用连杆机构几何约束求解(英文)

Geometric Constraint Solving with Linkages

引入连杆机构作为新的工具 ,且证明这是完备的 ,也就是说 ,所有能构造性描述的图形能被连杆机构作出 ,这一类包括了所有只含距离约束的约束问题 .作为一个应用 ,说明了超出 Owen和 Hoffmann的三角分解方法之外的最简单的约束图能被转化为纯几何构造形式 .为了求解起源于连杆构造的方程 ,提出了一种基于动态轨迹生成的几何方法 .

This paper introduces linkages as new drawing tool and shows that this tool is complete, i.e., all diagrams that can be described constructively can be drawn with linkages. This class includes the constraint problems with distance constraints only. As an application, the authors show that the simplest constrained graph which is beyond the scope of Owen and Hoffmann's popular triangle decomposition methods can be transformed to purely geometric constructive form. To solve the equations derived from linkage constructions, a geometric method which is based on dynamic locus generation is proposed.