{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T00:31:41Z","timestamp":1772757101782,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,20]],"date-time":"2018-08-20T00:00:00Z","timestamp":1534723200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"MINECO\/FEDER","award":["HAR2015-63503-P"],"award-info":[{"award-number":["HAR2015-63503-P"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, the geometric modeling and virtual reconstruction of the double-acting steam engine designed by Agust\u00edn de Betancourt in 1789 are shown. For this, the software Autodesk Inventor Professional is used, which has allowed us to obtain its geometric documentation. The material for the research is available on the website of the Betancourt Project of the Canary Orotava Foundation for the History of Science. Almost all parts of the steam engine are drawn on the sheets, but due to the absence of scale and space, it is insufficient to obtain an accurate and reliable 3D CAD (Computer-Aided Design) model. For this reason a graphic scale has been adopted so that the dimensions of the elements are coherent. Also, it has been necessary to make some dimensional and geometric hypotheses, as well as restrictions of movement (degrees of freedom). Geometric modeling has made it possible to know that the system is balanced with the geometric center of the rocker arm shaft, and presents an energetic symmetry whose axis is the support of the parallelogram where the shaft rests: calorific energy to the left and mechanical energy to the right, with the rocker arm acting as a transforming element from one to the other.<\/jats:p>","DOI":"10.3390\/sym10080351","type":"journal-article","created":{"date-parts":[[2018,8,20]],"date-time":"2018-08-20T11:23:06Z","timestamp":1534764186000},"page":"351","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Agust\u00edn de Betancourt\u2019s Double-Acting Steam Engine: Geometric Modeling and Virtual Reconstruction"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9001-1050","authenticated-orcid":false,"given":"Jos\u00e9 Ignacio","family":"Rojas-Sola","sequence":"first","affiliation":[{"name":"Department of Engineering Graphics, Design and Projects, University of Ja\u00e9n, Campus de las Lagunillas, s\/n, 23071 Ja\u00e9n, Spain"}]},{"given":"Bel\u00e9n","family":"Gal\u00e1n-Moral","sequence":"additional","affiliation":[{"name":"University of Ja\u00e9n, Campus de las Lagunillas, s\/n, 23071 Ja\u00e9n, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1407-5903","authenticated-orcid":false,"given":"Eduardo","family":"De la Morena-De la Fuente","sequence":"additional","affiliation":[{"name":"Research Group \u2018Engineering Graphics and Industrial Archaeology\u2019, University of Ja\u00e9n, Campus de las Lagunillas, s\/n, 23071 Ja\u00e9n, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,20]]},"reference":[{"key":"ref_1","unstructured":"Mu\u00f1oz Bravo, J. 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