【摘要】：三維幾何約束求解對(duì)于裝配建模、裝配工藝規(guī)劃和并行工程等多個(gè)領(lǐng)域的研究都有重要意義。雖然對(duì)幾何約束系統(tǒng)的求解在過去幾十年有大量的文獻(xiàn)研究,但是仍有許多問題尚待解決,尤其是在三維幾何約束求解領(lǐng)域。為此,本文對(duì)三維幾何約束系統(tǒng)的建模、分析、分解和求解等方面的關(guān)鍵問題進(jìn)行了研究,提出一種以抽象的具有共性的球體、盒體及球盒體統(tǒng)一表達(dá)三維幾何實(shí)體的模型。探索解耦性的高效求解,建立三維幾何約束系統(tǒng)求解的統(tǒng)一表達(dá)理論及求解技術(shù)體系,為高效三維幾何約束求解器的實(shí)現(xiàn)提供基礎(chǔ)理論。 在幾何約束系統(tǒng)中,幾何實(shí)體之間的約束關(guān)系是非常復(fù)雜的,如何建立有效的幾何約束系統(tǒng)模型,是幾何約束系統(tǒng)研究的基礎(chǔ)。本文首先研究了幾何約束系統(tǒng)建模問題。以幾何約束歐拉參數(shù)表達(dá)為基礎(chǔ),借鑒E.J.Haug簡(jiǎn)潔統(tǒng)一的基本約束表達(dá)方式,研究幾何約束和幾何實(shí)體共性的表達(dá)問題,并抽象出球體、盒體和球盒體三種基本幾何實(shí)體表達(dá)空間幾何體,建立幾何約束系統(tǒng)模型,形成幾何約束系統(tǒng)表達(dá)層。 以無向圖建立三維幾何約束系統(tǒng),約束圖中的頂點(diǎn)的自由度和約束形式存在變化,因此,需要研究高效的分解策略,并適用操作性強(qiáng)的求解模式。針對(duì)三維裝配姿態(tài)約束和位置約束的可解耦性,采用基于球面幾何的方法研究可解耦構(gòu)型姿態(tài)的求解,將單個(gè)姿態(tài)約束映射為球面上的一點(diǎn),通過建立球平面坐標(biāo)系,則球面上的點(diǎn)可映射為球平面上的二維點(diǎn),三維空間問題轉(zhuǎn)換為二維平面問題,其求解難度降低,幾何推理意義明顯。位置約束的求解擬采用解析的方法。 本文運(yùn)用三維幾何領(lǐng)域的相關(guān)知識(shí),通過分析幾何約束系統(tǒng)的內(nèi)在等價(jià)性,結(jié)合圖論的理論,提出三維幾何約束系統(tǒng)的等價(jià)性分析方法。該方法對(duì)幾何約束圖的拓?fù)浣Y(jié)構(gòu)進(jìn)行優(yōu)化,采用等價(jià)的方法拆除、縮減和分離約束閉環(huán),并且在不需要考慮約束系統(tǒng)中的冗余約束,可以處理過約束、完整約束和欠約束,實(shí)現(xiàn)三維幾何約束系統(tǒng)在幾何意義上的最大分解。 本文的研究?jī)?nèi)容在原型系統(tǒng)WhutVAS中得到實(shí)現(xiàn),并通過實(shí)例驗(yàn)證了研究?jī)?nèi)容的可行性和有效性。
[Abstract]:3D geometric constraint solving is very important for assembly modeling, assembly process planning and concurrent engineering. Although there has been a lot of literature research on geometric constraint system in the past few decades, there are still many problems to be solved, especially in the field of 3D geometric constraint solution. Therefore, the key problems in modeling, analysis, decomposition and solution of 3D geometric constraint system are studied in this paper, and a model of representing 3D geometric entities by abstract and common sphere, box and spherical box is proposed. This paper explores the efficient solution of decoupling, establishes the unified representation theory and technical system for solving 3D geometric constraint system, and provides the basic theory for the realization of efficient 3D geometric constraint solver. In geometric constraint system, the constraint relationship between geometric entities is very complex. How to establish an effective geometric constraint system model is the foundation of geometric constraint system research. In this paper, the modeling problem of geometric constrained systems is studied. Based on the Euler parameter representation of geometric constraints, the representation of geometric constraints and geometric entity commonalities is studied by using E.J.Haug 's simple and uniform basic constraint expression method, and the sphere is abstracted. Three basic geometric entities, box and spherical box, express spatial geometry, establish geometric constraint system model, and form geometric constraint system representation layer. The degree of freedom and the constraint form of the vertex in the constraint graph are changed by using the undirected graph to establish the three-dimensional geometric constraint system. Therefore, it is necessary to study the efficient decomposition strategy and apply the solution mode with strong maneuverability. Aiming at the decoupling of 3D assembly attitude constraint and position constraint, the method based on spherical geometry is used to study the solution of decoupled configuration attitude. The single attitude constraint is mapped to a point on the sphere, and the spherical plane coordinate system is established. Then the points on the sphere can be mapped to the two-dimensional points on the spherical plane, and the three-dimensional space problem can be transformed into the two-dimensional plane problem. The difficulty of solving the problem is reduced and the significance of geometric reasoning is obvious. The analytical method is used to solve the position constraint. In this paper, by analyzing the intrinsic equivalence of geometric constraint systems and combining the theory of graph theory, an equivalent analysis method of 3D geometric constraint systems is proposed by using the relevant knowledge in the field of 3D geometry. This method optimizes the topological structure of geometric constraint graph, and adopts equivalent method to remove, reduce and separate the closed loop of constraints, and can deal with overconstraints, complete constraints and underconstraints without considering the redundant constraints in the constraint system. The maximum decomposition of 3D geometric constraint system in geometric sense is realized. The research content of this paper is realized in the prototype system WhutVAS, and the feasibility and effectiveness of the research content are verified by an example.
【學(xué)位授予單位】：武漢理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：TH164;TP391.7

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