{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:03:15Z","timestamp":1760148195482,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T00:00:00Z","timestamp":1680825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The paper presents a proposed mechanism, RPCR, for the coupling of two shafts with crossed axes. For the analytical kinematics, the Hartenberg\u2013Denavit methodology cannot be applied due to the planar pair occurrence. To apply the screw theory, the planar pair should be replaced by an assembly of cylindrical pairs, but this is also cumbersome. This work proposes an analytical solution obtained from the structural condition of planar joint based on the formulated expressions with respect to adequately chosen reference frames. A system of trigonometrical equations is obtained, but confusions may occur from classical solving; then, this paper presents the methodology with the correct approach. With the analytical solution for the displacements from the joints found, the conditions required for the constructive parameters of a realistic mechanism are found. The kinematical calculus of the mechanism is presented, and analytical relations are obtained for all relative motions from the pairs of the mechanism. The correctness of the analytical solutions is validated by the results of a numerical simulation.<\/jats:p>","DOI":"10.3390\/axioms12040357","type":"journal-article","created":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T04:04:16Z","timestamp":1680840256000},"page":"357","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Solution for the Kinematics of Non-H-D Couplings Applied to RPCR Mechanism"],"prefix":"10.3390","volume":"12","author":[{"given":"Stelian","family":"Alaci","sequence":"first","affiliation":[{"name":"Mechanics and Technologies Department, Stefan cel Mare University of Suceava, 720229 Suceava, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Florina-Carmen","family":"Ciornei","sequence":"additional","affiliation":[{"name":"Mechanics and Technologies Department, Stefan cel Mare University of Suceava, 720229 Suceava, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ionut-Cristian","family":"Romanu","sequence":"additional","affiliation":[{"name":"Mechanics and Technologies Department, Stefan cel Mare University of Suceava, 720229 Suceava, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toma-Marian","family":"Ciocirlan","sequence":"additional","affiliation":[{"name":"Mechanics and Technologies Department, Stefan cel Mare University of Suceava, 720229 Suceava, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mariana-Catalina","family":"Ciornei","sequence":"additional","affiliation":[{"name":"Physiology Department, Carol Davila University of Medicine and Pharmacy, 020021 Bucharest, Romania"},{"name":"Medical Engineering Faculty, University Politehnica of Bucharest, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1115\/1.4011045","article-title":"A kinematic notation for lower-pair mechanisms based on matrices","volume":"22","author":"Denavit","year":"1955","journal-title":"J. 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