Path Generative Model Based on Conditional β- Variational Auto Encoder for Mechanism Design

Abstract This paper introduces a novel methodology based on Conditional β-Variational Autoencoder (cβ-VAE) architecture to generate diverse types of planar four-bar mechanisms for a given coupler curve. This approach allows for the synthesis of linkages capable of tracing continuous paths, overcoming the overdetermined problem often encountered in linkage coupler-curve synthesis. The proposed deep generative model processes mechanisms alongside their coupler curves and types, generating a latent vector that enables the decoder to produce a variety of mechanisms tailored to specific conditions. The paper also introduces a comprehensive methodology for assessing the efficacy of the model, proposing three hierarchical metrics focused on reconstruction quality, novelty, and diversity of the predicted mechanisms. The methodology is scalable and applicable to various types of four-bar and higher-order mechanisms, enhancing the model’s utility by including an additional step for computing cognates of predicted mechanisms, thereby generating more efficient solutions. The key contributions of this work lie in the development of a Conditional β-VAE model with attention layers for synthesizing multiple mechanisms, the creation of a unified representation for different types of four-bar mechanisms, the generation of an extensive dataset, the development of a unified algorithm for computing cognates, and the introduction of quantitative assessment metrics. This approach not only surmounts the limitations of traditional methods but also opens new avenues for mechanism design, providing a data-driven tool for exploring alternative designs and evaluating their performance in real-time.