{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,6]],"date-time":"2025-06-06T14:48:46Z","timestamp":1749221326077,"version":"3.37.0"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,3,9]],"date-time":"2009-03-09T00:00:00Z","timestamp":1236556800000},"content-version":"unspecified","delay-in-days":7464,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[1988,10]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>This paper presents a new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form.<\/jats:p><jats:p>The basic algorithm belongs to the class of customized algorithms that reduce the computational burden by taking into account the specific characteristics of the manipulator to be modelled. The output of the package is high-level computer program code for evaluation of various kinematic and dynamic variables: the homogeneous transformation matrix between the hand and base coordinate frame, Jacobian matrices, driving torques and the elements of dynamic model matrices. The dynamic model is based on the recursive Newton-Euler equations. The application of recursive symbolic relations yields nearly minimal numerical complexity. Further improvement of computational efficiency is achieved by introducing different computational rates for the terms depending on joint angles, velocities and accelerations. A comparative study of numerical complexity for several typical industrial robots is presented.<\/jats:p>","DOI":"10.1017\/s0263574700004677","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T13:21:08Z","timestamp":1236691268000},"page":"311-318","source":"Crossref","is-referenced-by-count":38,"title":["A new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form"],"prefix":"10.1017","volume":"6","author":[{"given":"M.","family":"Kir\u0107anski","sequence":"first","affiliation":[]},{"given":"M.","family":"Vukobratovi\u0107","sequence":"additional","affiliation":[]},{"given":"N.","family":"Kir\u0107anski","sequence":"additional","affiliation":[]},{"given":"A.","family":"Tim\u010denko","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,3,9]]},"reference":[{"key":"S0263574700004677_ref015","doi-asserted-by":"crossref","unstructured":"15. M. Vukobratovi\u0107 & N. Kir\u0107anski, Real-Time Dynamics of Manipulation Robots, Series: Scientific Fundamentals of Robotics, 4 (Springer-Verlag, Berlin, 1985).","DOI":"10.1007\/978-3-642-82198-1"},{"key":"S0263574700004677_ref006","doi-asserted-by":"publisher","DOI":"10.1177\/027836498300200301"},{"key":"S0263574700004677_ref019","doi-asserted-by":"crossref","unstructured":"19. Li C.J. , \u201cA New Method for Dynamic Analysis of Robot\u201d Proc. IEEE Int. Conf. on Robotics and Automation, San Francisco, 227\u2013233 (1986).","DOI":"10.1109\/ROBOT.1986.1087660"},{"key":"S0263574700004677_ref014","doi-asserted-by":"crossref","unstructured":"14. Kanade T. , Khosla P. & Tanaka N. , \u201cReal-Time Control of CMU Direct-Drive Arm II Using Customized Inverse Dynamics\u201d Proc. 23rd CDC, Las Vegas (1984).","DOI":"10.1109\/CDC.1984.272256"},{"volume-title":"Kinematics and Trajectory Synthesis of Manipulation Robots Series: Scientific Fundamentals of Robotics 3","year":"1985","author":"Vukobratovi\u0107","key":"S0263574700004677_ref025"},{"key":"S0263574700004677_ref027","doi-asserted-by":"crossref","unstructured":"27. Kir\u0107anski N. , Kir\u0107anski M. , Vukobratovi\u0107 M. & Tim\u010denko O. , \u201cAn Approach to Development of Real-Time Robot Models\u201d VI IFToMM Symp. on Theory and Practice of Robots and Manipulators, Krakov (1986).","DOI":"10.1007\/978-1-4684-6915-8_62"},{"key":"S0263574700004677_ref013","doi-asserted-by":"crossref","unstructured":"13. Horak D.T. , \u201cA Fast Computational Scheme for Dynamic Control of Manipulators Proc. 1984. American Control Conference, San Francisco, CA (06, 1984).","DOI":"10.23919\/ACC.1984.4788456"},{"key":"S0263574700004677_ref026","doi-asserted-by":"crossref","unstructured":"26. Armstrong B. , Khatib O. & Burdick J. , \u201cThe explicit Dynamic Model and Inertial Parameters of the PUMA 560 Arm\u201dProc. IEEE Int. Conf. on Robotics and Automation, San Francisco, 510\u2013519 (1986).","DOI":"10.1109\/ROBOT.1986.1087644"},{"key":"S0263574700004677_ref001","doi-asserted-by":"publisher","DOI":"10.1115\/1.3149599"},{"key":"S0263574700004677_ref018","article-title":"Computer Assisted Generation of Robot Dynamic Models in Analytical Form","volume":"2","author":"Vukobratovi\u0107","year":"1984","journal-title":"Acta Applicandea Mathematicae"},{"key":"S0263574700004677_ref023","doi-asserted-by":"crossref","unstructured":"23. M. Kir\u0107anski & M. Vukobratovi\u0107, \u201cComputer-Aided Generation of Manipulator Kinematic Models in Symbolic Form\u201d Proc. of 15th ISIR, Tokyo (1985).","DOI":"10.1007\/978-3-642-82198-1_4"},{"volume-title":"Robot Manipulators: Mathematics, Programming, and Control","year":"1981","author":"Paul","key":"S0263574700004677_ref003"},{"key":"S0263574700004677_ref010","doi-asserted-by":"crossref","unstructured":"10. Cesareo G. , Nicolo F. & Nicosia S. , \u201cDYMIR: A Code for Generating Dynamic Model of Robots\u201d Proc. 1st Int. IEEE Conf, on Robotics, Atlanta, GA (03, 1984) pp. 115\u2013120.","DOI":"10.1109\/ROBOT.1984.1087208"},{"key":"S0263574700004677_ref004","doi-asserted-by":"crossref","unstructured":"4. Hollerbach M.J. , \u201cA Recursive Lagrangian Formulation of Manipulator Dynamics and a Comparative Study of Dynamics Formulation Complexity\u201d IEEE Trans. on SMC SMC-10, No. 11, 730\u2013740 (11, 1980).","DOI":"10.1109\/TSMC.1980.4308393"},{"key":"S0263574700004677_ref005","unstructured":"5. Vukobratovi\u0107 M. & Potkonjak V. , \u201cContribution to Automatic Forming of Active Chain Models via Lagrangian Form\u201d ASME J. Appl. Mech. No. 1, 76\u201385 (1979)."},{"key":"S0263574700004677_ref007","unstructured":"7. Kir\u0107anski N. & Vukobratovi\u0107 M. , \u201cComputer Aided Procedure of Forming Robot Motion Equations in Analytical Forms\u201d Proc. VI IFToMM Congress, New Delhi (1983)."},{"key":"S0263574700004677_ref009","doi-asserted-by":"publisher","DOI":"10.1002\/rob.4620020408"},{"key":"S0263574700004677_ref008","unstructured":"8. Aldon M.J. & Legois A. , \u201cComputational Aspects in Robot Dynamics Modeling\u201d Proc. of Advanced Software in Robotics (Elsvier Science Publishers B.V., Liege, Belgium, 05 4\u20136, 1983) pp. 3\u201314."},{"key":"S0263574700004677_ref028","unstructured":"28. Kir\u0107anski N. , Vukobratovi\u0107 M. & Kir\u0107anski M. , \u201cGeneral-purpose software system for computer-aided generator of real-time robot dynamic models\u201d Proc. 7th World IFToMM Congress, Sevilla (1987)."},{"key":"S0263574700004677_ref021","doi-asserted-by":"crossref","unstructured":"[21] Burdick J. , \u201cAn Algorithm for Generation of Efficient Manipulator Dynamic Equations\u201d Proc. IEEE Int. Conf. on Robotics and Automation, San Francisco 212\u2013218 (1986).","DOI":"10.1109\/ROBOT.1986.1087659"},{"key":"S0263574700004677_ref012","unstructured":"12. Renaud M. , \u201cAn Efficient Iterative Analytical Procedure for Obtaining a Robot Manipulator Dynamic Model\u201d Proc. 1st Inter. Symp. of Robotics Research, Bretton Woods, New Hampshire, USA (1983)."},{"key":"S0263574700004677_ref016","doi-asserted-by":"publisher","DOI":"10.1002\/rob.4620020308"},{"key":"S0263574700004677_ref017","first-page":"561","article-title":"Une modelisation performante pour la commande dynamique de robots","volume":"6","author":"Khalil","year":"1985","journal-title":"RAIRO"},{"key":"S0263574700004677_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(73)90071-0"},{"key":"S0263574700004677_ref020","doi-asserted-by":"crossref","unstructured":"20. Izaguirre A. & Paul R. , \u201cAutomatic Generation of the Dynamic Equations of the Robot Manipulators Using a LISP Program\u201d Proc IEEE Int. Conf. on Robotics and Automation, San Francisco, 220\u2013227 (1986).","DOI":"10.1109\/ROBOT.1986.1087703"},{"key":"S0263574700004677_ref022","doi-asserted-by":"crossref","unstructured":"22. Khalil W. , Kleinfinger J.F. & Gautier M. , \u201cReducing the Computational Burden of the Dynamic Models of Robots\u201d Proc. IEEE Int. Conf. on Robotics and Automation, San Francisco, 525\u2013532 (1986).","DOI":"10.1109\/ROBOT.1986.1087680"},{"key":"S0263574700004677_ref024","unstructured":"24. M. Kir\u0107anski & M. Vukobratovi\u0107, \u201cA New Program Package for Generating Symbolic Kinematic Models of Arbitrary Serial-Link Manipulators\u201d 16th ISIR, Proceedings, 249\u2013259 (1986)."},{"key":"S0263574700004677_ref011","unstructured":"11. Murray J.J. & Neuman P.Ch. , \u201cComputational Dynamic Robot Modeling\u201d Proc. 27th Midwest Symp., on Circuits and Systems, Morgantown, WV (1984) pp. 479\u2013481."}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574700004677","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T04:57:31Z","timestamp":1738990651000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574700004677\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,10]]},"references-count":28,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1988,10]]}},"alternative-id":["S0263574700004677"],"URL":"https:\/\/doi.org\/10.1017\/s0263574700004677","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"type":"print","value":"0263-5747"},{"type":"electronic","value":"1469-8668"}],"subject":[],"published":{"date-parts":[[1988,10]]}}}