Abstract: Loops were an inherent feature of kinematic chain structures, and most of the existing researches and applications were focused on configuration synthesis, isomorphism determination and rigid sub-chain elimination based on loops. A new definition of basic loop set was proposed, and the dendrogram expression of kinematic chain and related theories were proposed, as well as the basic loop set extraction principles based on the holographic matrix expression of inter-component connection relations and complex hinge determination. The proposed method is simple in rules, easy to implement by computer programmatically, and may obtain the basic loop sets of kinematic chains with complex structures quickly, and the correctness and validity of the above theory were proved by examples.

Key words: basic loop set, dendrogram, shortest loop, loop characteristics

摘要： 环路是运动链结构的固有特征，已有研究和应用多集中在基于环路的构型综合、同构判定、刚性子链消除等方面。给出了基本环路集的新定义，提出了运动链的树状结构表达及相关理论，以及基于此的基本环路集提取原则，方便快捷地获得各种运动链的基本环路集。案例分析证明，所提方法规则简单，便于计算机程序化实现，可快速地获得结构复杂、对称性高的运动链的基本环路集。通过实例证明了上述理论的正确性和有效性。

关键词: 基本环路集, 树状结构, 最短环路, 环路特性