求解三维装配约束闭环的投影变换方法

A Projection Transformation Method for Solving 3D Assembly Geometric Constraint Closed-Loops

为避免直接迭代求解三维装配约束闭环带来的复杂非线性方程组,提出一种投影变换方法求解三维装配设计中的平面约束闭环问题.首先采用等价性分析方法消除伪装配约束闭环,运用无向图块分算法分解装配约束图;然后采用旋量理论将装配约束闭环子图转换为运动副约束图,通过分析运动副的特征参数确定可投影的装配约束闭环,并将其投影变换为二维几何约束系统;最后通过求解二维几何约束系统获得三维装配约束闭环的解.实例结果表明,该方法缩减了迭代求解的规模并降低了约束方程的复杂性,明显地提高了求解的效率和稳定性.

In order to avoid the iterative solution of complex nonlinear equations derived from 3D assembly geometric constraint closed-loops,a projection transformation approach is proposed to solve the planar geometric constraint closed-loop problem in 3D assembly design.Firstly,the equivalence analysis algorithm is adopted to eliminate pseudo geometric constraint closed-loops and the block finding algorithm of undirected graph is utilized to decompose geometric constraint graph.Then,the subgraphs of the geometric constraint closed-loops are converted to kinematic joint graphs using screw theory,and the characteristic parameters of the kinematic joints are analyzed to determine whether the geometric constraint closed-loops can be projected to the 2D plane.At last,the 3D geometric constraint closed-loops that can be projected to the 2D plane is transformed into 2D geometric constraint system,which will be solved to obtain the solution of the 3D geometric constraint closed-loops.The proposed method can downsize the constraint equations and variables that have to be solved simultaneously and reduce the complexity of constraint equations,so it can improve the efficiency and robustness of an assembly constraint solver significantly.