基于转化邻接矩阵的含复铰运动链描述与同构识别

针对机构分析与综合中复合铰链难以处理和含复铰运动链同构识别困难的问题,分析复合铰链的内部结构,提出引入Pin构件将复合铰链转化为多个并联单铰链的新方法,从而将含复铰运动链转化为只含单铰的简单运动链。定义运动链转换邻接矩阵,用于描述含复铰运动链,通过分析发现该矩阵的内涵性质丰富,方便运动链的分析。提出运用转换邻接矩阵的阶数、对角线元素矢量、矩阵特征值和特征矢量等参数识别判断含复铰运动链同构关系的方法,这些特征参数是含复铰运动链的不变量。实例证明,利用转化邻接矩阵可简单、方便、直观地描述含复铰运动链,其特征值和特征矢量用于识别含复铰运动链的同构关系,具有准确、高效和简便的特点。定义的转化邻接矩阵及其运用方法为复合铰链的处理以及含复铰运动链的识别提供了新的途径。

Representations & Isomorphism Identification of Planar Kinematic Chains with Multiple Joints Based on the Converted Adjacent Matrix

Handling multiple-joint and isomorphism identification of planar kinematic chains with multiple-joints is a hard work in the analysis and synthesis of mechanisms.A new approach is suggested to convert the multiple-joints to some parallel simple-joints by using a Pin-link to adjoin all the links on a multiple-joint.The converted adjacent matrix is defined to represent the kinematic chains with multiple-joints.According to some characteristic parameters of the converted adjacent matrix,a new method for isomorphism identification of planar kinematic chains is proposed.Some application examples show that the converted adjacent matrix can conveniently represent planar kinematic chains with multiple-joints,and the Eigen values and eigenvectors of the converted adjacent matrix can be used to identify the isomorphism of planar kinematic chains effectively and efficiently.A new way is provided to the analysis and synthesis of mechanisms with multiple-joints.