三维几何约束共性表达及解耦性的研究

发布时间：2018-11-27 19:29

【摘要】：三维几何约束求解对于装配建模、装配工艺规划和并行工程等多个领域的研究都有重要意义。虽然对几何约束系统的求解在过去几十年有大量的文献研究,但是仍有许多问题尚待解决,尤其是在三维几何约束求解领域。为此,本文对三维几何约束系统的建模、分析、分解和求解等方面的关键问题进行了研究,提出一种以抽象的具有共性的球体、盒体及球盒体统一表达三维几何实体的模型。探索解耦性的高效求解,建立三维几何约束系统求解的统一表达理论及求解技术体系,为高效三维几何约束求解器的实现提供基础理论。在几何约束系统中,几何实体之间的约束关系是非常复杂的,如何建立有效的几何约束系统模型,是几何约束系统研究的基础。本文首先研究了几何约束系统建模问题。以几何约束欧拉参数表达为基础,借鉴E.J.Haug简洁统一的基本约束表达方式,研究几何约束和几何实体共性的表达问题,并抽象出球体、盒体和球盒体三种基本几何实体表达空间几何体,建立几何约束系统模型,形成几何约束系统表达层。以无向图建立三维几何约束系统,约束图中的顶点的自由度和约束形式存在变化,因此,需要研究高效的分解策略,并适用操作性强的求解模式。针对三维装配姿态约束和位置约束的可解耦性,采用基于球面几何的方法研究可解耦构型姿态的求解,将单个姿态约束映射为球面上的一点,通过建立球平面坐标系,则球面上的点可映射为球平面上的二维点,三维空间问题转换为二维平面问题,其求解难度降低,几何推理意义明显。位置约束的求解拟采用解析的方法。本文运用三维几何领域的相关知识,通过分析几何约束系统的内在等价性,结合图论的理论,提出三维几何约束系统的等价性分析方法。该方法对几何约束图的拓扑结构进行优化,采用等价的方法拆除、缩减和分离约束闭环,并且在不需要考虑约束系统中的冗余约束,可以处理过约束、完整约束和欠约束,实现三维几何约束系统在几何意义上的最大分解。本文的研究内容在原型系统WhutVAS中得到实现,并通过实例验证了研究内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.
【学位授予单位】：武汉理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH164;TP391.7

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