{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T18:56:00Z","timestamp":1772736960178,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T00:00:00Z","timestamp":1687737600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52275032"],"award-info":[{"award-number":["52275032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["E2022203077"],"award-info":[{"award-number":["E2022203077"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["202230808010057"],"award-info":[{"award-number":["202230808010057"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015286","name":"Key Project of Hebei Natural Science Foundation","doi-asserted-by":"publisher","award":["52275032"],"award-info":[{"award-number":["52275032"]}],"id":[{"id":"10.13039\/501100015286","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015286","name":"Key Project of Hebei Natural Science Foundation","doi-asserted-by":"publisher","award":["E2022203077"],"award-info":[{"award-number":["E2022203077"]}],"id":[{"id":"10.13039\/501100015286","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015286","name":"Key Project of Hebei Natural Science Foundation","doi-asserted-by":"publisher","award":["202230808010057"],"award-info":[{"award-number":["202230808010057"]}],"id":[{"id":"10.13039\/501100015286","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015286","name":"Key Research and Development Plan of Hebei Province","doi-asserted-by":"publisher","award":["52275032"],"award-info":[{"award-number":["52275032"]}],"id":[{"id":"10.13039\/501100015286","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015286","name":"Key Research and Development Plan of Hebei Province","doi-asserted-by":"publisher","award":["E2022203077"],"award-info":[{"award-number":["E2022203077"]}],"id":[{"id":"10.13039\/501100015286","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015286","name":"Key Research and Development Plan of Hebei Province","doi-asserted-by":"publisher","award":["202230808010057"],"award-info":[{"award-number":["202230808010057"]}],"id":[{"id":"10.13039\/501100015286","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Traditional stiffness modeling methods do not consider all factors comprehensively, and the modeling methods are not unified, lacking a global stiffness model. Based on screw theory, strain energy and the virtual work principle, a static stiffness modeling method for redundant over-constrained parallel mechanisms (PMs) with clearance was proposed that considers the driving stiffness, branch deformation, redundant driving, joint clearance and joint contact deformation. First, the driving stiffness and branch deformation were considered. According to the strain energy and Castiliano\u2019s second theorem, the global stiffness matrix of the ideal joint mechanism was obtained. The offset of the branch was analyzed according to the restraint force of each branch. The mathematical relationship between the joint clearance and joint contact deformation and the end deformation was established. Based on the probability statistical model, the uncertainty of the offset value of the clearance joint and the contact area of the joint caused by the coupling of the branch constraint force was solved. Finally, taking a 2UPR-RR-2RPU redundant PM as an example, a stiffness simulation of the mechanism was carried out using the finite element method. The research results show that the high-precision stiffness modeling method proposed in this paper is correct, and provides an effective method for evaluating the stiffness performance of the PM.<\/jats:p>","DOI":"10.3390\/s23135916","type":"journal-article","created":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T02:11:22Z","timestamp":1687831882000},"page":"5916","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Research on High Precision Stiffness Modeling Method of Redundant Over-Constrained Parallel Mechanism"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4781-6301","authenticated-orcid":false,"given":"Sen","family":"Wang","sequence":"first","affiliation":[{"name":"Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004, China"},{"name":"College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}]},{"given":"Haoran","family":"Li","sequence":"additional","affiliation":[{"name":"Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004, China"},{"name":"College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}]},{"given":"Xueyan","family":"Han","sequence":"additional","affiliation":[{"name":"Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004, China"},{"name":"College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}]},{"given":"Jiahao","family":"Wei","sequence":"additional","affiliation":[{"name":"Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004, China"},{"name":"College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}]},{"given":"Tao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004, China"},{"name":"College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}]},{"given":"Shihua","family":"Li","sequence":"additional","affiliation":[{"name":"Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004, China"},{"name":"College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"53","DOI":"10.3901\/JME.2015.07.053","article-title":"Method for force analysis of the over-constrained parallel mechanism considering the link\u2019s spatial composite elastic deformations","volume":"51","author":"Xu","year":"2015","journal-title":"J. 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