{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:00:42Z","timestamp":1760241642426,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,6,15]],"date-time":"2018-06-15T00:00:00Z","timestamp":1529020800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100013704","name":"Conacyt","doi-asserted-by":"publisher","award":["7903"],"award-info":[{"award-number":["7903"]}],"id":[{"id":"10.13039\/501100013704","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>In this work, the kinematics of a spherical parallel manipulator composed of three peripheral limbs equipped with linear actuators and a passive center shaft is approached by means of the theory of screws. The displacement analysis is carried out solving closure equations, which are obtained upon simple linear combinations of the components of two unit vectors describing the orientation of the moving platform. After, the input-output equations of velocity and acceleration of the spherical parallel manipulator are systematically obtained by resorting to reciprocal-screw theory. This strategy avoids the computation of the passive joint velocity and acceleration rates of the robot manipulator. Numerical examples illustrate the efficiency of the proposed method.<\/jats:p>","DOI":"10.3390\/robotics7020029","type":"journal-article","created":{"date-parts":[[2018,6,15]],"date-time":"2018-06-15T11:21:20Z","timestamp":1529061680000},"page":"29","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Kinematics of the 3(RPSP)-S Fully Spherical Parallel Manipulator by Means of Screw Theory"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8208-0432","authenticated-orcid":false,"given":"Jaime","family":"Gallardo-Alvarado","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Instituto Tecnologico de Celaya, TecNM, Av. Tecnologico y A Garcia Cubas, Celaya 38010, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0735-1060","authenticated-orcid":false,"given":"Ramon","family":"Rodriguez-Castro","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Instituto Tecnologico de Celaya, TecNM, Av. Tecnologico y A Garcia Cubas, Celaya 38010, Mexico"}]},{"given":"Luciano","family":"Perez-Gonzalez","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Instituto Tecnologico de Celaya, TecNM, Av. Tecnologico y A Garcia Cubas, Celaya 38010, Mexico"}]},{"given":"Carlos R.","family":"Aguilar-Najera","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Instituto Tecnologico de Celaya, TecNM, Av. Tecnologico y A Garcia Cubas, Celaya 38010, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1119\/1.12267","article-title":"Finite rotations and angular velocity","volume":"48","author":"Peres","year":"1980","journal-title":"Am. J. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1115\/1.3267395","article-title":"Instantaneous kinematics of a plane in spherical motion","volume":"105","author":"Ting","year":"1983","journal-title":"ASME J. Mech. Trans. Autom. Des."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1115\/1.3260722","article-title":"Euler parameters in computational kinematics and dynamics. Part 1","volume":"107","author":"Nikravesh","year":"1985","journal-title":"ASME J. Mech. Trans. Autom. Des."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Angeles, J. (1988). Rational Kinematics, Springer.","DOI":"10.1007\/978-1-4612-3916-1"},{"key":"ref_5","unstructured":"Chiang, C.H. (1988). Kinematics of Spherical Mechanisms, Cambridge University Press."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1023\/A:1004853828657","article-title":"A simple method for the determination of angular velocity and acceleration of a spherical motion through quaternions","volume":"35","year":"2000","journal-title":"Meccanica"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3","DOI":"10.3390\/robotics1010003","article-title":"A Review of active mechanical driving principles of spherical robots","volume":"1","author":"Chase","year":"2012","journal-title":"Robotics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/S0094-114X(99)00005-1","article-title":"Avoiding singular configurations in finite position synthesis of spherical 4R linkages","volume":"35","author":"McCarthy","year":"2000","journal-title":"Mech. Mach. Theory"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"McCarthy, J.M., and Soh, G.S. (2011). Geometric Design of Linkages, Springer. [2nd ed.].","DOI":"10.1007\/978-1-4419-7892-9"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.mechmachtheory.2008.02.007","article-title":"Some improvements on the exact kinematic synthesis of spherical 4R function generators","volume":"44","year":"2009","journal-title":"Mech. Mach. Theory"},{"key":"ref_11","first-page":"1236","article-title":"A Simple Synthesis Method of Spherical 4R Linkages Reaching Four Positions","volume":"199\u2013200","author":"Yang","year":"2011","journal-title":"Adv. Mater. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.mechmachtheory.2015.04.015","article-title":"Synthesis method for the spherical 4R mechanism with minimum center of mass acceleration","volume":"93","year":"2015","journal-title":"Mech. Mach. Theory"},{"key":"ref_13","unstructured":"Asada, H., and Granito, J. (1985, January 25\u201328). Kinematic and static characterization of wrist joints and their optimal design. Proceedings of the IEEE International Conference on Robotics and Automation, St. Louis, MO, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1017\/S0263574714001945","article-title":"Optimization and analysis of a redundant 4R spherical wrist mechanism for a shoulder exoskeleton","volume":"32","author":"Lo","year":"2014","journal-title":"Robotica"},{"key":"ref_15","unstructured":"Gosselin, C.M., and Hamel, J.F. (1994, January 8\u201313). The Agile Eye: A high-performance three-degree-of-freedom camera-orienting device. Proceedings of the IEEE International Conference on Robotics and Automation, San Diego, CA, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1177\/027836499701600503","article-title":"Development and experimentation of a fast 3-DOF camera-orienting device","volume":"16","author":"Gosselin","year":"1997","journal-title":"Int. J. Robot. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1017\/S0263574701003873","article-title":"Design of spherical parallel mechanisms for application to laparoscopic surgery","volume":"20","author":"Li","year":"2002","journal-title":"Robotica"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1109\/TMECH.2013.2245143","article-title":"Design of a novel 4-DOF wrist-type surgical instrument with enhanced rigidity and dexterity","volume":"19","author":"Hong","year":"2014","journal-title":"IEEE ASME Trans. Mechatron."},{"key":"ref_19","first-page":"021006-1-15","article-title":"Lessons learned from kinematics research applied to medical device design","volume":"140","author":"Erdman","year":"2018","journal-title":"ASME J. Biomech. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1115\/1.3258984","article-title":"The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator","volume":"111","author":"Gosselin","year":"1989","journal-title":"ASME J. Mech. Transm. Autom. Des."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1115\/1.2912772","article-title":"A global performance index for the kinematic optimization of robotic manipulators","volume":"113","author":"Gosselin","year":"1991","journal-title":"ASME J. Mech. Des."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/S0094-114X(03)00116-2","article-title":"Topology optimisation and singularity analysis of a 3-SPS parallel manipulator with a passive constraining spherical joint","volume":"39","author":"Alici","year":"2004","journal-title":"Mech. Mach. Theory"},{"key":"ref_23","unstructured":"Bonev, I.A., and Gosselin, C.M. (2005, January 18\u201322). Singularity loci of spherical parallel mechanisms. Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1017\/S0263574708004402","article-title":"Modelling of a special class of spherical parallel manipulators with Euler parameters","volume":"27","author":"Bai","year":"2009","journal-title":"Robotica"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.mechmachtheory.2009.06.007","article-title":"Optimum design of spherical parallel manipulator for a prescribed workspace","volume":"45","author":"Bai","year":"2010","journal-title":"Mech. Mach. Theory"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"044501","DOI":"10.1115\/1.4002077","article-title":"A formula that produces a unique solution to the forward displacement analysis of a quadratic spherical parallel manipulator: The agile eye","volume":"2","author":"Kong","year":"2010","journal-title":"ASME J. Mech. Robot."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"111","DOI":"10.4173\/mic.2012.3.3","article-title":"Multiobjective optimum design of a 3-RRR spherical parallel manipulator with kinematic and dynamic dexterities","volume":"33","author":"Wu","year":"2012","journal-title":"Model. Identif. Control"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1017\/S0263574714001751","article-title":"Redundantly actuated 3-RRR spherical parallel manipulator used as a haptic device: Improving dexterity and eliminating singularity","volume":"33","author":"Saafi","year":"2015","journal-title":"Robotica"},{"key":"ref_29","first-page":"98","article-title":"Numerical optimal control of a spherical parallel manipulator based on unique kinematic solutions","volume":"21","author":"Shintemirov","year":"2016","journal-title":"IEEE ASME Trans. Mechatron."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.mechmachtheory.2015.07.012","article-title":"Design and transmission analysis of an asymmetrical spherical parallel manipulator","volume":"94","author":"Wu","year":"2015","journal-title":"Mech. Mach. Theory"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.robot.2016.12.005","article-title":"Optimal torque distribution for a redundant 3-RRR spherical parallel manipulator used as a haptic medical device","volume":"89","author":"Saafi","year":"2017","journal-title":"Robot. Auton. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1016\/j.mechmachtheory.2017.11.019","article-title":"Workspace characterization and kinematic analysis of general spherical parallel manipulators revisited via graphical based approaches","volume":"122","author":"Arrouk","year":"2018","journal-title":"Mech. Mach. Theory"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"021007","DOI":"10.1115\/1.4038971","article-title":"Kinematic analysis of a novel kinematically redundant spherical parallel manipulator","volume":"10","author":"Gosselin","year":"2018","journal-title":"ASME J. Mech. Robot."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Li, X., Liu, J., Chen, W., and Bai, S. (2018). Integrated design, modeling and analysis of a novel spherical motion generator driven by electromagnetic principle. Robot. Auton. Syst., in press.","DOI":"10.1016\/j.robot.2018.04.006"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2114","DOI":"10.1017\/S0263574715000752","article-title":"A closed-form solution for the position analysis of a novel fully spherical parallel manipulator","volume":"33","author":"Enferadi","year":"2015","journal-title":"Robotica"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"061020","DOI":"10.1115\/1.4034884","article-title":"Simplified kinematics for a parallel manipulator generator of the Sch\u00f6nflies motion","volume":"8","author":"Abedinnasab","year":"2016","journal-title":"ASME J. Mech. Robot."},{"key":"ref_37","unstructured":"Craig, J.J. (1986). Introduction to Robotics: Mechanics & Control, Addison-Wesley Publishing Company."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1115\/1.1469549","article-title":"Jacobian analysis of limited-DOF parallel manipulators","volume":"124","author":"Joshi","year":"2002","journal-title":"ASME J. Mech. Des."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Gallardo-Alvarado, J. (2016). Kinematic Analysis of Parallel Manipulators by Algebraic Screw Theory, Springer International Publishing.","DOI":"10.1007\/978-3-319-31126-5"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.mechmachtheory.2012.06.008","article-title":"Singularity analysis of a four degree-of-freedom parallel manipulator based on an expanded 6\u00d76 Jacobian matrix","volume":"57","author":"Choi","year":"2012","journal-title":"Mech. Mach. Theory"}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/7\/2\/29\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:08:54Z","timestamp":1760195334000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/7\/2\/29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,15]]},"references-count":40,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["robotics7020029"],"URL":"https:\/\/doi.org\/10.3390\/robotics7020029","relation":{},"ISSN":["2218-6581"],"issn-type":[{"type":"electronic","value":"2218-6581"}],"subject":[],"published":{"date-parts":[[2018,6,15]]}}}