中文摘要：

针对几何约束系统中不可构造的柔性复合顶点的求解问题，引入等价约束，分裂部分约束以打破柔性复合顶点的强耦合性，形成只包含简单顶点的求解序列。基于等价约束的性质和结构拓扑，研究了求解序列顶点存在与不存在实数解情况下，雅可比矩阵的求解方法，从而以少量分裂约束方程组对等价约束变量的等价迭代，或者柔性复合顶点的局部迭代，取代柔性复合顶点的整体数值迭代求解，降低迭代的维数，算法实现于几何约束求解引擎CBA（constraint broadcast automation）中。

英文摘要：

The solution of non-constructible flexible merge patterns is a key issue for geometric constraint system. In this paper, an equivalent iteration method for solving flexible merge patterns is proposed. In such a method, the strongly coupled connected components are broken by introducing equivalent constraints and tearing part of the constraints, and a solving sequence which only includes basic geometric elements is obtained. If values of equivalent constraint variables are given, every vertex of the solving sequence has a closed solution. On the basis of properties and structure of equivalent constraint, equivalent iteration Jacobian matrix can be worked out linearly if the vertexes of the solving sequence have real solution ; otherwise, local iteration is performed. The solution of non-constructible flexible merge patterns can be accomplished by equivalent constraint variable iteration, rather than undertaking simbeen successfully implemented in our geometric constraint solver, CBA.