摘要
由于现有几何约束分解方法无法分解三维装配几何约束闭环系统,故常采用数值迭代方法对其进行求解,但存在效率低、稳定性差等问题.为此,通过分析几何约束闭环图的拓扑结构和串联运动链的结构约束,提出基于串联运动链结构约束等价替换的三维几何约束闭环系统的递归分解方法.该方法通过不断地引入几何约束组合等价替换串联运动链的结构约束,从几何约束闭环系统中分离出可独立求解的子系统,实现几何约束闭环系统的递归分解.该方法可将此前许多必须整体迭代求解的三维几何约束闭环系统分解为一系列可解析求解的2个刚体之间的几何约束系统,明显提高了约束求解的效率和稳定性.最后用实例验证了方法的正确性和有效性.
Numerical methods are always employed to solve 3D assembly geometric constraint system with closed-loops which can not be decomposed by the existing decomposition methods, but their inherent inefficiency and instability can not be overcome. In this paper, with the analysis of the structural constraint of serial kinematic chain and the topological structure of geometric constraint closed-loop graph, a recursive decomposition algorithm for 3D geometric constraint system with closed- loops is proposed. The basic idea of the proposed algorithm is to introduce the equivalent geometric constraint combination to substitute the structural constraint of serial kinematic chain, and separate the geometric constraint subsystems which can be solved independently from the geometric constraint system with closed-loops. The proposed method can decompose most 3D geometric constraint closed- loop systems which are always solved by numerical method into a series of geometric constraint subsystems between two rigid bodies which can be solved by analytical or reasoning method, so that the computational efficiency and stability can be improved dramatically. Finally, a typical example has been given to validate the correctness and effectiveness of the proposed method.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2013年第9期1296-1303,共8页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金项目(50875092)
国家自然科学基金重点项目(60736019)
关键词
三维装配
几何约束
约束闭环
等价替换
递归分解
3D assembly
geometric constraint
closed-loop
equivalent substitution
recursive decomposition
