations of six kinds of metamorphic forms are established. Theexamples show that the method can analyze the configuration transformation of MVTreasonably.
(5) Focusing on the innovative mechanism synthesis by using of patentresources, based on the function trimming of TRIZ and Catalog Design, thedissertation proposes a patent oriented and competitive patent circumvented processmodel of mechanism synthesis re-innovating. The application example indicates thatthis process model can feasibly direct the mechanism synthesis in the innovativedesign of products.
In summary, the dissertation develops the rigorous mathematical expression toTSM system and clarifies the relationship among different TSMs. By using severalinnovation methods and combining with mathematical methods as well as mechanicalprinciples, the dissertation conducts basic research works on the systematical modelsof stable and variable topological mechanisms. The problems for describing andanalyzing the topological structure with multiple joints and metamorphic kinematicpairs are investigated. A patent oriented and competitive patent circumvented processmodel of mechanism synthesis innovation in product design is proposed. Thisdissertation provides new theories and methods for mechanism research andinnovative design of mechanical products.
引文
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