{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T12:33:42Z","timestamp":1770899622863,"version":"3.50.1"},"reference-count":52,"publisher":"Cambridge University Press (CUP)","issue":"12","license":[{"start":{"date-parts":[[2017,1,31]],"date-time":"2017-01-31T00:00:00Z","timestamp":1485820800000},"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":[[2017,12]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>In this paper, we study the kinematic effects of number of legs in 6-DOF UPS parallel manipulators. A group of 3-, 4-, and 6-legged mechanisms are evaluated in terms of the kinematic performance indices, workspace, singular configurations, and forward kinematic solutions. Results show that the optimum number of legs varies due to priorities in kinematic measures in different applications. The non-symmetric Wide-Open mechanism enjoys the largest workspace, while the well-known Gough\u2013Stewart (3\u20133) platform retains the highest dexterity. Especially, the redundantly actuated 4-legged mechanism has several important advantages over its non-redundant counterparts and different architectures of Gough\u2013Stewart platform. It has dramatically less singular configurations, a higher manipulability, and at the same time less sensitivity. It is also shown that the forward kinematic problem has 40, 16, and 1 solution(s), respectively for the 6-, 3-, and the 4-legged mechanisms. Superior capabilities of the 4-legged mechanism make it a perfect candidate to be used in more challenging 6-DOF applications in assembly, manufacturing, biomedical, and space technologies.<\/jats:p>","DOI":"10.1017\/s0263574716000862","type":"journal-article","created":{"date-parts":[[2017,1,31]],"date-time":"2017-01-31T08:15:29Z","timestamp":1485850529000},"page":"2257-2277","source":"Crossref","is-referenced-by-count":13,"title":["Kinematic effects of number of legs in 6-DOF UPS parallel mechanisms"],"prefix":"10.1017","volume":"35","author":[{"given":"Mohammad H.","family":"Abedinnasab","sequence":"first","affiliation":[]},{"given":"Farzam","family":"Farahmand","sequence":"additional","affiliation":[]},{"given":"Bahram","family":"Tarvirdizadeh","sequence":"additional","affiliation":[]},{"given":"Hassan","family":"Zohoor","sequence":"additional","affiliation":[]},{"given":"Jaime","family":"Gallardo-Alvarado","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2017,1,31]]},"reference":[{"key":"S0263574716000862_ref49","doi-asserted-by":"publisher","DOI":"10.1002\/rcs.2"},{"key":"S0263574716000862_ref19","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026440021125"},{"key":"S0263574716000862_ref22","unstructured":"O. Aghababai , Design, Kinematic and Dynamic Analysis and Optimization of a 6 DOF Redundantly Actuated Parallel Mechanism for Use in Haptic Systems MSc Thesis (Tehran, Iran: Sharif University of Technology, 2005)."},{"key":"S0263574716000862_ref17","doi-asserted-by":"publisher","DOI":"10.1115\/1.1641189"},{"key":"S0263574716000862_ref14","doi-asserted-by":"crossref","unstructured":"S. Shayya , S. Krut , O. Company , C. Baradat and F. Pierrot , \u201cA Novel 4 dofs (3t-1r) Parallel Manipulator with Actuation Redundancy\u2013Workspace Analysis,\u201d In MeTrApp'2013: 2nd Conference on Mechanisms, Transmissions and Applications, vol. 17, no. Mechanisms and Machine Science (Bilbao, Spain, October 2\u20134, 2013), pp. 317\u2013324.","DOI":"10.1007\/978-94-007-7485-8_39"},{"key":"S0263574716000862_ref52","volume-title":"Robotic Applications in Neurosurgery","author":"Eljamel","year":"2008"},{"key":"S0263574716000862_ref12","doi-asserted-by":"crossref","unstructured":"T. Ropponen and Y. Nakamura , \u201cSingularity-Free Parameterization and Performance Analysis of Actuation Redundancy,\u201d Proceedings of the IEEE International Conference on Robotics and Automation, vol. 2, Cincinnati, Ohio, USA, (1990) pp. 806\u2013811.","DOI":"10.1109\/ROBOT.1990.126087"},{"key":"S0263574716000862_ref39","doi-asserted-by":"publisher","DOI":"10.1108\/01439910510582309"},{"key":"S0263574716000862_ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2016.2516025"},{"key":"S0263574716000862_ref33","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9064-8_33"},{"key":"S0263574716000862_ref26","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1109\/TRO.2004.835456","article-title":"Generalized stewart-gough platforms and their direct kinematics","volume":"21","author":"Gao","year":"2005","journal-title":"IEEE Trans. Robot."},{"key":"S0263574716000862_ref31","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574709005359"},{"key":"S0263574716000862_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.rcim.2014.04.004"},{"key":"S0263574716000862_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/S0094-114X(02)00044-7"},{"key":"S0263574716000862_ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechatronics.2015.06.003"},{"key":"S0263574716000862_ref51","doi-asserted-by":"publisher","DOI":"10.1227\/01.NEU.0000153929.68024.CF"},{"key":"S0263574716000862_ref50","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.amjsurg.2004.08.004","article-title":"Robotics in neurosurgery","volume":"188","author":"Mc","year":"2004","journal-title":"Am. J. Surg."},{"key":"S0263574716000862_ref40","doi-asserted-by":"crossref","unstructured":"M. Tavakoli , A. Marjovi , L. Marques and A. T. De Almeida , \u201c3dclimber: A Climbing Robot for Inspection of 3d Human Made Structures,\u201d Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, IROS, Nice, France (2008) pp. 4130\u20134135.","DOI":"10.1109\/IROS.2008.4651024"},{"key":"S0263574716000862_ref3","doi-asserted-by":"publisher","DOI":"10.1243\/PIME_PROC_1965_180_029_02"},{"key":"S0263574716000862_ref16","unstructured":"B.-J. Yi , R. A. Freeman and D. Tesar , \u201cOpen-Loop Stiffness Control of Overconstrained MechanismsRrobotic Linkage Systems,\u201d Proceedings of the IEEE International Conference on Robotics and Automation, vol. 3, Scottsdale, Arizona, USA (1989) pp. 1340\u20131345."},{"key":"S0263574716000862_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(95)00068-A"},{"key":"S0263574716000862_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s11633-013-0753-6"},{"key":"S0263574716000862_ref46","doi-asserted-by":"crossref","unstructured":"A. Baghani , M. N. Ahmadabadi and A. Harati , \u201cKinematics Modeling of a Wheel-Based Pole Climbing Robot (ut-pcr),\u201d Proceedings of the 2005 IEEE International Conference on Robotics and Automation, ICRA, Barcelona, Spain (2005), pp. 2099\u20132104.","DOI":"10.1109\/ROBOT.2005.1570423"},{"key":"S0263574716000862_ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2004.842341"},{"key":"S0263574716000862_ref27","doi-asserted-by":"publisher","DOI":"10.1163\/156855308X292556"},{"key":"S0263574716000862_ref48","doi-asserted-by":"publisher","DOI":"10.1016\/S0921-8890(02)00360-3"},{"key":"S0263574716000862_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2013.09.006"},{"key":"S0263574716000862_ref32","volume-title":"Robot Analysis: The Mechanics of Serial and Parallel Manipulators","author":"Tsai","year":"1999"},{"key":"S0263574716000862_ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.rcim.2010.09.004"},{"key":"S0263574716000862_ref43","doi-asserted-by":"crossref","unstructured":"J. E. Clark , J. G. Cham , S. Bailey , E. M. Froehlich , P. K. Nahata , R. J. Full , M. R. Cutkosky , \u201cBiomimetic Design and Fabrication of a Hexapedal Running Robot,\u201d Proceedings of the IEEE International Conference on Robotics and Automation, ICRA, vol. 4, Seoul, South Korea (2001) pp. 3643\u20133649.","DOI":"10.1109\/ROBOT.2001.933183"},{"key":"S0263574716000862_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2013.03.001"},{"key":"S0263574716000862_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574710000330"},{"key":"S0263574716000862_ref28","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574711000129"},{"key":"S0263574716000862_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2005.10.012"},{"key":"S0263574716000862_ref38","doi-asserted-by":"publisher","DOI":"10.1115\/1.2912772"},{"key":"S0263574716000862_ref11","unstructured":"B.-J. Yi , D. Cox and D. Tesar , \u201cAnalysis and Design Criteria for a Redundantly Actuated 4-Legged Six Degree-of-Freedom Parallel Manipulator,\u201d Proceedings of the IEEE International Conference on Robotics and Automation, ICRA, vol. 4, Seoul, South Korea, IEEE (2001) pp. 3286\u20133293."},{"key":"S0263574716000862_ref21","doi-asserted-by":"crossref","unstructured":"Mohammad H. Abedinnasab , Yong-Jin Yoon and Hassan Zohoor (2012). \u201cExploiting Higher Kinematic Performance - Using a 4-Legged Redundant PM Rather than Gough-Stewart Platforms,\u201d in Serial and Parallel Robot Manipulators - Kinematics, Dynamics, Control and Optimization, Dr. Serdar Kucuk (Ed.), InTech, DOI: 10.5772\/32141.","DOI":"10.5772\/32141"},{"key":"S0263574716000862_ref35","doi-asserted-by":"publisher","DOI":"10.1177\/027836499201100605"},{"key":"S0263574716000862_ref47","doi-asserted-by":"publisher","DOI":"10.1109\/TRA.2003.810238"},{"key":"S0263574716000862_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-009-9504-1"},{"key":"S0263574716000862_ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2009.2037252"},{"key":"S0263574716000862_ref41","doi-asserted-by":"publisher","DOI":"10.1108\/01439911011037721"},{"key":"S0263574716000862_ref44","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1109\/TRO.2007.909786","article-title":"Smooth vertical surface climbing with directional adhesion","volume":"24","author":"Kim","year":"2008","journal-title":"IEEE Trans. Robot."},{"key":"S0263574716000862_ref2","unstructured":"V. E. Gough and S. G. Whitehall , \u201cUniversal Tyre Test Machine,\u201d Proceedings of the 9th International Technical Congress FISITA, Birmingham, England (1962) pp. 117\u2013137."},{"key":"S0263574716000862_ref4","doi-asserted-by":"publisher","DOI":"10.4236\/mme.2012.23008"},{"key":"S0263574716000862_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s11465-012-0321-8"},{"key":"S0263574716000862_ref5","doi-asserted-by":"publisher","DOI":"10.1109\/70.56660"},{"key":"S0263574716000862_ref45","doi-asserted-by":"publisher","DOI":"10.1002\/rob.20238"},{"key":"S0263574716000862_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.rcim.2013.09.001"},{"key":"S0263574716000862_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(94)00069-W"},{"key":"S0263574716000862_ref36","doi-asserted-by":"publisher","DOI":"10.1016\/0921-8890(92)90039-2"},{"key":"S0263574716000862_ref29","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574709990749"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574716000862","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T18:58:26Z","timestamp":1555441106000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574716000862\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,31]]},"references-count":52,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["S0263574716000862"],"URL":"https:\/\/doi.org\/10.1017\/s0263574716000862","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1,31]]}}}