{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T15:29:00Z","timestamp":1758814140132},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2007,11,1]],"date-time":"2007-11-01T00:00:00Z","timestamp":1193875200000},"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":[[2007,11]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>This paper investigates the singular curves in the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a nonsingular change of assembly mode. The purpose of this study is twofold. First, it exposes a method to compute joint space singular curves of 3-<jats:italic>R<jats:underline>P<\/jats:underline>R<\/jats:italic> planar parallel manipulators. Second, it presents an algorithm for detecting and computing all cusp points in the joint space of these same manipulators.<\/jats:p>","DOI":"10.1017\/s0263574707003785","type":"journal-article","created":{"date-parts":[[2007,9,10]],"date-time":"2007-09-10T05:55:36Z","timestamp":1189403736000},"page":"717-724","source":"Crossref","is-referenced-by-count":21,"title":["Singular curves in the joint space and cusp points of 3-<i>R<u>P<\/u>R<\/i> parallel manipulators"],"prefix":"10.1017","volume":"25","author":[{"given":"Mazen","family":"Zein","sequence":"first","affiliation":[]},{"given":"Philippe","family":"Wenger","sequence":"additional","affiliation":[]},{"given":"Damien","family":"Chablat","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2007,11,1]]},"reference":[{"key":"S0263574707003785_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(94)00052-M"},{"key":"S0263574707003785_ref12","unstructured":"12. Wenger Ph. , \u201cA New General Formalism for the Kinematic Analysis for all Non-Redundant Manipulators,\u201d Proceeding International Conference on Robotics and Automation, Nice, France (1992) pp. 442\u2013447."},{"key":"S0263574707003785_ref8","doi-asserted-by":"publisher","DOI":"10.1115\/1.2826971"},{"key":"S0263574707003785_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-9587-7"},{"key":"S0263574707003785_ref6","doi-asserted-by":"publisher","DOI":"10.1115\/1.1582878"},{"key":"S0263574707003785_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-3406-1"},{"key":"S0263574707003785_ref19","doi-asserted-by":"crossref","unstructured":"19. Baili M. , Wenger P. and Chablat D. , \u201cA Classification of 3R Orthogonal Manipulators by the Topology of Their Workspace,\u201d Proceedings of the IEEE International Conference on Robotics and Automation, Louisiana (2004) pp. 1933\u20131938.","DOI":"10.1109\/ROBOT.2004.1308106"},{"key":"S0263574707003785_ref17","volume-title":"Geometry of Mechanisms","author":"Hunt","year":"1978"},{"key":"S0263574707003785_ref11","doi-asserted-by":"crossref","unstructured":"11. Burdick J. W. , \u201cA Classification of 3R regional manipulator Singularities and Geometries,\u201d Proceedings of the IEEE International Conference on Robotics and Automation, Sacramento, California (1991) pp. 2670\u20132675.","DOI":"10.1109\/ROBOT.1991.132033"},{"key":"S0263574707003785_ref2","doi-asserted-by":"publisher","DOI":"10.1109\/70.56660"},{"key":"S0263574707003785_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(92)90001-X"},{"key":"S0263574707003785_ref5","doi-asserted-by":"crossref","unstructured":"5. 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El Omri J. and Wenger P. , \u201cHow to Recognize Simply a Non-Singular Posture Changing 3-DOF Manipulator,\u201d Proceedings of the 7th International Conference on Advanced Robotics (1995) pp. 215\u2013222."},{"key":"S0263574707003785_ref14","doi-asserted-by":"crossref","unstructured":"14. Ottaviano E. , Husty M. and Ceccarelli M. , \u201cA Cartesian Representation for the Boundary Workspace of 3R Manipulators,\u201d Proceedings on Advances on Robots Kinematics (2004) pp. 247\u2013254.","DOI":"10.1007\/978-1-4020-2249-4_27"},{"key":"S0263574707003785_ref16","doi-asserted-by":"crossref","unstructured":"16. Zein M. , Wenger Ph. and Chablat D. , \u201cSingular Curves and Cusp Points in the Joint Space of 3-RPR Parallel Manipulators,\u201d Proceedings of the 2006 IEEE International Conference on Robotics and Automation, Orlando, Florida (May 2006) pp. 776\u2013782.","DOI":"10.1109\/ROBOT.2006.1641804"},{"key":"S0263574707003785_ref9","doi-asserted-by":"publisher","DOI":"10.1177\/02783649922066394"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574707003785","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,6]],"date-time":"2019-04-06T15:28:20Z","timestamp":1554564500000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574707003785\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11]]},"references-count":19,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2007,11]]}},"alternative-id":["S0263574707003785"],"URL":"https:\/\/doi.org\/10.1017\/s0263574707003785","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11]]}}}