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

This article introduces a novel methodology based on conditional $β$-variational autoencoder (c$β$-VAE) architecture to generate diverse types of planar four-bar mechanisms for a given coupler curve. Central to our contribution is the novel integration of cross- and self-attention layers within the VAE framework, facilitating an encoding and decoding process that captures the complex interdependencies of mechanism parameters and associated coupler curves. We propose a unified representation scheme for four-bar mechanisms with both revolute and prismatic joints, utilizing a consistent set of joints to describe each mechanism type. To support and validate our methodology, we have compiled an extensive dataset featuring both open and closed coupler curves of the aforementioned mechanism types. Furthermore, the article introduces three metrics aimed at quantifying the efficacy of our model, alongside an innovative algorithm designed to enhance the predictive outcomes by identifying and computing cognate mechanisms.