Jixie chuandong (Nov 2021)
A Method for Isomorphism Recognition of Kinematic Chain based on the Hamming Matrix and Connecting Rod Adjacency Matrix
Abstract
In the creative design of mechanical devices，the isomorphic kinematic chains should be eliminated to reduce the mechanism scheme for subsequent design and improve the design efficiency of mechanical device. A new method for isomorphism recognition of kinematic chains is proposed based on the Hamming matrix. Firstly，the Hamming matrix of kinematic chains is educed from the link adjacency matrix，then the square matrix of Hamming matrix and the cubic matrix of link adjacency matrix are integrable to obtain the product matrix of kinematic chains. Secondly，the elements of each row in the product matrix are ordered in descending to get the row sequences of the product matrix. Finally，the isomorphism recognition code (IRC) of the kinematic chain is obtained by the sum of the product of the element in the row sequence with the defined topological factor. The isomorphism recognition code does not change with the link labels，so if the isomorphism recognition codes of the kinematic chains are the same，they are isomorphic，otherwise they are not. The effectiveness of this method is proved by a large number of examples. Because of its simplicity，efficiency and convenience for computer execution，it can be considered as a new option for isomorphism screening.
