{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T15:02:07Z","timestamp":1767193327120,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,13]],"date-time":"2020-01-13T00:00:00Z","timestamp":1578873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007109","name":"Universit\u00e0 degli Studi di Ferrara","doi-asserted-by":"publisher","award":["FAR 2018"],"award-info":[{"award-number":["FAR 2018"]}],"id":[{"id":"10.13039\/501100007109","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Various 3-UPU architectures feature two rigid bodies connected to one another through three kinematic chains (limbs) of universal\u2013prismatic\u2013universal (UPU) type. They were first proposed in the last decade of the 20th century and have animated discussions among researchers for more-or-less two decades. Such discussions brought to light many features of lower-mobility parallel manipulators (PMs) that were unknown until then. The discussions also showed that such architectures may be sized into translational PMs, parallel wrists, or even reconfigurable (metamorphic) PMs. Even though commercial robots with these architectures have not yet been built, the interest in them remains. Consequently, a review of the literature on these architectures, highlighting their contribution to the progress of lower-mobility PM design, is still of interest for the scientific community. This paper aims at presenting a critical review of the results that have been obtained up until now.<\/jats:p>","DOI":"10.3390\/robotics9010005","type":"journal-article","created":{"date-parts":[[2020,1,15]],"date-time":"2020-01-15T03:20:22Z","timestamp":1579058422000},"page":"5","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["A Review of the Literature on the Lower-Mobility Parallel Manipulators of 3-UPU or 3-URU Type"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3925-3016","authenticated-orcid":false,"given":"Raffaele","family":"Di Gregorio","sequence":"first","affiliation":[{"name":"Department of Engineering, University of Ferrara, 44122 Ferrara, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,13]]},"reference":[{"key":"ref_1","unstructured":"Hunt, K.H. (1990). Kinematic Geometry of Mechanisms, Clarendon Press."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Lenarcic, J., and Parenti-Castelli, V. (1996). Kinematics of a Three-dof Platform with Three Extensible Limbs. Recent Advances in Robot Kinematics, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-009-1718-7"},{"key":"ref_3","unstructured":"Bonev, I., and Zlatanov, D. (2019, October 18). The Mystery of the Singular SNU Translational Parallel Robot. ParalleMIC-The Parallel Mechanisms Information Center, (http:\/\/www.parallemic.org) 12 June 2001. Available online: https:\/\/www.parallemic.org\/Reviews\/Review004.html."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1016\/S0094-114X(02)00021-6","article-title":"Kinematic sensitivity analysis of the 3-UPU parallel mechanism","volume":"37","author":"Han","year":"2002","journal-title":"Mech. Mach. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1090\/conm\/496\/09732","article-title":"A complete kinematic analysis of the SNU 3-UPU parallel robot","volume":"Volume 496","author":"Bates","year":"2009","journal-title":"Interactions of Classical and Numerical Algebraic Geometry"},{"key":"ref_6","unstructured":"Zlatanov, D., Bonev, I.A., and Gosselin, C.M. (2002, January 11\u201315). Constraint singularities of parallel mechanisms. Proceedings of the IEEE International Conference on Robotics and Automation, Washington, DC, USA."},{"key":"ref_7","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_8","doi-asserted-by":"crossref","unstructured":"Lenaric, J., and Thomas, F. (2002). Investigation of singularities and self-motions of the 3-UPU robot. Advances in Robot Kinematics, Kluwer.","DOI":"10.1007\/978-94-017-0657-5"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1109\/TRA.2003.814507","article-title":"Singularities of Parallel Manipulators: A Geometric Treatment","volume":"19","author":"Liu","year":"2003","journal-title":"IEEE Trans. Rob. Autom."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lenarcic, J., and Husty, M.L. (1998). A Translational 3-DOF Parallel Manipulator. Advances in Robot Kinematics: Analysis and Control, Kluwer.","DOI":"10.1007\/978-94-015-9064-8"},{"key":"ref_11","unstructured":"Di Gregorio, R., and Parenti-Castelli, V. (1999, January 30). Influence of the geometric parameters of the 3\u2013UPU parallel mechanism on the singularity loci. Proceedings of the International Workshop on Parallel Kinematic Machines (PKM\u201999), Milan, Italy."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1115\/1.1471530","article-title":"Mobility analysis of the 3\u2013UPU parallel mechanism assembled for a pure translational motion","volume":"124","year":"2002","journal-title":"ASME J. Mech. Des."},{"key":"ref_13","unstructured":"Kecskeme\u00e9thy, A., Schneider, M., and Woernle, C. (1999). Singularity loci and dimensional design of a translational 3-dof fully-parallel manipulator. Advances in Multibody Systems and Mechatronics, Technische Universit\u00e4t Graz. Institut f\u00fcr Mechanik und Getriebelehre."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1023\/A:1010359523780","article-title":"Workspace and Optimal Design of a Pure Translational Parallel Manipulator","volume":"35","author":"Bubani","year":"2000","journal-title":"Meccanica"},{"key":"ref_15","unstructured":"Di Gregorio, R., and Parenti-Castelli, V. (2000, January 13\u201315). Benefits of twisting the legs in the 3-UPU Tsai mechanism. Proceedings of the Year 2000 Parallel Kinematic Machines International Conference, Ann Arbor, MI, USA."},{"key":"ref_16","unstructured":"Zieli\u0144ska, T., and Zieli\u0144ski, C. (2006). A New Approach for the evaluation of kinematic and static performances of a family of 3-UPU translational manipulators. Romansy 16: Robot Design, Dynamics, and Control, Springer."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1017\/S0263574713000696","article-title":"Practical feasibility of a high-precision 3-UPU parallel mechanism","volume":"32","author":"Bhutani","year":"2014","journal-title":"Robotica"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.mechmachtheory.2013.11.010","article-title":"Novel design solution to high precision 3 axes translational parallel mechanism","volume":"75","author":"Bhutani","year":"2014","journal-title":"Mech. Mach. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Lenarcic, J., and Stanisic, M.M. (2000). A three-dof tripod for generating spherical rotation. Advances in Robot Kinematics, Springer.","DOI":"10.1007\/978-94-011-4120-8"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/S0094-114X(02)00066-6","article-title":"Kinematics of the 3-UPU wrist","volume":"38","year":"2003","journal-title":"Mech. Mach. Theory"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1109\/TRO.2004.829475","article-title":"Statics and singularity loci of the 3-UPU wrist","volume":"20","year":"2004","journal-title":"IEEE Trans. Robot."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.mechmachtheory.2017.08.019","article-title":"Path planning of a 3-UPU wrist manipulator for sun tracking in central receiver tower systems","volume":"119","author":"Ghosal","year":"2018","journal-title":"Mech. Mach. Theory"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1299\/jamdsm.1.81","article-title":"Kinematic analysis and synthesis of a 3-URU pure rotational parallel mechanism with respect to singularity and workspace","volume":"1","author":"Huda","year":"2007","journal-title":"J. Adv. Mech. Des. Syst. Manuf."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"874","DOI":"10.1299\/jamdsm.2.874","article-title":"Kinematic Design of 3-URU Pure Rotational Parallel Mechanism with Consideration of Uncompensatable Error","volume":"2","author":"Huda","year":"2008","journal-title":"J. Adv. Mech. Des. Syst. Manuf."},{"key":"ref_25","unstructured":"Lenar\u010di\u010d, J., and Thomas, F. (2002). Constraint Singularities as C-Space Singularities. Advances in Robot Kinematics: Theory and Applications, Springer."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ferraresi, C., and Quaglia, G. (2018). A Novel Reconfigurable 3-URU Parallel Platform. Advances in Service and Industrial Robotics, Springer.","DOI":"10.1007\/978-3-319-61276-8"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Sarabandi, S., Grosch, P., Porta, J.M., and Thomas, F. (2018, January 20\u201322). A Reconfigurable Asymmetric 3-UPU Parallel Robot. Proceedings of the 2018 International Conference on Reconfigurable Mechanisms and Robots (ReMAR2018), Deft, The Netherlands.","DOI":"10.1109\/REMAR.2018.8449859"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/S0094-114X(98)00051-2","article-title":"The lie group of rigid body displacements, a fundamental tool for mechanism design","volume":"34","year":"1999","journal-title":"Mech. Mach. Theory"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1299\/jsmec.45.730","article-title":"Geometric Analysis of Overconstrained Parallel Manipulators with Three and Four Degrees of Freedom","volume":"45","author":"Zhao","year":"2002","journal-title":"JSME Int. J. Ser. C"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhao, T.S., Li, Y.W., Chen, J., and Wang, J.C. (2006, January 1\u20133). Novel Four-DOF Parallel Manipulator Mechanism and Its Kinematics. Proceedings of the 2006 IEEE Conference on Robotics, Automation and Mechatronics (RAM 2006), Bangkok, Thailand.","DOI":"10.1109\/RAMECH.2006.252672"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Lenarcic, J., and Khatib, O. (2014). Kinematics Analysis and Singularity Loci of a 4-UPU Parallel Manipulator. Advances in Robot Kinematics, Springer.","DOI":"10.1007\/978-3-319-06698-1"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"041020","DOI":"10.1115\/1.4029501","article-title":"Extra Modes of Operation and Self-Motions in Manipulators Designed for Schoenflies Motion","volume":"7","author":"Coste","year":"2015","journal-title":"ASME J. Mech. Rob."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1007\/s11465-013-0282-6","article-title":"A rolling 3-UPU parallel mechanism","volume":"8","author":"Miao","year":"2013","journal-title":"Front. Mech. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"011005","DOI":"10.1115\/1.4000527","article-title":"Generation of under-actuated manipulators with non-holonomic joints from ordinary manipulators","volume":"2","author":"Grosch","year":"2010","journal-title":"ASME J. Mech. Rob."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Roberson, R.E., and Schwertassek, R. (1988). Dynamics of Multibody Systems, Springer.","DOI":"10.1007\/978-3-642-86464-3"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Palpacelli, M., Carbonari, L., Palmieri, G., and Callegari, M. (2018). Design of a Lockable Spherical Joint for a Reconfigurable 3-URU Parallel Platform. Robotics, 7.","DOI":"10.3390\/robotics7030042"}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/9\/1\/5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:33:05Z","timestamp":1760365985000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/9\/1\/5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,13]]},"references-count":36,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["robotics9010005"],"URL":"https:\/\/doi.org\/10.3390\/robotics9010005","relation":{},"ISSN":["2218-6581"],"issn-type":[{"type":"electronic","value":"2218-6581"}],"subject":[],"published":{"date-parts":[[2020,1,13]]}}}