含复铰运动链支路矩阵描述方法及同构判定

The Description and Isomorphism Identification of the Kinematic Chain With Multiple Joints Based on Branch Matrix

在运动链构型综合过程中,相似运动链的同构判定是一个复杂且耗时的问题。提出了一种含复铰运动链支路矩阵的同构判定新方法。针对运动链中复合铰链难以识别和处理问题,提出了一种多元构件编号及支路矩阵描述方法,从而有效描述了运动链中的构件和复合铰链等信息,并且该方法具有运动链结构描述的唯一性。然后,提出了支路矩阵的素数乘积法对含复合铰链运动链进行同构判定。利用支路矩阵的多元构件编号方法可直观地比较不同运动链的对应关系,通过比较支路矩阵最后一行和素数乘积数组进行同构判定。通过案例证明该方法准确、有效且简便。

In the synthesis process of kinematic chain,the isomorphism determination of similar kinematic chains is a complicated and time-consuming problem.A new method to isomorphism determination of the kinematic chain with multiple joints based on the branch matrix is presented.In view of the difficulty in the analysis and identification of multiple joints in the kinematic chain,a multivariate component numbering and branch matrix description method of the kinematic chains is proposed which can effectively describe the links in the kinematic chain with multiple joints,and is unique in description.Afterwards,a new way which multiplied by primes in the branch matrices to identify isomorphism of the kinematic chain with multiple joints is proposed.The correspondence of different kinematic chains can be directly compared using the method.By comparing the last line of branch matrix and product of prime number array isomorphism,isomorphism determination is achieved.This method is proved to be accurate,effective and simple by several case studies.