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中文摘要：
对近十年提出的7种自由度（Degree of freedom,DOF）公式及其主要特点进行回顾。给出基于约束分析的DOF公式的统一形式与基于运动分析的DOF公式的基本形式。给出基于运动分析的DOF计算方法与基于约束分析的DOF计算方法。基于DOF公式,确定机构的拓扑结构特征,如机构的DOF、动平台的方位特征集及其维数、独立位移方程数、过约束度、冗余自由度,判定消极运动副与选取驱动副等。揭示DOF公式的物理内涵,即DOF公式表述了机构DOF、拓扑结构与运动方位特征三者之间的映射关系,而机构的拓扑结构和方位特征的运动过程不变性是构建这一映射关系的理论基础。
英文摘要：
A review of seven significant DOF formulas proposed over the past ten years with their main characteristics is presented.On this basis,significant aspect related DOF on their basic form of constraint-analysis-based DOF formulas of motion-analysis-based DOF formulas is presented,their procedures are given.The characteristics of a mechanism topology structure are determined based on DOF formulas,such as mechanism DOF,position and orientation characteristic（POC） set of moving platform and its dimension,number of independent position equations,over constraint degree,redundant DOF and the determination of passive and active kinematic pairs.The mapping relationship among mechanism DOF,topology structure and POC set is further revealed with the invariance property of the mechanism topology structure and the POC set as the theoretical foundation for constructing this mapping relationship is presented.
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