The judgment of the rigid subchain is a difficult problem in the synthesis of kinematic chain.By analyzing the kinematic chain of each closed loop in the kinematic chain,a method is proposed to determine whether there is the rigid subchain in the kinematic chain. According to the composition of the basic loop of the kinematic chain,the method of establishing the basic loop matrix is proposed. Through the operation of the basic loop matrix,the combined closed loop in the kinematic chain is obtained. The rigid subchain in the kinematic chain is got by combining the rigid subchain identification method. By the operation of the basic loop matrix,the closed loop of the rigid subchain is eliminated,and the kinematic chain without the rigid subchain is obtained. Finally,computer programming is used to realize the automatic recognition and elimination of the rigid subchain.