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However, existing numerical Jacobian identification methods for parallel manipulators often exhibit nonlinear, workspace-dependent inaccuracies and require frequent recalibration, limiting their reliability and clinical applicability. To address these challenges, this study presents an analytical kinematic framework for a hybrid parallel\u2013serial robot designed for retinal surgery, known as the steady-hand eye robot (SHER 3.0). Closed-form solutions for forward and inverse kinematics, as well as analytical formulations of the direct and inverse Jacobians, are derived to ensure consistent motion estimation across the workspace. The kinematic performance of SHER 3.0 is analyzed to evaluate the manipulability and workspace efficiency. Building on these models, a model predictive control strategy is implemented on SHER 3.0, which maintains the remote center of motion constraint at the sclerotomy with submillimeter accuracy, with a root mean square error of 0.55\u00b10.12 mm, in a pilot study in a teleoperation experiment. Experimental results demonstrate the effectiveness of the proposed analytical models and control framework in enhancing robot motion stability and robustness of the controller in maintaining the remote center of motion constraints, enabling safe robot-assisted retinal microsurgery.<\/jats:p>","DOI":"10.1115\/1.4072676","type":"journal-article","created":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T17:27:05Z","timestamp":1788542825000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":0,"title":["Analytical Kinematic Model and Remote Center of Motion Control of a Parallel-Serial Steady-Hand Eye Robot"],"prefix":"10.1115","volume":"18","author":[{"given":"Botao","family":"Zhao","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00za53h95","id-type":"ROR","asserted-by":"publisher"}],"name":"Johns Hopkins University Laboratory for Computational Sensing and Robotics, , , \u00a0","place":["Baltimore, MD, 21218"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mojtaba","family":"Esfandiari","sequence":"additional","affiliation":[{"name":"Johns Hopkins University Laboratory for Computational Sensing and Robotics, , , \u00a0","place":["Baltimore, MD, 21218"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Teng","family":"Long","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00za53h95","id-type":"ROR","asserted-by":"publisher"}],"name":"Johns Hopkins University Laboratory for Computational Sensing and Robotics, , , \u00a0","place":["Baltimore, MD, 21218"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yub","family":"Heo","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00za53h95","id-type":"ROR","asserted-by":"publisher"}],"name":"Johns Hopkins University Laboratory for Computational Sensing and Robotics, , , \u00a0","place":["Baltimore, MD, 21218"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haochen","family":"Wei","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00za53h95","id-type":"ROR","asserted-by":"publisher"}],"name":"Johns Hopkins University Laboratory for Computational Sensing and Robotics, , , \u00a0","place":["Baltimore, MD, 21218"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adnan","family":"Munawar","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00za53h95","id-type":"ROR","asserted-by":"publisher"}],"name":"Johns Hopkins University Laboratory for Computational Sensing and Robotics, , , \u00a0","place":["Baltimore, MD, 21218"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Gehlbach","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00za53h95","id-type":"ROR","asserted-by":"publisher"}],"name":"Johns Hopkins School of Medicine Wilmer Eye Institute, , , \u00a0","place":["Baltimore, MD, 21287"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Kazanzides","sequence":"additional","affiliation":[{"name":"Johns Hopkins University Laboratory for Computational Sensing and Robotics, , , \u00a0","place":["Baltimore, MD, 21218"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Iulian","family":"Iordachita","sequence":"additional","affiliation":[{"name":"Johns Hopkins University Laboratory for Computational Sensing and Robotics, , , \u00a0","place":["Baltimore, MD, 21218"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"33","published-online":{"date-parts":[[2026,9,16]]},"reference":[{"key":"2026091610543932500_CIT0001","doi-asserted-by":"crossref","DOI":"10.1201\/9781003590408","volume-title":"Parallel Robots: Mechanics and Control","author":"Taghirad","year":"2025"},{"issue":"4","key":"2026091610543932500_CIT0002","doi-asserted-by":"publisher","first-page":"041012","DOI":"10.1115\/1.4055571","article-title":"A Trajectory Planning Approach for Delta Robots Considering Both Motion Smoothness and Dynamic Stress","volume":"15","author":"Ni","year":"2023","journal-title":"ASME J. 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