{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:54:55Z","timestamp":1760237695434,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T00:00:00Z","timestamp":1592524800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The paper uses Kane\u2019s formalism to study two degrees of freedom (DOF) mechanisms with elastic elements = employed in a wind water pump. This formalism represents an alternative, in our opinion, that is simpler and more economical to Lagrange\u2019s equation, used mainly by researchers in this type of application. In the problems where the finite element method (FEM) is applied, Kane\u2019s equations were not used at all. The automated computation causes it to be reconsidered in the case of mechanical systems with a high DOF. Analyzing the planar transmission mechanism, these equations were applied for the study of an elastic element. An analysis was then made of the results obtained for this type of water pump. The matrices coefficients of the obtained equations were symmetric or skew-symmetric.<\/jats:p>","DOI":"10.3390\/sym12061030","type":"journal-article","created":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T12:19:55Z","timestamp":1592569195000},"page":"1030","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Kane\u2019s Formalism Used to the Vibration Analysis of a Wind Water Pump"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4748-1951","authenticated-orcid":false,"given":"Gabriel Leonard","family":"Mitu","sequence":"first","affiliation":[{"name":"COMAT, SA, str. Zizinului, nr.111, 500002 Brasov, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eliza","family":"Chircan","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Transilvania University of Bra\u0219ov, B-dulEroilor 20, 500036 Bra\u0219ov, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maria Luminita","family":"Scutaru","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Transilvania University of Bra\u0219ov, B-dulEroilor 20, 500036 Bra\u0219ov, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8679-2579","authenticated-orcid":false,"given":"Sorin","family":"Vlase","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Transilvania University of Bra\u0219ov, B-dulEroilor 20, 500036 Bra\u0219ov, Romania"},{"name":"Technical Sciences Academy of Romania, B-dul Dacia 26, 030167 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1115\/1.3428335","article-title":"A General Method for Kineto-Elastodynamic Analysis and Synthesis of Mechanisms","volume":"94","author":"Erdman","year":"1972","journal-title":"J. Eng. Ind."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/0094-114X(80)90003-8","article-title":"Kineto-Elastodynamic Analysis of Mechanisms by Finite Element Method","volume":"15","author":"Nath","year":"1980","journal-title":"Mech. Mach. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/0094-114X(86)90057-1","article-title":"A survey of Finite Element Techniques for Mechanism Design","volume":"21","author":"Thompson","year":"1986","journal-title":"Mech. Mach. Theory"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s11044-006-9009-3","article-title":"A 3D Finite Element Method for Flexible Multibody Systems","volume":"15","author":"Gerstmayr","year":"2006","journal-title":"Multibody Syst. Dyn."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1007\/s00161-018-0722-y","article-title":"Motion equation for a flexible one-dimensional element used in the dynamical analysis of a multibody system","volume":"31","author":"Vlase","year":"2019","journal-title":"Contin. Mech."},{"key":"ref_6","first-page":"676","article-title":"Dynamical Response of a Multibody System with Flexible Elements with a General Three-Dimensional Motion","volume":"57","author":"Vlase","year":"2012","journal-title":"Rom. J. Phys."},{"key":"ref_7","first-page":"476","article-title":"Finite Element Analysis of a Two-Dimensional Linear Elastic Systems with a Plane \u201crigid Motion\u201d","volume":"59","author":"Vlase","year":"2014","journal-title":"Rom. J. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Negrean, I., Cri\u0219an, A.-D., and Vlase, S. (2020). A New Approach in Analytical Dynamics of Mechanical Systems. Symmetry, 12.","DOI":"10.3390\/sym12010095"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Vlase, S., Marin, M., and Scutaru, M.L. (2020). Maggi\u2019s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements. Mathematics, 8.","DOI":"10.3390\/math8030399"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Mehrjooee, O., Dehkordi, S.F., and Korayem, M.H. (2019). Dynamic modeling and extended bifurcation analysis of flexible-link manipulator. Mech. Based Des. Struct. Mach.","DOI":"10.1080\/15397734.2019.1665542"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.apm.2018.08.035","article-title":"Motion equations of cooperative multi flexible mobile manipulator via recursive Gibbs-Appell formulation","volume":"65","author":"Korayem","year":"2019","journal-title":"Appl. Math. Model."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2041","DOI":"10.1007\/s11071-017-3569-z","article-title":"Derivation of dynamic equation of viscoelastic manipulator with revolute-prismatic joint using recursive Gibbs-Appell formulation","volume":"89","author":"Korayem","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Haug, E.J. (2018). Extension of Maggi and Kane Equations to Holonomic Dynamic Systems. J. Comput. Nonlinear Dyn., 13.","DOI":"10.1115\/1.4041579"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Vlase, S., Negrean, I., Marin, M., and Scutaru, M.L. (2020). Energy of Accelerations Used to Obtain the Motion Equations of a Three-Dimensional Finite Element. Symmetry, 12.","DOI":"10.3390\/sym12020321"},{"key":"ref_15","first-page":"152","article-title":"Application of the Maggi equations to mathematical modeling of a robotic underwater vehicle as an object with superimposed non-holonomic constraints treated as control laws","volume":"180","year":"2012","journal-title":"Mechatron. Syst. Mech. Mater."},{"key":"ref_16","unstructured":"Malvezzi, F., Matarazzo Orsino, R.M., and Hess Coelho, T.A. (2017, January 5\u201310). Lagrange\u2019s, Maggi\u2019s and Kane\u2019s equations to the dynamic modelling of serial manipulator. Proceedings of the DINAME 2017-XVII International Symposium on Dynamic Problems of Mechanics, ABCM, S\u00e3o Sebasti\u00e3o, Brazil."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1115\/1.3173031","article-title":"Kane\u2019s equations with undetermined multipiers-application to constrained multibody systems","volume":"54","author":"Wang","year":"1987","journal-title":"ASME J. Appl. Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1115\/1.3167189","article-title":"Multibody dynamics","volume":"50","author":"Kane","year":"1983","journal-title":"ASME J. Appl. Mech."},{"key":"ref_19","first-page":"511","article-title":"An order n formulation for robotic systems","volume":"38","author":"Rosenthal","year":"1990","journal-title":"J. Astronaut. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1092","DOI":"10.2514\/3.21132","article-title":"Block-diagonal equations for multibodyelastodynamics with geometric stiffness and constraints","volume":"16","author":"Banerjee","year":"1993","journal-title":"J. Guid. Control Dyn."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1023\/A:1022566107679","article-title":"Improved order-N performance algorithm for the simulation of constrained multi-rigid-body dynamic systems","volume":"9","author":"Anderson","year":"2003","journal-title":"Multibody Syst. Dyn."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/027836498300200301","article-title":"Use of Kane\u2019s Dynamical Equations in Robotics","volume":"2","author":"Kane","year":"1983","journal-title":"Int. J. Robot. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"79","DOI":"10.2514\/2.5017","article-title":"New Form of Kane\u2019s Equations of Motion for Constrained Systems","volume":"26","author":"Bajodah","year":"2003","journal-title":"J. Guid. Control Dyn."},{"key":"ref_24","unstructured":"Scutaru, M.L. (2014). Models for the Study of Mechanical Response of the Solids and Systems of Solids. [Ph.D. Thesis, Transylvania University]."},{"key":"ref_25","first-page":"1585","article-title":"Improved rigidity of composite circular plates through radial ribs","volume":"233","author":"Itu","year":"2019","journal-title":"Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Nastac, S., Debeleac, C., and Vlase, S. (2019). Hysteretically Symmetrical Evolution of Elastomers-Based Vibration Isolators within alpha-Fractional Nonlinear Computational Dynamics. Symmetry, 11.","DOI":"10.3390\/sym11070924"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Papastavridis, J.G. (2002). Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; For Engineers, Physicists, and Mathematicians, Oxford University Press.","DOI":"10.1115\/1.1553435"},{"key":"ref_28","unstructured":"Roithmayr, C.M., and Hodges, D.H. (2016). Dynamics: Theory and Application of Kane\u2019s Method, Cambridge University Press. [1st ed.]."},{"key":"ref_29","unstructured":"Ursu-Fisher, N. (2015). Elements of Analitical Mechanics, House of Science Book Press."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/6\/1030\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:40:48Z","timestamp":1760175648000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/6\/1030"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,19]]},"references-count":29,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["sym12061030"],"URL":"https:\/\/doi.org\/10.3390\/sym12061030","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,6,19]]}}}