{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T18:35:38Z","timestamp":1773167738432,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,9]],"date-time":"2020-11-09T00:00:00Z","timestamp":1604880000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2017YFC0602000"],"award-info":[{"award-number":["2017YFC0602000"]}]},{"name":"Science and Technology Development Project of Jilin Province","award":["20190303061SF"],"award-info":[{"award-number":["20190303061SF"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we propose a novel kinematic and inverse dynamic model for the flybar-less (FBL) swashplate mechanism of a small-scale unmanned helicopter. The swashplate mechanism is an essential configuration of helicopter flight control systems. It is a complex, multi-loop chain mechanism that controls the main rotor. In recent years, the demand for compact swashplate designs has increased owing to the development of small-scale helicopters. The swashplate mechanism proposed in this paper is the latest architectures used for hingeless rotors without a Bell-Hiller mixer. Firstly, the kinematic analysis is derived from the parallel manipulators concepts. Then, based on the principle of virtual work, a methodology for deriving a closed-form dynamic equation of the FBL swashplate mechanism is developed. Finally, the correctness and efficiency of the presented analytical model are demonstrated by numerical examples and the influence factors of the loads acted on actuators are discussed.<\/jats:p>","DOI":"10.3390\/sym12111849","type":"journal-article","created":{"date-parts":[[2020,11,9]],"date-time":"2020-11-09T19:08:29Z","timestamp":1604948909000},"page":"1849","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Novel Comprehensive Kinematic and Inverse Dynamic Model for the Flybar-Less Swashplate Mechanism: Application on a Small-Scale Unmanned Helicopter"],"prefix":"10.3390","volume":"12","author":[{"given":"Jianbo","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rongqiang","family":"Guan","sequence":"additional","affiliation":[{"name":"College of Automotive Engineering, Jilin Engineering Normal University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7318-1290","authenticated-orcid":false,"given":"Yongming","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linqiang","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Raptis, I.A., and Valavanis, K.P. (2011). Linear and Nonlinear Control of Small-Scale Unmanned Helicopters, Springer.","DOI":"10.1007\/978-94-007-0023-9"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"208","DOI":"10.2514\/1.9279","article-title":"Swashplateless Helicopter Rotor with Trailing-Edge Flaps","volume":"41","author":"Shen","year":"2004","journal-title":"J. Aircraft."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1007\/s12555-010-0306-5","article-title":"Nonlinear dynamic modeling and control of a small-scale helicopter","volume":"8","author":"Song","year":"2010","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1023\/A:1009843930506","article-title":"The kinematics of the swashplate mechanism of a VTOL unmanned aerial vehicle","volume":"3","author":"Lange","year":"1999","journal-title":"Multibody Syst. Dyn."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/s11044-012-9321-z","article-title":"Dynamics analysis of a 3-RRP spherical parallel manipulator using the natural orthogonal complement","volume":"29","author":"Akbarzadeh","year":"2013","journal-title":"Multibody Syst. Dyn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1023\/A:1009874504407","article-title":"The dynamics of the swashplate mechanism of a VTOL unmanned aerial vehicle","volume":"5","author":"Lange","year":"2001","journal-title":"Multibody Syst. Dyn."},{"key":"ref_7","first-page":"616","article-title":"Analysis of a swashplate mechanism of the hingeless rotor hub with the flybar in a model helicopter, Part I: Kinematics","volume":"4","author":"Sabaapour","year":"2010","journal-title":"Trans. Jpn. Soc. Mech. Eng."},{"key":"ref_8","first-page":"258","article-title":"Analysis of a swashplate mechanism of the hingeless rotor hub with the flybar in a model helicopter, Part II: Dynamics","volume":"4","author":"Sabaapour","year":"2010","journal-title":"Trans. Jpn. Soc. Mech. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1115\/1.533540","article-title":"Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work","volume":"122","author":"Tsai","year":"1999","journal-title":"J. Mech. Des."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s11044-015-9452-0","article-title":"A fast inverse kinematic solution for the nonlinear actuating mechanisms of a small-scale helicopter","volume":"35","author":"Khaligh","year":"2015","journal-title":"Multibody Syst. Dyn."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Saffarian, M., and Fahimi, F. (2008, January 7\u201310). A comprehensive kinematic analysis of a model helicopter\u2019s actuating mechanism. Proceedings of the AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.2008-133"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1002\/rob.20002","article-title":"Mathematical modeling and experimental identification of an unmanned helicopter robot with flybar dynamics","volume":"21","author":"Kim","year":"2004","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ren, B., Sarabia, M., Chen, C., Fua, C.H., and Lee, T.H. (2012). Modeling, Control and Coordination of Helicopter Systems, Springer.","DOI":"10.1007\/978-1-4614-1563-3"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.protcy.2014.09.079","article-title":"State Estimation for a Small Scale Flybar-less Helicopter","volume":"15","year":"2014","journal-title":"Proc. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"801874","DOI":"10.1155\/2015\/801874","article-title":"Chaotic Artificial Bee Colony Algorithm for System Identification of a Small-Scale Unmanned Helicopter","volume":"2015","author":"Ding","year":"2015","journal-title":"Int. J. Aerosp. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.mechmachtheory.2016.12.009","article-title":"Inverse dynamic modeling and analysis of a coaxial helicopter\u2019s swashplate mechanism","volume":"113","author":"Yuan","year":"2017","journal-title":"Mech. Mach. Theory"},{"key":"ref_17","unstructured":"Merlet, J.P. (2006). Parallel Robots, Springer."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1016\/S0094-114X(98)00081-0","article-title":"A general strategy based on the Newton\u2013Euler approach for the dynamic formulation of parallel manipulators","volume":"34","author":"Dasgupta","year":"1999","journal-title":"Mech. Mach. Theory"},{"key":"ref_19","first-page":"598","article-title":"Recursive Newton-Euler formulation for flexible dynamic manufacturing analysis of open-loop robotic systems","volume":"29","author":"Hwang","year":"2006","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.mechmachtheory.2008.02.003","article-title":"Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism","volume":"44","author":"Abdellatif","year":"2009","journal-title":"Mech. Mach. Theory"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2103","DOI":"10.1023\/A:1027351523184","article-title":"Superconducting State in the Lagrangian Formalism of the Generalized Hubbard Model","volume":"42","author":"Zandron","year":"2003","journal-title":"Int. J. Theor. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1007\/s10409-018-0761-4","article-title":"Closed-form dynamics of a hexarot parallel manipulator by means of the principle of virtual work","volume":"34","author":"Pedrammehr","year":"2018","journal-title":"Acta Mech. Sin."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/s11071-010-9659-9","article-title":"Inverse dynamics analysis of a general spherical star-triangle parallel manipulator using principle of virtual work","volume":"61","author":"Enferadi","year":"2010","journal-title":"Nonlinear Dyn."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s11044-005-9003-1","article-title":"Dynamics Modelling of Hexaslides using the Decoupled Natural Orthogonal Complement Matrices","volume":"15","author":"Rao","year":"2006","journal-title":"Multibody Syst. Dyn."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1885","DOI":"10.1007\/s00707-016-1611-8","article-title":"First-order form, Lagrange\u2019s form, and Gibbs\u2013Appell\u2019s form of Kane\u2019s equations","volume":"227","author":"Tu","year":"2016","journal-title":"Acta Mech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s11044-008-9121-7","article-title":"Solving the kinematics and dynamics of a modular spatial hyper-redundant manipulator by means of screw theory","volume":"20","year":"2008","journal-title":"Multibody Syst. Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Lin, C.-J., and Chen, C.-T. (2016). Reconfiguration for the Maximum Dynamic Wrench Capability of a Parallel Robot. Appl. Sci., 6.","DOI":"10.3390\/app6030080"},{"key":"ref_28","unstructured":"Tsai, L.W. (1999). Robot. Analysis: The Mechanics of Serial and Parallel Manipulators, Wiley."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/11\/1849\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:31:16Z","timestamp":1760178676000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/11\/1849"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,9]]},"references-count":28,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["sym12111849"],"URL":"https:\/\/doi.org\/10.3390\/sym12111849","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,9]]}}}