基于纽结理论空间连杆曲线相似性判定

Determination of Similarity between Spatial Linkages Coupler Curve Based on Knot Theory

为了解决空间连杆曲线与预定轨迹的匹配问题,利用纽结理论中反映空间曲线几何形态的绞拧数作为指标,将曲线各子段对分成若干个等价类,对每个等价类中各曲线子段对进行刚体变换而近似匹配,通过对刚体变换进行聚类分析得到曲线的匹配关系,从而得到两者的相似度.实例分析表明,该方法有效地解决了空间连杆曲线与预定轨迹的匹配问题,也为任意曲线间的匹配提供了一个新的思路.

In order to solve the matching problem of 3-D coupler-curves, the substructures of coupler-curves were classified into different equivalence classes based on writhing numbers, which is borrowed from knot theory and can describe characters of spatial curves to some extent. The paper calculates the transformations （rotation and translation） using unit quaternion method in each equivalence class. Finally, the transformations are clustered to find the optimal matching relation and the similarity is obtained. An example of matching coupler-curves of RUSR mechanism was given.