{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,4]],"date-time":"2024-08-04T14:02:24Z","timestamp":1722780144494},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2009,3,9]],"date-time":"2009-03-09T00:00:00Z","timestamp":1236556800000},"content-version":"unspecified","delay-in-days":5303,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[1994,9]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>This paper presents an algorithm that solves the inverse kinematics problem of all six degrees of freedom manipulators, \u201cgeneral\u201d or \u201cspecial\u201d. A manipulator is represented by a chain of characters that symbolizes the position of prismatic and revolute joints in the manipulator and the special geometry that may exist between its joint axes. One form of the loop closure equation is chosen and the Raghavan and Roth method is used to obtain symbolically a square matrix. The determinant of this matrix yields the characteristic polynomial of the manipulator in one of the kinematic variables. As an example of the use of this algorithm we present the solution to the inverse kinematics problem of the <jats:bold>GMF Arc<\/jats:bold> Mate welding manipulator. In spite of its geometry, this industrial manipulator has a non-trivial solution to its inverse kinematics problem.<\/jats:p>","DOI":"10.1017\/s0263574700017975","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T09:13:24Z","timestamp":1236676404000},"page":"421-430","source":"Crossref","is-referenced-by-count":19,"title":["Inverse kinematics of six-degree of freedom \u201cgeneral\u201d and \u201cspecial\u201d manipulators using symbolic computation"],"prefix":"10.1017","volume":"12","author":[{"given":"C.","family":"Mavroidis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F. B.","family":"Ouezdou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Bidaud","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,3,9]]},"reference":[{"key":"S0263574700017975_ref016","unstructured":"Design of Solvable 6R Manipulators (Ph.D. Thesis, Georgia, Institute of Technology, 1990)."},{"key":"S0263574700017975_ref015","unstructured":"15. Peiper D.L. and Roth B. The Kinematics of Manipulators under computer Control\u201d Proceedings of the 2nd International Congress for the Theory of Machines and Mechanisms, Zakopane, Poland (1969) pp. 159\u2013160,"},{"key":"S0263574700017975_ref017","unstructured":"16. Smith D.R. , Design of Solvable 6R Manipulators (Ph.D. Thesis, Georgia, Institute of Technology, 1990)."},{"key":"S0263574700017975_ref004","doi-asserted-by":"publisher","DOI":"10.1115\/1.3258791"},{"key":"S0263574700017975_ref021","volume-title":"R\u00e9solution du probl\u00e8me g\u00e9ometrique inverse pour les manipulateurs s\u00e9rie \u00e0 6 degr\u00e9s de libert\u00e9","author":"Mavroidis","year":"1993"},{"key":"S0263574700017975_ref019","doi-asserted-by":"publisher","DOI":"10.1016\/0921-8890(91)90026-H"},{"key":"S0263574700017975_ref013","first-page":"619","article-title":"Inverse Kinematics of General 6R and 5R, P serial manipulators","volume":"47","author":"Kohlli","year":"1992","journal-title":"Flexible Mechanisms, Dynamics and Analysis, ASME DE"},{"key":"S0263574700017975_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(88)90107-3"},{"key":"S0263574700017975_ref003","doi-asserted-by":"publisher","DOI":"10.1177\/027836498500400203"},{"key":"S0263574700017975_ref014","first-page":"129\u2013137","article-title":"Inverse Kinematics of General 4R2P, 3R3P, 4R1C, 2R2C, and 3C serial manipulators","volume":"45","author":"Kohli","year":"1992","journal-title":"Spatial Mechanisms, and Mechanical Systems, ASME DE"},{"key":"S0263574700017975_ref018","first-page":"359\u2013366","article-title":"Structural Parameters which Reduce the Number of Manipulators Configurations","volume":"45","author":"Mavroidis","year":"1992","journal-title":"Robotics, Spatial Mechanisms, and Mechanical Systems, ASME DE"},{"key":"S0263574700017975_ref020","unstructured":"19. Rieseler H. and Wahl F.M. , \u201cFast Symbolic Computation of the Inverse Kinematics of Robots\u201d Proceedings of the 1990 IEEE Conference on Robotics and Automation, San Diego (1990) pp. 462\u2013467."},{"key":"S0263574700017975_ref011","unstructured":"11. Raghavan M. and Roth B. , \u201cInverse Kinematics of the General 6R Manipulator and Related Linkages\u201d Proceedings of the ASME, Design Technical Conference, Chicago, Illinois, DE 25, 59\u201365 (1992)."},{"key":"S0263574700017975_ref005","doi-asserted-by":"publisher","DOI":"10.1115\/1.3258708"},{"key":"S0263574700017975_ref009","first-page":"263","volume-title":"Proceedings of the 5th International Symposium on Robotics Research","author":"Raghavan","year":"1990"},{"key":"S0263574700017975_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574700005476"},{"key":"S0263574700017975_ref002","unstructured":"2. Pieper D.L. , The kinematics of Manipulators under Computer Control (Ph.D. thesis, Stanford University 1968)."},{"key":"S0263574700017975_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(87)90070-X"},{"key":"S0263574700017975_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(88)90106-1"},{"key":"S0263574700017975_ref010","unstructured":"10. Raghavan M. and Roth B. , \u201cA General Solution for the Inverse Kinematics of all Series Chains\u201d Proceedings of the 8th CISM-IFToMM Symposium on Robots and Manipulators (Romansy 90), Cracow, Poland (1990) pp. 24\u201331."},{"key":"S0263574700017975_ref012","unstructured":"12. Manocha D. and Canney J.F. , \u201cReal Time Inverse Kinematics for General 6R Manipulators\u201d Proceedings of the 1992 IEEE International Conference on Robotics and Automation,Nice,France (1992) pp. 383\u2013388."}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574700017975","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T22:54:08Z","timestamp":1557874448000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574700017975\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,9]]},"references-count":21,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1994,9]]}},"alternative-id":["S0263574700017975"],"URL":"https:\/\/doi.org\/10.1017\/s0263574700017975","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,9]]}}}