Detection of Isomorphism and Inversions of Kinematic Chains Using an Evolutionary Approach

In this study, the focus is on identifying isomorphic structures in kinematic chains, which are crucial for their structural synthesis. Existing methods for detecting isomorphism are computationally intensive and time-consuming and often rely on direct communication between chain links. To address this, a new and unique approach using the Relative Least Effective Distance Matrix (RLEDM) was proposed. RLEDM considers the relative positions of each link in relation to the others, significantly improving the accuracy of isomorphism detection. The main goal is to develop a simpler and more efficient technique that surpasses the current methods and advances kinematic chain analysis and synthesis. To implement this approach, a graph is constructed from the given kinematic chain, with edge representing links and vertices representing the nodes. The Floyd–Warshall algorithm was then employed to calculate the Least Distance Matrix (LDM) from this graph. The RELDM is derived from the LDM by capturing the relative distances between the links. To validate its effectiveness, extensive testing was conducted on various kinematic chains, including eight, ten-link single-degree-of-freedom chains, nine-link two-degree-of-freedom chains, and ten-link three-degree-of-freedom chains. Counterexamples involving ten-link and twelve-link single-degree-of-freedom kinematic chains are also considered. All computations and analyses were performed using Python code within the Google Colab environment. By adopting this innovative methodology, researchers aim to revolutionize kinematic chain analysis and contribute to advancements in this vital field of study. The proposed approach offers a promising solution for enhancing the efficiency and accuracy of isomorphism detection in the kinematic chains.