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A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann\u2013Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.<\/jats:p>","DOI":"10.1017\/s0263574715000661","type":"journal-article","created":{"date-parts":[[2015,8,17]],"date-time":"2015-08-17T08:00:44Z","timestamp":1439798444000},"page":"511-520","source":"Crossref","is-referenced-by-count":9,"title":["A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann\u2013Cayley algebra"],"prefix":"10.1017","volume":"35","author":[{"given":"Kefei","family":"Wen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"TaeWon","family":"Seo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeh Won","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2015,8,17]]},"reference":[{"key":"S0263574715000661_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2006.07.006"},{"key":"S0263574715000661_ref21","volume-title":"Advanced Spatial Mechanism","author":"Huang","year":"2006"},{"key":"S0263574715000661_ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2009.2017132"},{"key":"S0263574715000661_ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TRA.2004.824644"},{"key":"S0263574715000661_ref12","doi-asserted-by":"crossref","unstructured":"A. Degani and A. Wolf , \u201cGraphical Singularity Analysis of Planar Parallel Manipulators,\u201d Proceedings of the 2006 IEEE International Conference on Robotics and Automation, Orlando, Florida (May, 2006).","DOI":"10.1109\/ROBOT.2006.1641800"},{"key":"S0263574715000661_ref6","doi-asserted-by":"publisher","DOI":"10.1115\/1.2988472"},{"key":"S0263574715000661_ref25","doi-asserted-by":"publisher","DOI":"10.1177\/0278364908095918"},{"key":"S0263574715000661_ref23","doi-asserted-by":"publisher","DOI":"10.1109\/TRA.2004.824644"},{"key":"S0263574715000661_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s12541-013-0185-9"},{"key":"S0263574715000661_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2011.11.015"},{"key":"S0263574715000661_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0094-114X(03)00105-8"},{"key":"S0263574715000661_ref28","unstructured":"N. L. White and T. McMillan , Cayley Factorization, IMA Preprint Series # 371, University of Minenesota, 206 Church St, S.E., Minneapolis, MN, USA (1987)."},{"key":"S0263574715000661_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-28247-5_19"},{"key":"S0263574715000661_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2006.03.008"},{"key":"S0263574715000661_ref27","first-page":"419","article-title":"The bracket of 2-extensors","volume":"40","author":"White","year":"1983","journal-title":"Congressus Numerantium"},{"key":"S0263574715000661_ref1","doi-asserted-by":"publisher","DOI":"10.1115\/1.3258540"},{"key":"S0263574715000661_ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2006.878958"},{"key":"S0263574715000661_ref4","unstructured":"Y. H. Chung , J. H. Choo and J. W. Lee , \u201cSenSation: A New 2-DOF Parallel Mechanism for Haptic Device,\u201d Proceedings 2nd Workshop on Computational Kinematics, Seoul, South Korea (May 20\u201322, 2001) pp. 45\u201356."},{"key":"S0263574715000661_ref8","doi-asserted-by":"publisher","DOI":"10.1109\/70.56660"},{"key":"S0263574715000661_ref13","doi-asserted-by":"publisher","DOI":"10.1177\/027836402760475342"},{"key":"S0263574715000661_ref15","doi-asserted-by":"publisher","DOI":"10.1115\/1.4004123"},{"key":"S0263574715000661_ref2","volume-title":"Parallel Robot","author":"Merlet","year":"2006"},{"key":"S0263574715000661_ref24","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1974533185"},{"key":"S0263574715000661_ref14","article-title":"Type synthesis of 3-DOF spherical parallel manipulators based on screw theory","volume":"126","author":"Kong","year":"2004","journal-title":"J. Mech. Des."},{"key":"S0263574715000661_ref5","doi-asserted-by":"crossref","unstructured":"G. F. Liu , Y. L. Wu , X. Z. Wu , Y. Y. Kuen and Z. X. Li , \u201cAnalysis and Control of Redundant Parallel Manipulators,\u201d Proceedings of the 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea (May 21\u201326, 2001).","DOI":"10.1109\/ROBOT.2001.933201"},{"key":"S0263574715000661_ref9","doi-asserted-by":"publisher","DOI":"10.1115\/1.1582878"},{"key":"S0263574715000661_ref10","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198562450.001.0001","volume-title":"Robots and Screw Theory","author":"Davidson","year":"2004"},{"key":"S0263574715000661_ref3","doi-asserted-by":"crossref","unstructured":"A. K. Dash , I. Chen , S. H. Yeo and G. Yang , \u201cSingularity-Free path Planning of Parallel Manipulators using Clustering Algorithm and Line Geometry,\u201d Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan (Sept. 14\u201319, 2003).","DOI":"10.1109\/ROBOT.2003.1241685"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574715000661","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T15:28:46Z","timestamp":1718033326000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574715000661\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,17]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,3]]}},"alternative-id":["S0263574715000661"],"URL":"https:\/\/doi.org\/10.1017\/s0263574715000661","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,8,17]]}}}