基于邻接图的变胞机构的矩阵描述及演算

Adjacency Graph Based Matrix Representations and Operations of Metamorphic Mechanisms

邻接矩阵法可以对杆件的数目变化进行表示和演算,但这种方法对于变胞机构中复合铰链的构态变换及描述铰链的邻接关系变化的情况不完全适用,且矩阵所含信息较少,不能直观地反映机构构态特性.为此,应用邻接图表示机构的拓扑结构,并提出了描述机构详细信息的铰链邻接矩阵,此矩阵可与初等变换矩阵构造变胞方程,从而实现机构从初始构态到任意构态的矩阵演算.通过实例验证可知,基于邻接图的矩阵描述和演算方法获得的结果包含直观和全面的机构构态信息,便于计算机辅助分析.

Metamorphic mechanisms are widely studied and applied in theory and practice because of their characteristics of variable topological structures. The adjacency matrix is used in representation and operation of link changes. But this method is not available in configuration transformation with multiple joints and characteristics change of joints of metamorphic mechanisms, also the information of the matrix is poor. So it doesn＇t represent the configurations of metamorphic mechanisms intuitively. This article used adjacency graph to represent the topology of mechanism. The adjacency matrix of joint was proposed to represent the concrete information of the metamorphic mechanism. The metamorphic equation is con- strueted by multiplying elementary matrixes, and it is used to describe the transformations from one con- figuration to another. The verified examples indicate that the results obtained with the method have intui- tive and comprehensive information of the configuration, and the method is easy to computer aided analy- sis.