Identification of Kinematic Chains Isomorphism Based on the Distance between Non-binary Vertices

— This paper proposes a method for identifying isomorphisms between different kinematic chains that is highly efficient, reliable, and simple, with a short CPU running time (KC). In contrast to many methods proposed by researchers in this field, which require significant computing time, particularly in kinematic chains with a large number of bars. Isomorphism identification is critical for designers in order to avoid duplicate solutions and focus all of their energy and creativity on novel, independent kinematic chain solutions. The shortest path between non-binary bars is primarily used in this article to solve the problem of isomorphism identification. The computational complexity and efficiency of the method are evaluated and compared to existing published methods for a variety of cases, including 8-bar, 10-bar, 12-bar, three-complex 13-bar, 15-bar, 28-bar, and 42-bar single-joint kinematic chains. These comparisons demonstrate the superiority of the proposed method.