ANALELE UNIVERSITĂłII EFTIMIE MURGU REŞIłA ANUL XXI, NR. 1, 2014, ISSN Florin Bausic, Alexandru Cosmescu, Filip Gărdăreanu

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1 ANALELE UNIVERSITĂłII ETIMIE MURGU REŞIłA ANUL XXI, NR.,, ISSN lorin Bausi, Aleandru Cosesu, ilip Gărdăreanu Stability Analysis for Hand-ar-forear Dynai Syste In this paper we propose a odel with four degrees of freedo for hand-ar-forear dynai syste. Using eperiental data fro [9] by eans of the Siulin progra, is built blo diagra to siulate the dynai syste otion and phase diagras are drawn by using Matlab. ro the interpretation of these diagras result, for a set of paraeters (,,, O, ω ), stable oves for the hand-ar-forear dynai syste. Keywords: stability, dinai syste, Siulin, Matlab. The dynai odel proposed or the dynai hand-ar-forear syste is proposed, in igure, a odel with four degrees of freedo. 5 igure. A four degrees of freedo for the hand-ar-forear dynai syste 6

2 6 -thub; -pal and four fingers; -forear; -ar. Deterination of differential equations of otion Using Lagrange's equations (II), the differential equations of otion in atri for are: where: Matri differential equation () is developed being obtained the syste: [ ]{ } [ ]{ } [ ]{ } { } K C M [ ] M is the atri of inertia [ ] K is the stiffness atri [ ] C is the daping atri { } t sin O ω is the olun vetor of the eitation fore ( ) ( ) ( ) ( ) t sin ω () () () () (5) (6)

3 To deterine the otion and speed laws, in order to analyze the dynai stability of the syste, will use Siulin. or this purpose the differential equations syste (6) to rewrite as follows.. Using Siulin software By rewriting the syste of equations (6) result: [ sinωt] [ ( ) ( ) ] (7) [ ( ) ( ) ] [ ] or eah of the four differential equations of the syste (7), will opose one subsyste with predefined blos fro Siulin library. or eaple, the differential equation: sin in Siulin have a blo diagra shown in igure. [ t] ω (8) v_ v / s v s _ Add subsiste -deget are igure. Siulin blo diagra of the subsyste -thub We obtain siilar blo diagra for the other three differential equations. 6

4 All these blo shees it enapsulates and onnets in a blo diagra of the whole hand-ar-forear syste dynai, shown in igure. igure. Blo diagra of the hand-ar-forear dynai syste. The siulation results Net figure was drawn the speed variation depending on displaeent under a sinusoidal disturbane fores ating on the thub, using eperiental data fro [9]. our graphis were obtained, naely: igure. The forear state spae diagra igure 5. The ar state spae diagra 6

5 igure 6. The pal state spae diagra igure 7. The thub state spae diagra 5. Conlusions ro the analysis of four displaeent speed harts under the fore sinωt and onsidering into aount all the eleents that ae up the daping syste finds that all these representations are yli losed urves. ro the analysis of four diagras, displaeent speed under the disruptive fore sinωt and taing into aount the daping of all the eleents that ae up syste, notes that all these representations are yli losed urves. Aording to haos theory, if a representation in spae of states (veloity, displaeent) is a losed yle urve, then the syste is stable. This ethod of siulation has a future appliation the study of anipulators stability installed or ounted on a vehile arrier siilar to those shown in the figure below: igure 8. Eeples of anipulators 6

6 Referenes [] Panaitesu-Liess R., Modele bioeanie asoiate organisului uan, Teza de dotorat, Buuresti,. [] Nihita G., Modelarea sisteului dinai brat-antebrat-âna, Teza de disertatie, Buuresti,. [] Dian D., A ehanial odel for the vibration eitation of the huan hand and ar syste, International zeitshess feir angeiveliz physiologi 7, 958. [] Abras C.., Modelling the vibration harateristis of the huan hand by the driving point ehanial ipedane ethod, Ph.D. Thesis, North Carolina State University, 97. [5] Reynolds D.D., Soedel W., Dynai Response of the hand-ar syste to a sinusoidal input, Journal of Sound Vibration, 97, 9-5. [6] Miwa T.Y., Yoneawa Y., Nara A., Kanada K., Baba K., Vibration isolators for portable vibrating tool. Part-. Industrial Health 7, Agrinder, 979, 85-. [7] Mishow J.W., Suggs C.W., Hand-ar vibration part-, vibration response to the huan hand. Journal of Sound and Vibration, 977, 5; 5 [8] Meltzer G., A vibration odel for the huan hand-ar syste, Proeedings of the International Syposiu on Man under Vibration Suffering and Protetion, Udine, Italy, 979, -. [9] Patil M.K., Palanihay M.S., Ghista D.N., Dynai response of huan body seated on a trator and effetiveness of suspension systes, SAE Paper 779, 977, pag [] Panaitesu-Liess R., Analiza răspunsului dinai al organisului uan în interatiune u fenoenele vibratorii, Referat în adrul dotoratului, Buuresti,. [] Bauşi., Diaonu Cr., Dinaia Masinilor, Ed. Conspress, Buuresti. Adresses: Professor PhD, eng. lorin Bausi, The Departent of Tehnial Mehanis and Mehaniss, Tehnial University of Civil Engineering, Buharest, aulty of Tehnologial Equipent, Calea Plevnei no. 59, ode, setor, Buharest, florin.bausi@utb.ro Eng. Aleandru Cosesu - Advaned Mehanial Systes (Master, nd year of study), aulty of Tehnologial Equipent, Calea Plevnei no. 59, ode, setor, Buharest; ilip Gărdăreanu - nd year of study, aulty of Tehnologial Equipent, Calea Plevnei no. 59, ode, setor, Buharest. 65