{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T14:35:05Z","timestamp":1777300505319,"version":"3.51.4"},"reference-count":43,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T00:00:00Z","timestamp":1774656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007053","name":"Korea Institute of Energy Technology Evaluation and Planning","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007053","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The automated synthesis of planar linkage mechanisms has long been a challenge in mechanism design, requiring both geometric feasibility and motion accuracy. Recent advances in data-driven and neural network\u2013based methods have shown promise in automating linkage synthesis, improving efficiency and scalability compared to traditional analytical or optimization-based techniques. Nevertheless, existing data-driven approaches remain limited in handling diverse joint configurations and often suffer from unstable optimization when refining linkage geometries. This study proposes a unified framework that combines deep learning with physics-based modeling for the automated synthesis of one-degree-of-freedom planar linkages. The method integrates (1) large-scale dataset generation using a spring-connected link model (SLM) capable of representing revolute, prismatic, and pin\u2013slot joints; (2) contrastive graph learning for efficient retrieval of candidate linkages through embedding similarity between paths and graphs; and (3) a two-stage optimization process that refines linkage geometry via global\u2013local search. The SLM enables feasibility evaluation based on strain energy, providing smooth design sensitivities and enhanced optimization stability. Experimental results demonstrate that the proposed method achieves superior accuracy across both seen and unseen target paths, outperforming conventional topology optimization approaches. Overall, the framework offers a promising direction for automating and accelerating the design of complex linkage systems by combining deep learning with advanced optimization techniques.<\/jats:p>","DOI":"10.1093\/jcde\/qwag034","type":"journal-article","created":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T12:44:32Z","timestamp":1774701872000},"page":"252-272","source":"Crossref","is-referenced-by-count":0,"title":["Automated synthesis of planar linkage mechanisms with diverse joint types via spring-connected link models and contrastive graph learning"],"prefix":"10.1093","volume":"13","author":[{"given":"Chan-Yeong","family":"Park","sequence":"first","affiliation":[{"name":"Sejong University Department of Mechanical Engineering, , 209, Neungdong-ro, Gwangjin-gu, Seoul 05006 ,","place":["Republic of Korea"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5243-9440","authenticated-orcid":false,"given":"Gang-Won","family":"Jang","sequence":"additional","affiliation":[{"name":"Sejong University Department of Mechanical Engineering, , 209, Neungdong-ro, Gwangjin-gu, Seoul 05006 ,","place":["Republic of Korea"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2026,3,28]]},"reference":[{"key":"2026042709374604500_bib1","doi-asserted-by":"publisher","first-page":"1784","DOI":"10.1016\/j.mechmachtheory.2009.03.003","article-title":"Performance of EAs for four-bar linkage synthesis","volume":"44","author":"Acharyya","year":"2009","journal-title":"Mechanism and Machine Theory"},{"key":"2026042709374604500_bib2","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1016\/S0094-114X(02)00051-4","article-title":"Optimal synthesis of mechanisms with genetic algorithms","volume":"37","author":"Cabrera","year":"2002","journal-title":"Mechanism and machine theory"},{"key":"2026042709374604500_bib3","doi-asserted-by":"crossref","first-page":"6345","DOI":"10.52202\/068431-0459","article-title":"Learning contrastive embedding in low-dimensional space","volume":"35","author":"Chen","year":"2022","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026042709374604500_bib4","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1007\/s11431-011-4736-y","article-title":"Analytical geometry method of planetary gear trains","volume":"55","author":"Chen","year":"2012","journal-title":"Science China Technological Sciences"},{"key":"2026042709374604500_bib5","doi-asserted-by":"publisher","first-page":"964","DOI":"10.59287\/icaens.1117","article-title":"Two-position synthesis of the four-bar planar linkage mechanisms using artificial neural networks","volume-title":"5th International Conference on Applied Engineering and Natural Sciences. Konya, Turkey","author":"Denizhan","year":"2023"},{"key":"2026042709374604500_bib6","doi-asserted-by":"publisher","first-page":"121402","DOI":"10.1115\/1.4044396","article-title":"Computational creativity via assisted variational synthesis of mechanisms using deep generative models","volume":"141","author":"Deshpande","year":"2019","journal-title":"Journal of Mechanical Design"},{"key":"2026042709374604500_bib7","doi-asserted-by":"publisher","first-page":"073303","DOI":"10.1115\/1.4062147","article-title":"GCP-HOLO: Generating high-order linkage graphs for path synthesis","volume":"145","author":"Fogelson","year":"2023","journal-title":"Journal of Mechanical Design"},{"key":"2026042709374604500_bib8","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1115\/1.4014881","article-title":"An analytical approach to the design of four-link mechanisms","volume":"76","author":"Freudenstein","year":"1954","journal-title":"Transactions of the American Society of Mechanical Engineers"},{"key":"2026042709374604500_bib9","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1007\/s00158-017-1712-6","article-title":"Topology optimization of planar linkage mechanisms for path generation without prescribed timing","volume":"56","author":"Han","year":"2017","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2026042709374604500_bib10","doi-asserted-by":"publisher","first-page":"822","DOI":"10.1109\/ICNN.1993.298663","article-title":"Synthesis of mechanical linkages using artificial neural networks and optimization","volume-title":"IEEE International Conference on Neural Networks","author":"Hoskins","year":"1993"},{"key":"2026042709374604500_bib11","doi-asserted-by":"publisher","first-page":"107928","DOI":"10.1016\/j.knosys.2021.107928","article-title":"Optimal synthesis of mechanisms using repellency evolutionary algorithm","volume":"239","author":"Huang","year":"2022","journal-title":"Knowledge-Based Systems"},{"key":"2026042709374604500_bib12","doi-asserted-by":"publisher","first-page":"V05BT08A062","DOI":"10.1115\/DETC2015-46073","article-title":"Automated synthesis of planar mechanisms with revolute, prismatic and pin-in-slot joints","volume-title":"International Design Engineering Technical Conferences and Computers and Information in Engineering Conference","author":"Huang","year":"2015"},{"key":"2026042709374604500_bib13","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/0094-114X(92)90008-6","article-title":"Computer-aided structural synthesis of planar kinematic chains with simple joints","volume":"27","author":"Hwang","year":"1992","journal-title":"Mechanism and Machine Theory"},{"key":"2026042709374604500_bib14","doi-asserted-by":"publisher","first-page":"bbab371","DOI":"10.1093\/bib\/bbab371","article-title":"Rossmann-toolbox: A deep learning-based protocol for the prediction and design of cofactor specificity in Rossmann fold proteins","volume":"23","author":"Kami\u0144ski","year":"2022","journal-title":"Briefings in Bioinformatics"},{"key":"2026042709374604500_bib15","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/j.mechmachtheory.2016.05.015","article-title":"Topology optimization of planar linkage systems involving general joint types","volume":"104","author":"Kang","year":"2016","journal-title":"Mechanism and Machine Theory"},{"key":"2026042709374604500_bib16","doi-asserted-by":"publisher","first-page":"1955","DOI":"10.1007\/s00158-017-1887-x","article-title":"Unified topology and joint types optimization of general planar linkage mechanisms","volume-title":"Structural and Multidisciplinary Optimization","author":"Kang","year":"2018"},{"key":"2026042709374604500_bib17","doi-asserted-by":"publisher","first-page":"105500","DOI":"10.1016\/j.engappai.2022.105500","article-title":"Synthesis of a six-bar mechanism for generating knee and ankle motion trajectories using deep generative neural network","volume":"117","author":"Kapsalyamov","year":"2023","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"2026042709374604500_bib18","doi-asserted-by":"publisher","first-page":"1412","DOI":"10.1002\/nme.5573","article-title":"Topology optimization of vehicle rear suspension mechanisms","volume":"113","author":"Kim","year":"2018","journal-title":"International Journal for Numerical Methods in Engineering"},{"key":"2026042709374604500_bib19","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1002\/nme.4635","article-title":"Topology optimization of planar linkage mechanisms","volume":"98","author":"Kim","year":"2014","journal-title":"International Journal for Numerical Methods in Engineering"},{"key":"2026042709374604500_bib20","doi-asserted-by":"publisher","first-page":"1497","DOI":"10.1007\/s00158-020-02669-2","article-title":"A novel space-constrained vehicle suspension mechanism synthesized by a systematic design process employing topology optimization","volume":"62","author":"Kim","year":"2020","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2026042709374604500_bib21","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1093\/jcde\/qwae084","article-title":"Deep generative model-based synthesis framework of four-bar linkage mechanisms with target conditions","volume":"11","author":"Lee","year":"2024","journal-title":"Journal of Computational Design and Engineering"},{"key":"2026042709374604500_bib22","doi-asserted-by":"publisher","DOI":"10.1115\/1.4006741","article-title":"Structure synthesis of single-driven metamorphic mechanisms based on the augmented Assur groups","author":"Li","year":"2012"},{"key":"2026042709374604500_bib23","doi-asserted-by":"publisher","first-page":"041001","DOI":"10.1115\/1.4029116","article-title":"Assur-group inferred structural synthesis for planar mechanisms","volume":"7","author":"Li","year":"2015","journal-title":"Journal of Mechanisms and Robotics"},{"key":"2026042709374604500_bib24","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/978-3-540-72960-0_2","article-title":"Four-bar mechanism synthesis for n desired path points using simulated annealing","volume-title":"Advances in Metaheuristics for Hard Optimization","author":"Mart\u00ednez-Alfaro","year":"2008"},{"key":"2026042709374604500_bib25","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.1109\/LRA.2023.3234771","article-title":"Scene: Reasoning about traffic scenes using heterogeneous graph neural networks","volume":"8","author":"Monninger","year":"2023","journal-title":"IEEE Robotics and Automation Letters"},{"key":"2026042709374604500_bib26","unstructured":"Nobari A. H., Srivastava A., Gutfreund D., Ahmed F. (2022). Links: A dataset of a hundred million planar linkage mechanisms for data-driven kinematic design. arXiv preprint. arXiv:2208.14567 (deposited on August 30, 2022)10.48550\/arXiv.2208.14567 \u00a0(7 April 2026, date last accessed)."},{"key":"2026042709374604500_bib27","article-title":"Link: Learning joint representations of design and performance spaces through contrastive learning for mechanism synthesis","volume-title":"arXiv preprint","author":"Nobari","year":"2024"},{"key":"2026042709374604500_bib28","doi-asserted-by":"publisher","first-page":"011008","DOI":"10.1115\/1.4063726","article-title":"An invariant representation of coupler curves using a variational autoencoder: Application to path synthesis of four-bar mechanisms","volume":"24","author":"Nurizada","year":"2024","journal-title":"Journal of Computing and Information Science in Engineering"},{"key":"2026042709374604500_bib29","doi-asserted-by":"publisher","first-page":"111405","DOI":"10.1115\/1.4044229","article-title":"Deep generative design: Integration of topology optimization and generative models","volume":"141","author":"Oh","year":"2019","journal-title":"Journal of Mechanical Design"},{"key":"2026042709374604500_bib30","doi-asserted-by":"publisher","DOI":"10.1115\/1.2912743","article-title":"Topological analysis of single-degree-of-freedom planetary gear trains","author":"Olson","year":"1991"},{"key":"2026042709374604500_bib31","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1177\/02783649211069156","article-title":"Joint search of optimal topology and trajectory for planar linkages","volume":"42","author":"Pan","year":"2023","journal-title":"The International Journal of Robotics Research"},{"key":"2026042709374604500_bib32","doi-asserted-by":"publisher","first-page":"113305","DOI":"10.1115\/1.4068488","article-title":"Global-local search for topology optimization of linkage mechanisms using spring-connected link model","volume":"147","author":"Park","year":"2025","journal-title":"Journal of Mechanical Design"},{"key":"2026042709374604500_bib33","doi-asserted-by":"publisher","first-page":"1335","DOI":"10.1016\/j.mechmachtheory.2011.05.013","article-title":"Synthesis of mechanisms for single and hybrid tasks using differential evolution","volume":"46","author":"Pe\u00f1u\u00f1uri","year":"2011","journal-title":"Mechanism and Machine theory"},{"key":"2026042709374604500_bib34","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1017\/S0890060400001700","article-title":"Genetic algorithm synthesis of four-bar mechanisms","volume":"10","author":"Roston","year":"1996","journal-title":"AI EDAM"},{"key":"2026042709374604500_bib35","doi-asserted-by":"publisher","DOI":"10.1115\/1.1899178","article-title":"Synthesis of compliant mechanisms for path generation using genetic algorithm","author":"Saxena","year":"2005"},{"key":"2026042709374604500_bib36","doi-asserted-by":"publisher","first-page":"1851","DOI":"10.1007\/s12046-017-0737-2","article-title":"A new hybrid teaching\u2013learning particle swarm optimization algorithm for synthesis of linkages to generate path","volume":"42","author":"Singh","year":"2017","journal-title":"S\u0101dhan\u0101"},{"key":"2026042709374604500_bib37","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/s00158-024-03857-0","article-title":"Topology optimization of linkage mechanisms using spring-connected link model","volume":"67","author":"Tran","year":"2024","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2026042709374604500_bib38","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/S0094-114X(00)00037-9","article-title":"Dimensional synthesis of planar mechanisms using neural networks: Application to path generator linkages","volume":"36","author":"Vasiliu","year":"2001","journal-title":"Mechanism and Machine Theory"},{"key":"2026042709374604500_bib39","article-title":"Graph attention networks","volume-title":"arXiv preprint arXiv:1710.10903 (deposited on October 30, 2017; accessed on April 7, 2026)","author":"Veli\u010dkovi\u0107","year":"2017"},{"key":"2026042709374604500_bib40","doi-asserted-by":"publisher","first-page":"V02AT03A009","DOI":"10.1115\/DETC2018-85529","article-title":"Kinematic synthesis using reinforcement learning","volume-title":"International Design Engineering Technical Conferences and Computers and Information in Engineering Conference","author":"Vermeer","year":"2018"},{"key":"2026042709374604500_bib41","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1093\/jcde\/qwae015","article-title":"Research on four-bar linkage trajectory synthesis using extreme gradient boosting and genetic algorithm","volume":"11","author":"Wang","year":"2024","journal-title":"Journal of Computational Design and Engineering"},{"key":"2026042709374604500_bib42","doi-asserted-by":"publisher","first-page":"104375","DOI":"10.1016\/j.mechmachtheory.2021.104375","article-title":"Big data approach for the simultaneous determination of the topology and end-effector location of a planar linkage mechanism","volume":"163","author":"Yim","year":"2021","journal-title":"Mechanism and Machine Theory"},{"key":"2026042709374604500_bib43","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1115\/DETC2011-48503","article-title":"Kinematic synthesis of planar, shape-changing rigid-body mechanisms with prismatic joints","volume":"54839","author":"Zhao","year":"2011","journal-title":"International Design Engineering Technical Conferences and Computers and Information in Engineering Conference"}],"container-title":["Journal of Computational Design and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jcde\/advance-article-pdf\/doi\/10.1093\/jcde\/qwag034\/67631425\/qwag034.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/13\/4\/252\/67631425\/qwag034.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/13\/4\/252\/67631425\/qwag034.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T13:37:55Z","timestamp":1777297075000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jcde\/article\/13\/4\/252\/8554182"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,28]]},"references-count":43,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,4,1]]}},"URL":"https:\/\/doi.org\/10.1093\/jcde\/qwag034","relation":{},"ISSN":["2288-5048"],"issn-type":[{"value":"2288-5048","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,4]]},"published":{"date-parts":[[2026,3,28]]}}}