{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:38:54Z","timestamp":1760150334505,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T00:00:00Z","timestamp":1700006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Center of Excellence (CoE) Research on AI and Simulation-Based Engineering at Exascale (RAISE)","award":["951733","101101903","101083762"],"award-info":[{"award-number":["951733","101101903","101083762"]}]},{"name":"EuroCC 2","award":["951733","101101903","101083762"],"award-info":[{"award-number":["951733","101101903","101083762"]}]},{"name":"European Digital Innovation Hub Iceland (EDIH-IS)","award":["951733","101101903","101083762"],"award-info":[{"award-number":["951733","101101903","101083762"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This study introduces an approach for modeling an arm of a Stewart platform to analyze the location of sections with a high deflection among the arms. Given the dynamic nature of the Stewart platform, its arms experience static and dynamic loads. The static loads originate from the platform\u2019s own weight components, while the dynamic loads arise from the movement or holding of equipment in a specific position using the end-effector. These loads are distributed among the platform arms. The arm encompasses various design categories, including spring-mass, spring-mass-damper, mass-actuator, and spring-mass-actuator. In accordance with these designs, joint points should be strategically placed away from critical sections where maximum buckling or deformation is prominent. The current study presents a novel model employing Euler\u2019s formula, a fundamental concept in buckling analysis, to propose this approach. The results align with experimental and numerical reports in the literature that prove the internal force of the platform arm is affecting the arm stiffness. The equal stiffness of an arm is related to its internal force and its deflection. The study demonstrates how higher levels of dynamic loading influence the dynamic platform, causing variations in the maximum arm\u2019s buckling deflection, its precise location, and the associated deflection slope. Notably, in platform arms capable of adjusting their tilt angles relative to the vertical axis, the angle of inclination directly correlates with deflection and its gradient. The assumption of linearity in Euler\u2019s formula seems to reveal distinctive behavior in deflection gradients concerning dynamic mechanisms.<\/jats:p>","DOI":"10.3390\/computation11110227","type":"journal-article","created":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T10:51:37Z","timestamp":1700045497000},"page":"227","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Buckling Assessment in the Dynamics Mechanisms, Stewart Platform Case Study: In the Context of Loads and Joints, Deflection Positions Gradient"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5706-314X","authenticated-orcid":false,"given":"Reza","family":"Hassanian","sequence":"first","affiliation":[{"name":"The Faculty of Industrial Engineering, Mechanical Engineering and Computer Science, University of Iceland, 102 Reykjavik, Iceland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1810-9330","authenticated-orcid":false,"given":"Morris","family":"Riedel","sequence":"additional","affiliation":[{"name":"The Faculty of Industrial Engineering, Mechanical Engineering and Computer Science, University of Iceland, 102 Reykjavik, Iceland"},{"name":"Juelich Supercomputing Centre, 52428 J\u00fclich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1007\/s00170-005-0166-y","article-title":"Design and development of 3\u2013DOF modular micro parallel kinematic manipulator","volume":"31","author":"Ng","year":"2006","journal-title":"Int. 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