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基于构件关系拓扑图论的机构自由度和奇异分析 被引量:3

Analysis on degree of freedom and singularity of mechanism based on topological graph theory of components relationship
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摘要 在分析机构图论现状的前提下,对机构中常用运动副、机构运动基本单元的移动基和转动基的空间活动能力进行描述定义,基于机构由构件通过关节连接而成的事实,提出一种新的构件关系拓扑图论描述方法。该方法以构件框、约束构件框、构件关系线、约束构件关系线、相邻构件空间相对活动能力关系为要素,对串联机构、并联机构、混联机构进行新的图论描述。基于支链空间活动能力维度和机构空间活动能力维度定义,以实例形式给出混联机构自由度的分析方法,并得到机构非奇异的充要条件,在此基础上推出机构出现奇异的充要条件,引入机构运动支链输入基位置极限的同时/同化、同时/非同化、独自出现位置极限的三分法,得到给定混联机构出现位置奇异、姿态奇异、位置和姿态奇异的情形数,并给出了一般形式的串联、并联、混联机构的奇异组合和情形数的分析途径。 Under the precondition of analyzing current state of mechanism graph theory, spatial moving capability of movement base and rotation base of the kinematic pair and basic unit of mechanism movement commonly used in mechanism is described and defined. Based on the fact that the mechanism is composed of components through joint connection, a new topological graph theory description method for components relationship is suggested. By taking component pane, constrained component pane, component relationship line, constrained component relationship line, spatial relative moving capability between adjacent components as the essential factors, this method carries out new graph theory description for serial mechanism, parallel mechanism and hybrid mechanism. Based on the definition of spatial movement ability dimensionality of the branch chain and the spatial movement ability dimensionality of the mechanism, the analysis method for the degree of freedom (DOF) of hybrid mechanism is given in the form of actual example, and the necessary and sufficient condition of non-singularity of mechanism is obtained. And then, the necessary and sufficient condition of singularity of mechanism is deduced, the trichotomy of position limit for input base of the branch chain of the mechanism movement is introduced: simultaneous/assimilative, simultaneous/non-assimilative, and separate position limits. The position singularity , posture singularity and position and number of position singularity and posture singularity with a given hybrid mechanism is obtained, and the analysis approach for singularity combination of serial, parallel and hybrid mechanisms and numbers in common form is also obtained.
出处 《机械设计》 CSCD 北大核心 2010年第7期60-64,共5页 Journal of Machine Design
关键词 机构 图论 集合 自由度 奇异 mechanism graph theory assemble degree of freedom singularity
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