{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T12:38:13Z","timestamp":1762605493753},"reference-count":55,"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 article synthezises the most important results on the kinematics of cuspidal manipulators i.e. nonredundant manipulators that can change posture without meeting a singularity. The characteristic surfaces, the uniqueness domains and the regions of feasible paths in the workspace are defined. Then, several sufficient geometric conditions for a manipulator to be noncuspidal are enumerated and a general necessary and sufficient condition for a manipulator to be cuspidal is provided. An explicit DH-parameter-based condition for an orthogonal manipulator to be cuspidal is derived. The full classification of 3R orthogonal manipulators is provided and all types of cuspidal and noncuspidal orthogonal manipulators are enumerated. Finally, some facts about cuspidal and noncuspidal 6R manipulators are reported.<\/jats:p>","DOI":"10.1017\/s0263574707003761","type":"journal-article","created":{"date-parts":[[2007,9,10]],"date-time":"2007-09-10T09:55:46Z","timestamp":1189418146000},"page":"677-689","source":"Crossref","is-referenced-by-count":33,"title":["Cuspidal and noncuspidal robot manipulators"],"prefix":"10.1017","volume":"25","author":[{"given":"Philippe","family":"Wenger","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2007,11,1]]},"reference":[{"key":"S0263574707003761_ref34","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-2249-4_27"},{"key":"S0263574707003761_ref11","doi-asserted-by":"crossref","unstructured":"11. Wenger P. and El Omri J. , \u201cChanging Posture for Cuspidal Robots,\u201d Proceedings of the IEEE International Conference on Robotics and Automation (1996) pp. 3173\u20133178.","DOI":"10.1109\/ROBOT.1996.509195"},{"key":"S0263574707003761_ref16","doi-asserted-by":"publisher","DOI":"10.1109\/70.163780"},{"key":"S0263574707003761_ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2004.829467"},{"key":"S0263574707003761_ref32","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(87)90010-3"},{"key":"S0263574707003761_ref36","first-page":"439","article-title":"Design and optimization of 3R manipulators using the workspace features","volume":"172","author":"Bergamaschi","year":"2006","journal-title":"Appl. Math. Comput."},{"key":"S0263574707003761_ref1","doi-asserted-by":"crossref","unstructured":"1. Borrel P. and Liegeois A. , \u201cA Study of Manipulator Inverse Kinematic Solutions With Application to Trajectory Planning and Workspace Determination,\u201d Proceedings of the IEEE International Conference on Robotics and Automation (1986) pp. 1180\u20131185.","DOI":"10.1109\/ROBOT.1986.1087554"},{"key":"S0263574707003761_ref25","volume-title":"Performance Evaluation of Programmable Robots and Manipulators","author":"Roth","year":"1975"},{"key":"S0263574707003761_ref6","doi-asserted-by":"crossref","unstructured":"6. Smith D. R. and Lipkin H. , \u201cHigher Order Singularities of Regional Manipulators,\u201d Proceedings of the IEEE International Conference on Robotics and Automation, Atlanta, GA (1993) pp. 194\u2013199.","DOI":"10.1109\/ROBOT.1993.291982"},{"key":"S0263574707003761_ref21","unstructured":"21. Ranjbaran F. and Angeles J. , \u201cOn Positioning Singularities of 3-Revolute Robotic Manipulators,\u201d Proceedings of the 12th Symposium on Engineering Applications in Mechanics, Montreal, CA, (1994) pp. 273\u2013282."},{"key":"S0263574707003761_ref5","doi-asserted-by":"publisher","DOI":"10.1115\/1.2919287"},{"key":"S0263574707003761_ref20","doi-asserted-by":"publisher","DOI":"10.1115\/1.1828460"},{"key":"S0263574707003761_ref39","doi-asserted-by":"crossref","unstructured":"39. 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Parenti C.V. and Innocenti C. , \u201cPosition Analysis of Robot Manipulators : Regions and Subregions,\u201d Proceedings of the International Conference on Advances in Robot Kinematics (1988) pp. 150\u2013158."},{"key":"S0263574707003761_ref4","unstructured":"4. Wenger P. , \u201cA New General Formalism for the Kinematic Analysis of All Non-Redundant Manipulators,\u201d Proceedings of the IEEE International Conference on Robotics and Automation (1992) pp. 442\u2013447."},{"key":"S0263574707003761_ref3","unstructured":"3. Burdick J. W. , \u201cKinematic Analysis and Design of Redundant Manipulators\u201d Ph.D. Dissertation (Stanford, CA: Stanford University, 1988)."},{"key":"S0263574707003761_ref49","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511569265.024"},{"key":"S0263574707003761_ref9","unstructured":"9. El Omri J. and Wenger P. , \u201cHow to Recognize Simply a Nonsingular Posture Changing 3-DOF Manipulator,\u201d Proceedings of the 7th International Conference on Advanced Robotics (1995) pp. 215\u2013222."},{"key":"S0263574707003761_ref15","unstructured":"15. Baili M. , Wenger P. and Chablat D. , \u201cClassification of one Family of 3R Positioning Manipulators,\u201d Proceedings of the 11th International Conference on Advanced Robotics (2003) pp. 1849\u20131854."},{"key":"S0263574707003761_ref17","doi-asserted-by":"crossref","unstructured":"17. 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, (2004) pp. 1933\u20131938.","DOI":"10.1109\/ROBOT.2004.1308106"},{"key":"S0263574707003761_ref30","doi-asserted-by":"publisher","DOI":"10.1115\/1.3258710"},{"key":"S0263574707003761_ref40","unstructured":"40. Pieper D. L. , The Kinematics of Manipulators Under Computer Control, Ph.D. Thesis (Stanford, CA: Stanford University, 1968)."},{"key":"S0263574707003761_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-2249-4_24"},{"key":"S0263574707003761_ref22","unstructured":"22. Urbanic A. and Lenarcic J. , \u201cKinematic Considerations on General 3R Manipulators,\u201d Proceedings of the 3rd International Workshop on Robotic in the Alpe-Adria, Slovenia (1994) pp. 293\u2013298."},{"key":"S0263574707003761_ref23","doi-asserted-by":"publisher","DOI":"10.1115\/1.2826117"},{"key":"S0263574707003761_ref26","doi-asserted-by":"publisher","DOI":"10.1115\/1.3254968"},{"key":"S0263574707003761_ref28","first-page":"62","article-title":"On the workspace of mechanical manipulators","volume":"105","author":"Yang","year":"1983","journal-title":"ASME J. Mech. 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Baili M. , \u201cAnalysis and Classification of 3R Orthogonal Manipulators, Ph.D. Thesis (in French) (Nantes, France: Ecole Centrale de Nantes, 2004)."},{"key":"S0263574707003761_ref46","article-title":"New robot improves cost-efficiency of spot welding","volume":"3","author":"Hemmingson","year":"1996","journal-title":"ABB Rev."},{"key":"S0263574707003761_ref47","doi-asserted-by":"crossref","unstructured":"47. Zoppi M. , \u201cEffective Backward Kinematics for an Industrial 6R Robot,\u201d Proceedings of the ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Montreal, Canada, (2002).","DOI":"10.1115\/DETC2002\/MECH-34256"},{"key":"S0263574707003761_ref48","doi-asserted-by":"publisher","DOI":"10.1115\/1.2919373"},{"key":"S0263574707003761_ref50","doi-asserted-by":"publisher","DOI":"10.1115\/1.2826679"},{"key":"S0263574707003761_ref27","doi-asserted-by":"publisher","DOI":"10.1115\/1.3256412"},{"key":"S0263574707003761_ref51","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/978-94-015-9064-8_12","volume-title":"Advances on Robot Kinematics","author":"Wenger","year":"1998"},{"key":"S0263574707003761_ref54","doi-asserted-by":"crossref","unstructured":"54. Kong X. and Gosselin C. M. , \u201cDetermination of the Uniqueness Domains of 3-RPR Planar Parallel Manipulators With Similar Platforms,\u201d Proceedings of the 2000 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Baltimore, MD (2000).","DOI":"10.1115\/DETC2000\/MECH-14094"},{"key":"S0263574707003761_ref55","unstructured":"55. Wenger P. , and Chablat D. , \u201cThe Kinematic Analysis of a Symmetrical Three-Degree-of-Freedom Planar Parallel Manipulator,\u201d Proceedings of the CISM-IFToMM Symposium on Robot Design, Dynamics and Control, Montreal, (2004). pp. 1\u20137."},{"key":"S0263574707003761_ref8","doi-asserted-by":"crossref","unstructured":"8. 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