{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T05:22:38Z","timestamp":1772342558317,"version":"3.50.1"},"reference-count":70,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T00:00:00Z","timestamp":1751500800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Quaternions are used in various applications, especially in those where it is necessary to model and represent rotational movements, both in the plane and in space, such as in the modeling of the movements of robots and mechanisms. In this article, a methodology to model the rigid rotations of coupled bodies by means of unit quaternions is presented. Two parallel robots were modeled: a planar RRR robot and a spatial motion PRRS robot using the proposed methodology. Inverse kinematic problems were formulated for both models. The planar RRR robot model generated a system of 21 nonlinear equations and 18 unknowns and a system of 36 nonlinear equations and 33 unknowns for the case of space robot PRRS; both systems of equations were of the polynomial algebraic type. The systems of equations were solved using the Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno nonlinear programming algorithm and Mathematica V12 symbolic computation software. The modeling methodology and the algebra of unitary quaternions allowed the systematic study of the movements of both robots and the generation of mathematical models clearly and functionally.<\/jats:p>","DOI":"10.3390\/robotics14070094","type":"journal-article","created":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T10:45:11Z","timestamp":1751539511000},"page":"94","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Methodology for Modeling Coupled Rigid Multibody Systems Using Unitary Quaternions: The Case of Planar RRR and Spatial PRRS Parallel Robots"],"prefix":"10.3390","volume":"14","author":[{"given":"Francisco Cuenca","family":"Jim\u00e9nez","sequence":"first","affiliation":[{"name":"Engineering Design Department, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Ciudad de M\u00e9xico 04510, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eusebio Jim\u00e9nez","family":"L\u00f3pez","sequence":"additional","affiliation":[{"name":"Research and Development Department, Universidad Tecnol\u00f3gica del Sur de Sonora-Universidad La Salle Noroeste-ITESCA, Cuidad Obreg\u00f3n 85190, Sonora, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3131-1509","authenticated-orcid":false,"given":"Mario Acosta","family":"Flores","sequence":"additional","affiliation":[{"name":"Faculty of Chemical Sciences and Engineering, Universidad Aut\u00f3noma del Estado de Morelos, Cuernacava 62209, Morelos, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1069-3499","authenticated-orcid":false,"given":"F.","family":"Pe\u00f1u\u00f1uri","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Universidad Aut\u00f3noma de Yucat\u00e1n, M\u00e9rida 97160, Yucat\u00e1n, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5361-7763","authenticated-orcid":false,"given":"Ricardo Javier Pe\u00f3n","family":"Escalante","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Universidad Aut\u00f3noma de Yucat\u00e1n, M\u00e9rida 97160, Yucat\u00e1n, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan Jos\u00e9 Delf\u00edn","family":"V\u00e1zquez","sequence":"additional","affiliation":[{"name":"Research and Development Department, Tecnol\u00f3gico Nacional de M\u00e9xico\/ITS de Cajeme, Cuidad Obreg\u00f3n 85024, Sonora, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wu, H. 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