求解三维装配几何约束闭环系统的约束变换方法  

Constraint Transformation Method for Solving 3D Geometric Constraint System of Closed-loop Assemblies

作　　者：黄学良[1] 李娜[1] 陈立平[2] 

机构地区：[1]中国工程物理研究院总体工程研究所,绵阳621900 [2]华中科技大学国家CAD支撑软件工程技术研究中心,武汉430074

出　　处：《机械科学与技术》2014年第1期57-64,共8页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金重点项目(60736019)资助

摘　　要：采用等价性分析方法消除三维几何约束系统中的伪约束闭环,并将几何约束图分解为单边子图、独立闭环子图和耦合闭环子图;采用螺旋理论识别出装配几何约束组合对应的运动副约束,将约束闭环子图映射为运动副约束图;通过分析运动副约束图的拓扑结构选择切除约束,建立装配几何约束闭环系统的相对坐标表达,将约束闭环系统的整体迭代求解转换为切除部分约束与相对坐标的迭代求解。该方法降低了数值迭代求解的规模,考虑了约束方向对求解结果的影响,既提高了约束求解的效率和稳定性,又保证了约束求解结果的正确性。A constraint transformation method is put forward to solve geometric constraint system with closedloops for 3D assembly design. Firstly, the equivalence analysis method is employed to eliminate the pseudo closedloops of 3D geometric constraint system, whose geometric constraint graph will be decomposed into independentedge sub graph, independentloop subgraph, and couplingloop subgraph with the blockfinding algorithm of undirected graph. Then, the screw theory is utilized to recognize the kinematic pair from the assembly geometric constraint combination, and map the geometric constraint graph with closedloops to the kinematic pair graph. Based on the topological structure analysis of kinematic pair graph, some cutconstraints are determined to transform the closed loop structure of geometric constraint graph into the openloop structure, and the relative coordinate representation of constraint system is also established, so as to convert the whole iteration solution of geometric constraint system to the partial iteration solution of some cutconstraints and relative coordinates. The proposed method can reduced the size of constraint equations and variables that have to be solved simultaneously so that its stability and efficiency can be improved dramatically. Meanwhile, the proposed method can ensure the correctness of solution result via introdu cing additional direction constraint.

关 键 词：几何约束 约束闭环 等价性分析 约束变换 相对坐标 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]