{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T19:40:31Z","timestamp":1790970031677,"version":"4.1.0"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T00:00:00Z","timestamp":1769126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Higher Education, Science and Innovation of Slovenia, Slovenian Research and Innovation Agency","award":["TN-06-0106"],"award-info":[{"award-number":["TN-06-0106"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents the experimental validation of a computational kinematic model for a passive Stewart\u2013Gough platform equipped with modified Cardan joints. The introduced joint geometry significantly increases structural stiffness but invalidates the standard spherical joint assumption commonly used in hexapod kinematic formulations. To address this, we develop an efficient numerical optimization-based framework that solves both the direct and inverse kinematics without relying on simplified joint models. Furthermore, to enable autonomous and absolute pose measurement, each cylindrical leg joint of the platform is equipped with a LinACE\u2122 absolute linear encoder. This sensor integration transforms the passive mechanism into an IoT-enabled reconfigurable fixture capable of internally sensing, tracking, and recalling its own configuration. The direct kinematics are computed iteratively using a homogeneous transformation formulation and benchmarked against analytical models derived for ideal spherical joints. Experimental results demonstrate sub-millimeter accuracy in pose estimation, confirming the validity of the proposed kinematic model and highlighting the suitability of the sensor-equipped hexapod for industrial flexible fixturing applications.<\/jats:p>","DOI":"10.3390\/s26030771","type":"journal-article","created":{"date-parts":[[2026,1,26]],"date-time":"2026-01-26T16:13:48Z","timestamp":1769444028000},"page":"771","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Experimental Validation of the Direct Kinematics of a Passive Stewart-Gough Platform with Modified Cardan Joints Using Integrated Absolute Linear Encoders"],"prefix":"10.3390","volume":"26","author":[{"given":"Martin","family":"Bem","sequence":"first","affiliation":[{"name":"Department of Automatics, Biocybernetics, and Robotics, Jo\u017eef Stefan Institute, 1000 Ljubljana, Slovenia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3677-3972","authenticated-orcid":false,"given":"Ale\u0161","family":"Ude","sequence":"additional","affiliation":[{"name":"Department of Automatics, Biocybernetics, and Robotics, Jo\u017eef Stefan Institute, 1000 Ljubljana, Slovenia"},{"name":"Faculty of Electrical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8728-7731","authenticated-orcid":false,"given":"Bojan","family":"Nemec","sequence":"additional","affiliation":[{"name":"Department of Automatics, Biocybernetics, and Robotics, Jo\u017eef Stefan Institute, 1000 Ljubljana, Slovenia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.jmsy.2011.01.001","article-title":"Design of reconfigurable manufacturing systems","volume":"29","author":"Koren","year":"2010","journal-title":"J. Manuf. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"101979","DOI":"10.1016\/j.rcim.2020.101979","article-title":"Smart hardware integration with advanced robot programming technologies for efficient reconfiguration of robot workcells","volume":"66","author":"Ridge","year":"2020","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijmachtools.2017.07.004","article-title":"State-of-the-art in fixture systems for the manufacture and assembly of rigid components: A review","volume":"123","author":"Gameros","year":"2017","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Bem, M., Deni\u0161a, M., Ga\u0161par, T., Jereb, J., Bevec, R., Kova\u010d, I., and Ude, A. (2017, January 10\u201312). Reconfigurable fixture evaluation for use in automotive light assembly. 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