{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T06:01:36Z","timestamp":1771912896926,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,3,5]],"date-time":"2018-03-05T00:00:00Z","timestamp":1520208000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51375230"],"award-info":[{"award-number":["51375230"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51575256"],"award-info":[{"award-number":["51575256"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Intell Robot Syst"],"published-print":{"date-parts":[[2019,4]]},"DOI":"10.1007\/s10846-018-0800-1","type":"journal-article","created":{"date-parts":[[2018,3,5]],"date-time":"2018-03-05T06:35:55Z","timestamp":1520231755000},"page":"101-113","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Computationally Efficient Inverse Dynamics of a Class of Six-DOF Parallel Robots: Dual Quaternion Approach"],"prefix":"10.1007","volume":"94","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6193-2926","authenticated-orcid":false,"given":"XiaoLong","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"HongTao","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yao","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ShengZheng","family":"Kang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bai","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,5]]},"reference":[{"key":"800_CR1","unstructured":"Gough, V.: Contribution to discussion of papers on research in automobile stability, control and tyre performance. Proc. Auto Div. Inst. Mech. Eng. 171, 392\u2013394 (1956)"},{"key":"800_CR2","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1115\/1.3258540","volume":"105","author":"K Hunt","year":"1983","unstructured":"Hunt, K.: Structural kinematics of in-parallel-actuated robot-arms. J. Mech. Transmissions Autom. Design 105, 705\u2013712 (1983)","journal-title":"J. Mech. Transmissions Autom. Design"},{"key":"800_CR3","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/0094-114X(91)90023-W","volume":"26","author":"J-P Merlet","year":"1991","unstructured":"Merlet, J.-P., Gosselin, C.: Nouvelle architecture pour un manipulateur parall\u00e8le \u00e0 six degr\u00e9s de libert\u00e9. Mecha. Mach. Theor. 26, 77\u201390 (1991)","journal-title":"Mecha. Mach. Theor."},{"key":"800_CR4","unstructured":"Merlet, J.-P.: Parallel Robots. Springer Science & Business Media (2006)"},{"key":"800_CR5","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1016\/j.mechmachtheory.2017.07.017","volume":"117","author":"X Yang","year":"2017","unstructured":"Yang, X., Wu, H., Li, Y., Chen, B.: Dynamic isotropic design and decentralized active control of a six-axis vibration isolator via Stewart platform. Mecha. Mach. Theor. 117, 244\u2013252 (2017)","journal-title":"Mecha. Mach. Theor."},{"key":"800_CR6","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1109\/TMECH.2013.2296154","volume":"20","author":"JE McInroy","year":"2015","unstructured":"McInroy, J.E., O\u2019Brien, J.F., Allais, A.A.: Designing micromanipulation systems for decoupled dynamics and control. IEEE\/ASME Trans. Mechatron. 20, 553\u2013563 (2015)","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"800_CR7","doi-asserted-by":"publisher","first-page":"021001","DOI":"10.1115\/1.4005036","volume":"134","author":"Y Yun","year":"2012","unstructured":"Yun, Y., Li, Y.: Modeling and control analysis of a 3-PUPU dual compliant parallel manipulator for micro positioning and active vibration isolation. J. Dyn. Syst. Meas. Control 134, 021001 (2012)","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"800_CR8","doi-asserted-by":"crossref","unstructured":"McInroy, J.E., O\u2019Brien, J.F., Allais, A.A.: Designing Dynamics and Control of Isotropic Gough-Stewart Micromanipulators 2013 IEEE International Conference on Robotics and Automation (ICRA), pp. 1458\u20131464. IEEE (2013)","DOI":"10.1109\/ICRA.2013.6630763"},{"key":"800_CR9","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1016\/S0094-114X(97)00118-3","volume":"33","author":"B Dasgupta","year":"1998","unstructured":"Dasgupta, B., Mruthyunjaya, T.: A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator. Mecha. Mach. Theor. 33, 1135\u20131152 (1998)","journal-title":"Mecha. Mach. Theor."},{"key":"800_CR10","doi-asserted-by":"publisher","first-page":"993","DOI":"10.1016\/S0094-114X(97)00087-6","volume":"33","author":"B Dasgupta","year":"1998","unstructured":"Dasgupta, B., Mruthyunjaya, T.: Closed-form dynamic equations of the general Stewart platform through the Newton\u2013Euler approach. Mecha. Mach. Theor. 33, 993\u20131012 (1998)","journal-title":"Mecha. Mach. Theor."},{"key":"800_CR11","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1016\/j.jsv.2007.05.036","volume":"307","author":"P Mukherjee","year":"2007","unstructured":"Mukherjee, P., Dasgupta, B., Mallik, A.: Dynamic stability index and vibration analysis of a flexible Stewart platform. J. Sound Vibrat. 307, 495\u2013512 (2007)","journal-title":"J. Sound Vibrat."},{"key":"800_CR12","doi-asserted-by":"publisher","first-page":"1119","DOI":"10.1016\/j.mechmachtheory.2006.09.004","volume":"42","author":"J Wang","year":"2007","unstructured":"Wang, J., Wu, J., Wang, L., Li, T.: Simplified strategy of the dynamic model of a 6-UPS parallel kinematic machine for real-time control. Mecha. Mach. Theor. 42, 1119\u20131140 (2007)","journal-title":"Mecha. Mach. Theor."},{"key":"800_CR13","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1177\/0954405412463132","volume":"227","author":"H Hajimirzaalian","year":"2013","unstructured":"Hajimirzaalian, H., Ferraresi, C., Moosavi, H., Massah, M.: An analytical method for the inverse dynamic analysis of the Stewart platform with asymmetric-adjustable payload. Proc. Inst. Mecha. Eng. Part K: J. Multi-Body Dyn. 227, 162\u2013171 (2013)","journal-title":"Proc. Inst. Mecha. Eng. Part K: J. Multi-Body Dyn."},{"key":"800_CR14","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1016\/j.mechmachtheory.2012.02.002","volume":"52","author":"T Do Thanh","year":"2012","unstructured":"Do Thanh, T., Kotlarski, J., Heimann, B., Ortmaier, T.: Dynamics identification of kinematically redundant parallel robots using the direct search method. Mecha. Mach. Theor. 52, 277\u2013295 (2012)","journal-title":"Mecha. Mach. Theor."},{"key":"800_CR15","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1016\/j.mechmachtheory.2008.02.003","volume":"44","author":"H Abdellatif","year":"2009","unstructured":"Abdellatif, H., Heimann, B.: Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism. Mecha. Mach. Theor. 44, 192\u2013207 (2009)","journal-title":"Mecha. Mach. Theor."},{"key":"800_CR16","doi-asserted-by":"publisher","first-page":"2393","DOI":"10.1007\/s11071-015-2489-z","volume":"83","author":"H Kalani","year":"2016","unstructured":"Kalani, H., Rezaei, A., Akbarzadeh, A.: Improved general solution for the dynamic modeling of Gough\u2013Stewart platform based on principle of virtual work. Nonlinear Dyn. 83, 2393\u20132418 (2016)","journal-title":"Nonlinear Dyn."},{"key":"800_CR17","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/s11044-011-9281-8","volume":"27","author":"S Staicu","year":"2012","unstructured":"Staicu, S.: Matrix modeling of inverse dynamics of spatial and planar parallel robots. Multibody Syst. Dyn. 27, 239\u2013265 (2012)","journal-title":"Multibody Syst. Dyn."},{"key":"800_CR18","doi-asserted-by":"publisher","first-page":"1031","DOI":"10.1007\/s11071-011-0045-z","volume":"67","author":"Y Li","year":"2012","unstructured":"Li, Y., Staicu, S.: Inverse dynamics of a 3-PRC parallel kinematic machine. Nonlinear Dyn. 67, 1031\u20131041 (2012)","journal-title":"Nonlinear Dyn."},{"key":"800_CR19","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1016\/j.rcim.2010.07.011","volume":"27","author":"S Staicu","year":"2011","unstructured":"Staicu, S.: Dynamics of the 6-6 Stewart parallel manipulator. Robot. Comput.-Integra. Manuf. 27, 212\u2013220 (2011)","journal-title":"Robot. Comput.-Integra. Manuf."},{"key":"800_CR20","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10846-010-9469-9","volume":"63","author":"A Akbarzadeh","year":"2011","unstructured":"Akbarzadeh, A., Enferadi, J.: A virtual work based algorithm for solving direct dynamics problem of a 3-RRP spherical parallel manipulator. J. Intell. Robot. Syst. 63, 25\u201349 (2011)","journal-title":"J. Intell. Robot. Syst."},{"key":"800_CR21","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/s11071-010-9659-9","volume":"61","author":"J Enferadi","year":"2010","unstructured":"Enferadi, J., Akbarzadeh Tootoonchi, A.: Inverse dynamics analysis of a general spherical star-triangle parallel manipulator using principle of virtual work. Nonlinear Dyn. 61, 419\u2013434 (2010)","journal-title":"Nonlinear Dyn."},{"key":"800_CR22","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1007\/s11071-011-0043-1","volume":"67","author":"C Yang","year":"2012","unstructured":"Yang, C., Han, J., Zheng, S., Peter, O.O.: Dynamic modeling and computational efficiency analysis for a spatial 6-DOF parallel motion system. Nonlinear Dyn. 67, 1007\u20131022 (2012)","journal-title":"Nonlinear Dyn."},{"key":"800_CR23","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.rcim.2011.06.002","volume":"28","author":"C Yang","year":"2012","unstructured":"Yang, C., Huang, Q., Han, J.: Decoupling control for spatial six-degree-of-freedom electro-hydraulic parallel robot. Robot. Comput.-Integra. Manuf. 28, 14\u201323 (2012)","journal-title":"Robot. Comput.-Integra. Manuf."},{"key":"800_CR24","doi-asserted-by":"publisher","first-page":"1549","DOI":"10.1016\/j.mechmachtheory.2011.04.010","volume":"46","author":"Y Yun","year":"2011","unstructured":"Yun, Y., Li, Y.: A general dynamics and control model of a class of multi-DOF manipulators for active vibration control. Mecha. Mach. Theor. 46, 1549\u20131574 (2011)","journal-title":"Mecha. Mach. Theor."},{"key":"800_CR25","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1007\/s11071-010-9690-x","volume":"61","author":"Y Yun","year":"2010","unstructured":"Yun, Y., Li, Y.: Design and analysis of a novel 6-DOF redundant actuated parallel robot with compliant hinges for high precision positioning. Nonlinear Dyn. 61, 829\u2013845 (2010)","journal-title":"Nonlinear Dyn."},{"key":"800_CR26","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1016\/j.mechmachtheory.2009.12.001","volume":"45","author":"C Yang","year":"2010","unstructured":"Yang, C., Huang, Q., Jiang, H., Peter, O.O., Han, J.: PD Control with gravity compensation for hydraulic 6-DOF parallel manipulator. Mecha. Mach. Theor. 45, 666\u2013677 (2010)","journal-title":"Mecha. Mach. Theor."},{"key":"800_CR27","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/s11044-012-9321-z","volume":"29","author":"A Akbarzadeh","year":"2013","unstructured":"Akbarzadeh, A., Enferadi, J., Sharifnia, M.: Dynamics analysis of a 3-RRP spherical parallel manipulator using the natural orthogonal complement. Multibody Syst. Dyn. 29, 361\u2013380 (2013)","journal-title":"Multibody Syst. Dyn."},{"key":"800_CR28","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/s11044-005-9003-1","volume":"15","author":"ABK Rao","year":"2006","unstructured":"Rao, A.B.K., Saha, S., Rao, P.V.: Dynamics modelling of hexaslides using the decoupled natural orthogonal complement matrices. Multibody Syst. Dyn. 15, 159\u2013180 (2006)","journal-title":"Multibody Syst. Dyn."},{"key":"800_CR29","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/s11044-005-1143-9","volume":"14","author":"WA Khan","year":"2005","unstructured":"Khan, W.A., Krovi, V.N., Saha, S.K., Angeles, J.: Modular and recursive kinematics and dynamics for parallel manipulators. Multibody Syst. Dyn. 14, 419\u2013455 (2005)","journal-title":"Multibody Syst. Dyn."},{"key":"800_CR30","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1081\/SME-100104478","volume":"29","author":"SK Saha","year":"2001","unstructured":"Saha, S.K., Schiehlen, W.O.: Recursive kinematics and dynamics for parallel structured closed-loop multibody systems. Mecha. Struc. Mach. 29, 143\u2013175 (2001)","journal-title":"Mecha. Struc. Mach."},{"key":"800_CR31","doi-asserted-by":"publisher","first-page":"1037","DOI":"10.1109\/TRO.2014.2341312","volume":"30","author":"F Thomas","year":"2014","unstructured":"Thomas, F.: Approaching dual quaternions from matrix algebra. IEEE Trans. Robot. 30, 1037\u20131048 (2014)","journal-title":"IEEE Trans. Robot."},{"key":"800_CR32","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/s12206-017-1202-1","volume":"32","author":"Y Li","year":"2018","unstructured":"Li, Y., Yang, X., Wu, H., Chen, B.: Optimal design of a six-axis vibration isolator via Stewart platform by using homogeneous Jacobian matrix formulation based on dual quaternions. J. Mecha. Sci. Technol. 32, 11\u201319 (2018)","journal-title":"J. Mecha. Sci. Technol."},{"key":"800_CR33","doi-asserted-by":"publisher","first-page":"1162","DOI":"10.1109\/TRO.2012.2196310","volume":"28","author":"X Wang","year":"2012","unstructured":"Wang, X., Yu, C., Lin, Z.: A dual quaternion solution to attitude and position control for rigid-body coordination. IEEE Trans. Robot. 28, 1162\u20131170 (2012)","journal-title":"IEEE Trans. Robot."},{"key":"800_CR34","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.mechmachtheory.2016.08.003","volume":"107","author":"X Yang","year":"2017","unstructured":"Yang, X., Wu, H., Li, Y., Chen, B.: A dual quaternion solution to the forward kinematics of a class of six-DOF parallel robots with full or reductant actuation. Mecha. Mach. Theor. 107, 27\u201336 (2017)","journal-title":"Mecha. Mach. Theor."},{"key":"800_CR35","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/j.robot.2015.12.005","volume":"77","author":"E \u00d6zg\u00fcr","year":"2016","unstructured":"\u00d6zg\u00fcr, E., Mezouar, Y.: Kinematic modeling and control of a robot arm using unit dual quaternions. Robot. Auton. Syst. 77, 66\u201373 (2016)","journal-title":"Robot. Auton. Syst."},{"key":"800_CR36","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s11071-015-2350-4","volume":"83","author":"H Gui","year":"2016","unstructured":"Gui, H., Vukovich, G.: Dual-quaternion-based adaptive motion tracking of spacecraft with reduced control effort. Nonlinear Dyn. 83, 597\u2013614 (2016)","journal-title":"Nonlinear Dyn."},{"key":"800_CR37","doi-asserted-by":"crossref","unstructured":"Dooley, J., McCarthy, J.M.: Spatial Rigid Body Dynamics Using Dual Quaternion Components Proceedings of the 1991 IEEE International Conference on Robotics and Automation, 1991, pp. 90\u201395. IEEE (1991)","DOI":"10.1109\/ROBOT.1991.131559"},{"key":"800_CR38","first-page":"3","volume":"011004","author":"A Laulusa","year":"2008","unstructured":"Laulusa, A., Bauchau, O.A.: Review of classical approaches for constraint enforcement in multibody systems. J. Comput. Nonlinear Dyn. 011004, 3 (2008)","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"800_CR39","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1007\/s12206-011-1231-0","volume":"26","author":"S Pedrammehr","year":"2012","unstructured":"Pedrammehr, S., Mahboubkhah, M., Khani, N.: Improved dynamic equations for the generally configured Stewart platform manipulator. J. Mecha. Sci. Technol. 26, 711\u2013721 (2012)","journal-title":"J. Mecha. Sci. Technol."}],"container-title":["Journal of Intelligent & Robotic Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-018-0800-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10846-018-0800-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-018-0800-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T09:53:00Z","timestamp":1751449980000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10846-018-0800-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,5]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["800"],"URL":"https:\/\/doi.org\/10.1007\/s10846-018-0800-1","relation":{},"ISSN":["0921-0296","1573-0409"],"issn-type":[{"value":"0921-0296","type":"print"},{"value":"1573-0409","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,5]]},"assertion":[{"value":"11 October 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}