{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T18:11:49Z","timestamp":1783793509184,"version":"3.55.0"},"reference-count":45,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2025,3,10]],"date-time":"2025-03-10T00:00:00Z","timestamp":1741564800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2025,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper introduces an equivalent series mechanism model to improve ankle rehabilitation robots\u2019 ability to recurrence the complex movements of the anthropo-ankle and enhance human-machine locomotion compatibility. The model emulates the true anatomical architecture of the ankle joint and is integrated with a parallel rehabilitative mechanism. The rehabilitative robot includes dual virtual motion centers to mimic the ankle joint\u2019s intricate motion, accommodate individual patient variations, and address the rehabilitation requirements of both right and left feet. Firstly, a serial equivalence model of anthropo-ankle is developed based on the kinematic and anatomical characteristics of the human ankle. The type design for the 4-degree of freedom (4-DOF) parallel ankle rehabilitative robot is then conducted on the basis of the kinematical and restrictive properties of the anthropo-ankle equivalence kinematic model. Secondly, the mechanism\u2019s motion properties allow it to be equivalent to a series branch chain, enabling the establishment of an inverse kinematics model. The kinematical performance of the mechanisms is analyzed using the transmissibility and constrainability indices, followed by workspace analysis and dimensional optimization of the rehabilitative mechanism. Finally, a human-machine coupled rehabilitative simulation model is developed using OpenSim biomechanics software to evaluate the recovery effect.<\/jats:p>","DOI":"10.1017\/s0263574725000128","type":"journal-article","created":{"date-parts":[[2025,3,10]],"date-time":"2025-03-10T09:05:36Z","timestamp":1741597536000},"page":"1291-1313","source":"Crossref","is-referenced-by-count":5,"title":["Configuration design and dimensional synthesis of a novel 4-DOFs parallel ankle rehabilitative robot with dual virtual motion center"],"prefix":"10.1017","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8974-0942","authenticated-orcid":false,"given":"Jingke","family":"Song","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianjun","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0638-8897","authenticated-orcid":false,"given":"Jun","family":"Wei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenglei","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiankun","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7205-8653","authenticated-orcid":false,"given":"Cunjin","family":"Ai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,3,10]]},"reference":[{"key":"S0263574725000128_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2021.104436"},{"key":"S0263574725000128_ref14","doi-asserted-by":"crossref","unstructured":"[14] Liu, G. , Gao, J. , Yue, H. , Zhang, X. and Guangda, L. U. , \"Design and Kinematics Simulation of Parallel Robots for Ankle Rehabilitation,\" ICMA, Luoyang, China (2006) pp. 253\u2013258.","DOI":"10.1109\/IROS.2006.281710"},{"key":"S0263574725000128_ref2","first-page":"A14","article-title":"O-25Three-year functional outcomes of ankle joint injuries\u2019 treatment in professional soccer players","volume":"50","author":"Czamara","year":"2016","journal-title":"Br. J. Sports Med."},{"key":"S0263574725000128_ref31","volume-title":"Inman\u2019s Joint of the Ankle","author":"Stiehl","year":"1991"},{"key":"S0263574725000128_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s11517-022-02704-y"},{"key":"S0263574725000128_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9290(10)70165-2"},{"key":"S0263574725000128_ref24","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2023.3330052"},{"key":"S0263574725000128_ref4","doi-asserted-by":"publisher","DOI":"10.3390\/machines11080787"},{"key":"S0263574725000128_ref33","first-page":"311","volume-title":"Atlas of Orthoses and Assistive Devices","author":"Haskell","year":"2017"},{"key":"S0263574725000128_ref35","doi-asserted-by":"publisher","DOI":"10.1115\/1.4046031"},{"key":"S0263574725000128_ref36","doi-asserted-by":"publisher","DOI":"10.1115\/1.4026632"},{"key":"S0263574725000128_ref1","doi-asserted-by":"publisher","DOI":"10.2165\/00007256-200737010-00006"},{"key":"S0263574725000128_ref18","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2017.2734239"},{"key":"S0263574725000128_ref37","doi-asserted-by":"publisher","DOI":"10.1115\/1.4047540"},{"key":"S0263574725000128_ref38","doi-asserted-by":"publisher","DOI":"10.1016\/0141-5425(85)90043-3"},{"key":"S0263574725000128_ref22","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2023.3342556"},{"key":"S0263574725000128_ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2020.3022165"},{"key":"S0263574725000128_ref12","first-page":"1216","article-title":"A high-performance redundantly actuated parallel mechanism for ankle rehabilitation","volume":"28","author":"Saglia","year":"2009","journal-title":"IJRR"},{"key":"S0263574725000128_ref9","doi-asserted-by":"publisher","DOI":"10.3390\/act12060238"},{"key":"S0263574725000128_ref42","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-016-9591-z"},{"key":"S0263574725000128_ref43","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2018.2849580"},{"key":"S0263574725000128_ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.foot.2014.06.003"},{"key":"S0263574725000128_ref44","doi-asserted-by":"publisher","DOI":"10.1007\/s40141-014-0056-z"},{"key":"S0263574725000128_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574715000120"},{"key":"S0263574725000128_ref25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2019\/2161038","article-title":"Research on an ankle joint auxiliary rehabilitation robot with a rigid-flexible hybrid drive based on a 2-S\u2019PS\u2019 mechanism","volume":"2019","author":"Wang","year":"2019","journal-title":"Appl. Bionics Biomech."},{"key":"S0263574725000128_ref32","first-page":"183","article-title":"The joints of the ankle","volume":"127","author":"Beals","year":"1977","journal-title":"Western J. Med."},{"key":"S0263574725000128_ref45","doi-asserted-by":"publisher","DOI":"10.1097\/WNR.0000000000001615"},{"key":"S0263574725000128_ref10","doi-asserted-by":"publisher","DOI":"10.3390\/app13106109"},{"key":"S0263574725000128_ref13","doi-asserted-by":"publisher","DOI":"10.1023\/B:AURO.0000016866.80026.d7"},{"key":"S0263574725000128_ref26","doi-asserted-by":"publisher","DOI":"10.1115\/1.4036560"},{"key":"S0263574725000128_ref19","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574719000845"},{"key":"S0263574725000128_ref16","doi-asserted-by":"publisher","DOI":"10.1115\/1.4024736"},{"key":"S0263574725000128_ref20","doi-asserted-by":"publisher","DOI":"10.1115\/1.4035989"},{"key":"S0263574725000128_ref29","doi-asserted-by":"publisher","DOI":"10.1177\/0278364909104221"},{"key":"S0263574725000128_ref41","doi-asserted-by":"publisher","DOI":"10.1007\/s11517-023-03010-x"},{"key":"S0263574725000128_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2018.12.017"},{"key":"S0263574725000128_ref23","article-title":"Design and experiment of an ankle rehabilitation robot after fracture surgery","volume":"16","author":"Ni","year":"2024","journal-title":"J. Mech. Rob."},{"key":"S0263574725000128_ref40","doi-asserted-by":"publisher","DOI":"10.1115\/1.4036517"},{"key":"S0263574725000128_ref28","doi-asserted-by":"publisher","DOI":"10.1080\/17483107.2019.1578424"},{"key":"S0263574725000128_ref5","doi-asserted-by":"publisher","DOI":"10.1115\/1.4046031"},{"key":"S0263574725000128_ref27","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s11044-023-09955-z","article-title":"A new skeletal model for the ankle joint complex","volume":"60","author":"Da Silva","year":"2024","journal-title":"Multibody Syst. Dyn."},{"key":"S0263574725000128_ref6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008938121020"},{"key":"S0263574725000128_ref21","doi-asserted-by":"crossref","unstructured":"[21] Malosio, M. , Negri, S. P. , Pedrocchi, N. , Vicentini, F. , Caimmi, M. and Tosatti, L. M. , \u201cA Spherical Parallel Three Degrees-of-Freedom Robot for Ankle-Foot Neuro-Rehabilitation,\u201dIEEE Engineering in Medicine and Biology Society, San Diego, USA (2012) pp. 3356\u20133359.","DOI":"10.1109\/EMBC.2012.6346684"},{"key":"S0263574725000128_ref39","doi-asserted-by":"publisher","DOI":"10.1115\/1.4053826"},{"key":"S0263574725000128_ref30","doi-asserted-by":"crossref","unstructured":"[30] Weerasingha, A. H. , Pragnathilaka, A. D. K. H. , Withanage, W. P. K. , Ranaweera, R. K. P. S. and Gopura, R. A. R. C. , \"C-JAE: 3 DOF Robotic Ankle Exoskeleton with Compatible Joint Axes,\" Moratuwa Engineering Research Confererence (2018) pp. 270\u2013275.","DOI":"10.1109\/MERCon.2018.8422004"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574725000128","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T09:47:22Z","timestamp":1750326442000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574725000128\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,10]]},"references-count":45,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["S0263574725000128"],"URL":"https:\/\/doi.org\/10.1017\/s0263574725000128","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,10]]}}}