Improved Adjacency Matrix Description and Isomorphism Identification of Kinematic Chain with Multiple Joints
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摘要: 运动链的同构判定是一个较为复杂的问题，对于机构的型综合具有重大意义。本文中提出了一种含复铰运动链的描述及同构判定的新方法。首先，针对运动链中复合铰链难以分析、识别的问题，提出了一种改进关节邻接矩阵描述含复铰运动链的方法；接着，用特征码表示运动链的基本特征，作为同构的必要条件；然后，通过改进关节邻接矩阵构造了关节距离矩阵，并得到该矩阵的和列阵。通过判断特征码、和列阵两个结构恒量是否相等来判定运动链是否同构。最后，通过案例验证了该方法的有效性和可靠性。Abstract: The isomorphism identification of a kinematic chain is a complex problem, which is of great significance to the type synthesis of mechanisms. In this paper, a new method for describing and identifying the isomorphism of a kinematic chain with multiple joints is presented. Firstly, because of the difficulty in analyzing and recognizing multiple joints in a kinematic chain, an improved joint adjacency matrix is proposed to describe the kinematic chain with multiple joints. Then, the basic features of the kinematic chain are represented by feature codes because they are necessary conditions for isomorphism. Further, the joint distance matrix is constructed with the improved joint adjacency matrix, and its summation array is obtained. By distinguishing whether the structural constants of the feature codes and the summation array are equal, the isomorphism of the kinematic chain is identified. Finally, the validity and reliability of the method is verified with numerical examples.
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