Constraint Transformation Method for Solving 3D Geometric Constraint System of Closed-loop Assemblies
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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。Abstract: A constraint transformation method is put forward to solve geometric constraint system with closed-loops for 3D assembly design. Firstly, the equivalence analysis method is employed to eliminate the pseudo closed-loops of 3D geometric constraint system, whose geometric constraint graph will be decomposed into independent-edge sub-graph, independent-loop subgraph, and coupling-loop subgraph with the block-finding 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 closed-loops to the kinematic pair graph. Based on the topological structure analysis of kinematic pair graph, some cut-constraints are determined to transform the closed-loop structure of geometric constraint graph into the open-loop 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 cut-constraints 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 introducing additional direction constraint.
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Key words:
- algorithms /
- assembly /
- closed loop systems /
- conformal mapping /
- design
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[1] Kramer G A.Solving geometric constraints system:a case study in kinematics[M].Cambridge:MIT Press,1992 [2] Mullins S H,Anderson D C.A positioning algorithm for mechanical assemblies with closed kinematic chains in three dimensions[C] //Proceedings of the 2nd ACM Symposium on Solid Modeling and Applications,New York:ACM Press,1993:271-280 [3] 吴永明.三维几何约束闭环的动态识别与满足[J].计算机辅助设计与图形学学报,2000,12(8):624-629Wu Y M.Dynamic recognition and solution of 3D geometric constraint loops[J].Journal of Computer-Aided Design and Computer Graphics,2000,12(8):624-629(in Chinese) [4] Peng X B,Lee K W,Chen L P.A geometric constraint solver for 3D assembly modelling[J].International Journal of Advanced Manufacturing Technology,2005,28(5/6):561-570 [5] Kim J S,Kim K S,Lee J Y,et al.Solving 3D geometric constraints for closed-loop assemblies[J].International Journal of Advanced Manufacturing Technology,2004,23(9/10):755-761 [6] 夏鸿建,王波兴,陈立平.三维几何约束求解的变分方法[J].计算机辅助设计与图形学学报,2006,18(12):1878-1883Xia H J,Wang B X,Chen L P.Solving 3D assembly geometric constraints based on variation method[J].Journal of Computer-Aided Design and Computer Graphics,2006,18(12):1878-1883(in Chinese) [7] Bae D S,Haug E J.A recursive formulation for constrained mechanical system of dynamics:part II.closed-loop systems[J].Mechanics of Structures and Machines,1988,15(4):481-506 [8] 黄学良,陈立平,王波兴.求解三维装配约束闭环的投影变换法[J].计算机辅助设计与图形学学报,2010,22(12):2138-2146Huang X L,Chen L P,Wang B X.A projection transformation method for solving 3D assembly geometric constraint closed-loops[J].Journal of Computer-Aided Design and Computer Graphics,2010,22(12):2138-2146(in Chinese) [9] 黄学良,王波兴,陈立平,等.三维几何约束系统的等价性分析[J].软件学报,2011,22(5):1106-1120Huang X L,Wang B X,Chen L P,et al.Equivalence analysis of 3D geometric constraint systems[J].Journal of Software,2011,22(5):1106-1120(in Chinese)
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