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Abstract This article 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. 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. 

Abstract The design of single-degree-of-freedom spatial mechanisms tracing a given path is challenging due to the highly non-linear relationships between coupler curves and mechanism parameters. This work introduces an innovative application of deep learning to the spatial path synthesis of one-degree-of-freedom spatial revolute-spherical-cylindrical-revolute (RSCR) mechanisms, aiming to find the non-linear mapping between coupler curve and mechanism parameters and generate diverse solutions to the path synthesis problem. Several deep learning models are explored, including multi-layer perceptron (MLP), variational autoencoder (VAE) plus MLP, and a novel model using conditional -β− VAE (c −β− VAE). We found that the c -β– VAE model withβ= 10 achieves superior performance by predicting multiple mechanisms capable of generating paths that closely approximate the desired input path. This study also builds a publicly available database of over 5 million paths and their corresponding RSCR mechanisms. The database provides a solid foundation for training deep learning models. An application in the design of human upper-limb rehabilitation mechanism is presented. Several RSCR mechanisms closely matching the wrist and elbow path collected from human movements are found using our deep learning models. This application underscores the potential of RSCR mechanisms and the effectiveness of our model in addressing complex, real-world spatial mechanism design problems. 

Abstract In recent years, there has been a strong interest in applying machine learning techniques to path synthesis of linkage mechanisms. However, progress has been stymied due to a scarcity of high-quality datasets. In this article, we present a comprehensive dataset comprising nearly three million samples of 4-, 6-, and 8-bar linkage mechanisms with open and closed coupler curves. Current machine learning approaches to path synthesis also lack standardized metrics for evaluating outcomes. To address this gap, we propose six key metrics to quantify results, providing a foundational framework for researchers to compare new models with existing ones. We also present a variational autoencoder-based model in conjunction with a k-nearest neighbor search approach to demonstrate the utility of our dataset. In the end, we provide example mechanisms that generate various curves along with a numerical evaluation of the proposed metrics. 

Abstract This paper focuses on the representation and synthesis of coupler curves of planar mechanisms using a deep neural network. While the path synthesis of planar mechanisms is not a new problem, the effective representation of coupler curves in the context of neural networks has not been fully explored. This study compares four commonly used features or representations of four-bar coupler curves: Fourier descriptors, wavelets, point coordinates, and images. The results demonstrate that these diverse representations can be unified using a generative AI framework called variational autoencoder (VAE). This study shows that a VAE can provide a standalone representation of a coupler curve, regardless of the input representation, and that the compact latent dimensions of the VAE can be used to describe coupler curves of four-bar linkages. Additionally, a new approach that utilizes a VAE in conjunction with a fully connected neural network to generate dimensional parameters of four-bar linkage mechanisms is proposed. This research presents a novel opportunity for the automated conceptual design of mechanisms for robots and machines. 

Abstract This paper introduces a new method using deep neural networks for the interactive digital transformation and simulation of n-bar planar linkages, which consist of revolute and prismatic joints, based on hand-drawn sketches. Instead of relying solely on computer vision, our approach combines topological knowledge of linkage mechanisms with the outcomes of a convolutional deep neural network. This creates a framework for recognizing hand-drawn sketches. We generate a dataset of synthetic images that resemble hand-drawn sketches of linkage mechanisms. Next, we fine-tune a state-of-the-art deep neural network to detect discrete objects using building blocks that represent joints and links in various positions, sizes, and orientations within these sketches. We then conduct a topological analysis on the detected objects to construct a kinematic model of the sketched mechanisms. The results demonstrate the effectiveness of our algorithm in handling hand-drawn sketches and converting them into digital representations. This has practical implications for improving communication, analysis, organization, and classification of planar mechanisms.