邻接矩阵在平面机构分析中的应用

研究了邻接矩阵在平面机构自由度计算、同构识别和速度瞬心求解中的应用。揭示了邻接矩阵与机构自由度的关系。给出了同构运动链邻接矩阵的特征向量及特征值关系的充要条件 ,据此提出了识别机构运动链同构的方法。最后 ,提出了应用邻接矩阵自乘求解机构全部瞬心及求解给定瞬心最短路经的方法

Application of Adjacent Matrices of Mechanisms to the Analysis of Planar Mechanisms

The application of adjacent matrices of mechanisms to the determination of the degree of freedom, the identification of isomorphic chains and the detection of instant centers for mechanisms are studied. The relationship between the adjacent matrix and the degree of freedom of a mechanism is explained. The necessary and sufficient conditions of the eigenvalues and eigenvectors of these matrices for isomorphic chains have been proved. A new procedure to identify isomorphic chains is given. The method to find all instant centers and the shortest path leading to any instant center of a mechanism using square adjacent matrices has been explained.