Representations & Analysis of Spatial Kinematic Chains with Adjacent Matrix Based on Constraint Function

Abstract

Abstract:

According to the existing problems of structural representations and analysis methods of spatial kinematic chains, a new method based on constraint function and adjacent matrix was presented. The constraint function in form of vector was firstly defined according to the constraint features of kinematic pairs. Next, the properties of constraint function were analyzed. Then, an adjacent matrix of the kinematic chains with constraint functions as elements was proposed. At last, the topological structures of spatial mechanisms were represented and analyzed by using the constraint function and the adjacent matrix. The results show that the constraint function can be applied to all kinds of kinematic pairs, which can represent comprehensive information about the type, grade, DOF, direction, properties and their changes of kinematic pairs. And the adjacent matrix of kinematic chains can be used for non-instantaneous representations and analysis of all kinds of mechanisms, which can give an overall picture of the number of links and the number, the type, grade, direction, properties of kinematic pairs, as well as the type, DOF and the spatial layout of mechanism. Two examples show the intuition, effectiveness and simplicity of using constraint function of kinematic pairs and the adjacent matrix of spatial kinematic chains to represent and analyze spatial mechanisms.

Key words: spatial mechanism, kinematic pair, constraint function, kinematic chain, adjacent matrix

摘要：

针对目前空间机构结构描述和分析方法存在的不足,提出了基于约束函数和邻接矩阵的新方法。根据空间机构运动副的约束特征,定义了向量形式的空间机构运动副特征参数——约束函数及以约束函数为元素的空间机构特征参数矩阵——运动链邻接矩阵;分析了约束函数的性质;运用运动副约束函数和运动链邻接矩阵对空间机构的拓扑结构进行了描述和分析。结果表明,运动副约束函数适用于包括变拓扑结构的各类运动副,能综合描述运动副类型、级别、自由度、方位、性质等信息及其变化的情况;运动链邻接矩阵适用于各类机构的非瞬时描述与分析,能广泛描述运动链的构件数、运动副数目、类型、级别、方位、性质、机构类别、自由度、空间布局等诸多信息;示例证明了约束函数和邻接矩阵描述分析空间机构的直观性、有效性和简便性。基于约束函数和邻接矩阵的解决方案为空间机构的描述和分析提供了一种新的途径和方法。

关键词: 空间机构, 运动副, 约束函数, 运动链, 邻接矩阵

CLC Number:

TH112

LIU Jiang-Na, XU De-Ge. Representations & Analysis of Spatial Kinematic Chains with Adjacent Matrix Based on Constraint Function[J]. China Mechanical Engineering, 2012, 23(17): 2017-2022.

刘江南, 于德介. 基于约束函数的空间机构邻接矩阵描述与分析[J]. 中国机械工程, 2012, 23(17): 2017-2022.

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