COMPUTER AIDED ANALYSIS OF KINEMATICS AND KINETOSTATICS OF SIX-BAR LINKAGE MECHANISM THROUGH THE CONTOUR METHOD

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1 SINTIFI PROINGS XIV INTRNTIONL ONGRSS "MHINS. THNOLОGIS. MTRILS." 17 - SUMMR SSSION W ISSN 55-X PRINT ISSN 55-1 OMPUTR I NLYSIS OF KINMTIS N KINTOSTTIS OF SIX-R LINKG MHNISM THROUGH TH ONTOUR MTHO Pof.so.. Likj R. 1 Pof.so.zem Kku* MS. Qelj M 1 Pof.ss.. jmi X 1. Fult of Mehnil ngineeing Uniesit of Pishtin Hsn Pishtin Kosoo 1 zem.kku@uni-p.eu *oesponing utho bstt: In this ppe is pesente si-b linkge mehnism of the pump fo oil etusion. In this mehnism e intoue highe kinemti pis. imensions n othe inoming links e opte s neess. Fo the si-b linkge mehnisms is ie out the kinemti nlsis n fo ll linkges e shown the isplement eloit n eletion. The nlsis is pefome b Mth softwe while kinetostti nlsis is ie out using ontou Metho omping esults of two iffeent softwe s Mth n Woking Moel. The simultion pmetes e ompute fo ll points of the ontous of mehnism Kewos: MHNISM ONTOUR ISPLMNT VLOSITY LRTION 1. Intoution This ppe hs been omplete using Mth n Woking Moel softwe s. In this ppe is pesente si-b linkge n simple nk mehnism F s shown in the figue below. Fistl in this mehnism is etemine F n 5. eitie F epesents the spee of the slie F. Fom the gien o pitue.1 6 shoul be etemine. The msses e opte sine the moments of ineti nee to lulte. The kinemti pt of the ppe will be omplete b fining the eloities n eletions of eh point F fo the entes fom 1 to 6. In this w e etemine the ngul eletions n eloities of the linkges n 5. Whees fo the kinetostti pt will be etemine the etion foes of the points: X Y X Y X Y X Y X Y X F Y F NX F6 n M t whih e ting on the leing link. In the pitue e shown 5 boies: ight tingle o F slie b F. os os os os α... sin sin sin sin α Fig. Fou-b linkge n nk mehnism F Fig. 1 Si b-linkge mehnism F Gien t:.5eg...6[eg] 6.9 : α etemintion of ngleα of with 1 : Linkge I... 1 s shown in the Figue thee e 1 unknown sizes 1 equtions fo the fist fou boies fo the slie 1 equtions.. The nlsis of the positions eloities n eletions of si-b linkge mehnism In the figue is pesente the eloit pln fo the points n. lso e pesente ngul eloities n ngul eletions fo the points n. fte fining the eloities n eletions of these points the isplements eloities n eletions of these points with ngles n in funtion of e shown gphill. Outline is shown in this fom: 18[eg] 9[eg]... The eto eqution without the ontou I is:... Fom then esigne outline t n we he the following initil onitions: 57 YR I VOLUM VI P.P

2 p Fig. Veloit pln fo the points n sin os sin os sin os sin os α α p p 59.8[eg].96[eg] 1.18[eg] β Fin Zgj... 5 fte lultion of the lues b Mth softwe in the following e shown gphill the lues of positions eloities n eletions espetiel fo n : Fig. igms fo positions eloities n eletions.1 Position of the point The position of the point is lulte in ietion of n : ] / 1.[ os sin sin os s m... 6 Fig. 5 The position igms fo the position equtions of the point in ietion of n ] / [ sin os s m... 7 ngul eloit n eletion fo the point : ].5[eg.87[eg] The equtions fo position isplement eloit n eletion of the point In the following is shown the isplement of point long with eloities n eletions whih e pesente gphill b the igms i Mth pogm: os sin ; os sin sin os SINTIFI PROINGS XIV INTRNTIONL ONGRSS "MHINS. THNOLОGIS. MTRILS." 17 - SUMMR SSSION W ISSN 55-X PRINT ISSN 55-1 YR I VOLUM VI P.P

3 SINTIFI PROINGS XIV INTRNTIONL ONGRSS "MHINS. THNOLОGIS. MTRILS." 17 - SUMMR SSSION W ISSN 55-X PRINT ISSN The equtions fo position isplement eloit n eletion of the point Fo the point of nk Mehnism etemine the isplement n in the following pitues e shown eloities n eletions in the ietion n : b os ; b b sin ; b os ; sin b b os sin.. 1 Fig. 6 Veloities n eletion of point.1 The epession fo the mile point of the bs n In the following e ette the isplement fo the mile position of the bs n n othe isplement whih belong to these bs. e lso pesente the eloities n eletions of these bs n thei igms septel: : os ; sin...9 sin ; os : os ; sin...1 : sin ; os os ; sin..11 R sin ; R R5 9 os Fig. 8. igms of the eloities n eletion fo the. Kinetostti nlsis of the si-b linkge mehnism Fo the kinetostti pt will be pesente the kinetostti nlsis of si-b linkge mehnism b Mth softwe. Moments of ineti msses of boies e use in the following: m J J 1; m 15; m ; m5 15; m6 5; g m ; J m m. 1. ; J 5 m Linkge I: The equilibium onitions fo the point e equl to zeo. Si linkges e use fo the kinetostti nlsis. Fo the fist linkge e gien the following equilibium onitions X Y n X Y fo the mile points of the linkge point n fo the bo mss m. F 5 5 X M t X Y Y m ; Y os X os X Y m os sin... 1 Fig. 7 nk mehnism 59 YR I VOLUM VI P.P

4 SINTIFI PROINGS XIV INTRNTIONL ONGRSS "MHINS. THNOLОGIS. MTRILS." 17 - SUMMR SSSION Y X X X F m5 5 Y Y Y m 5 J 5 5 X X sin F 5 Y YF sin 5 Y W ISSN 55-X PRINT ISSN 55-1 X X Y Fig. 9. Linkge I quilibium onitions fo the point Linkge II lso fo the linkge II e witten the equilibium onitions whih e X Y X Y ente bo mss n moment of ineti fo the point. X X m ; Y Y m J X sin Y os.15 Y X sin X F Y F Fig. 1. Linkge IV of the pt F in ietion of n Linkge V Y m F m g Y X X F Y F F m 6 X Y Fig.1. Linkge II quilibium onitions fo the pt Linkge III X Y J X Y Y X Y m m Y X z Y b...16 H m Fi.g.1. Linkge V of the point F in ietion of n ll unknown pmetes fo the linkges in both ietions n e lulte b Mth. Fom point to the point Fin the Tnsmission moment M t : Sole : Fin X Y X Y X Y X Y X Y X Y F F M t In the following igms e gien the lues of ll unknown pmetes fo the positions ;.5; 1 b Mth softwe. This it ws ell tough wok sine the woking poess b Mth ws e slow espeill to follow the poeue whih is gien b kinetostti nlsis. Y X X X Y Y Fig.11. Linkge III of the points n ente 6 YR I VOLUM VI P.P

5 SINTIFI PROINGS XIV INTRNTIONL ONGRSS "MHINS. THNOLОGIS. MTRILS." 17 - SUMMR SSSION W ISSN 55-X PRINT ISSN 55-1 Fig.1. igms of kinetostti nlsis of the gien mehnism fo the points F n tnsmission moment Mt 5. Simultion fo si-b mehnism b Woking Moel softwe In the seon pt of this ppe is pefome the simultion fo ll points F n Mt time epenent of the si b linkge mehnism b Woking Moel whih is shown in the following. Fig.15.igms in Woking Moel fo ngul eloit n eletion n 5 Fig.16:. igms in Woking Moel fo equilibium points F n tnsmission moment M t in ietion 61 YR I VOLUM VI P.P

6 SINTIFI PROINGS XIV INTRNTIONL ONGRSS "MHINS. THNOLОGIS. MTRILS." 17 - SUMMR SSSION. Refeenes W ISSN 55-X PRINT ISSN 55-1 Fig.17.igms in Woking Moel fo equilibium points F n tnsmission moment Mt in ietion Shl : 8 isenjimi i Meknizme me Kompjute Ushtime etsh Fkulteti i Inhinieisë Meknike Pishtinë. Rehwl W. Luk K.7 Reseh of ouple ues of Geometil Poles of fist Oe Jounl of Mehnisms n Mnipultos ol. 6 n. pp Shl hmet Rmë Likj n Milin uqi. "Snthesis of m mehnism bse on gien pogm." IF Poeeings Volumes 6.8 1: 6-6. Potiis histophe G. " noel mehnism to poue figue-eight-shpe lose ues in the thee-imensionl spe." Poeeings of Thi Intentionl onfeene on peiments/poess/sstem Moeling/Simultion & Optimiztion thens. 9. Umesh hn. t ll 1. Snthesis of ouple ues with ombine pln m followe mehnisms b geneti lgoithm. Poeeing of n Intentionl onfeene on ompute ngineeing n Tehnolog heng hin. U.S. hn S.V. Joshi. 1. Snthesis n nlsis of ouple ues with ombine pln m followe mehnisms Intentionl Jounl of ngineeing Siene n tehnolog Vol. No. 6 pp. 1- Fig.18. igms fo n 5 time epenent une ommn RUN 6. onlusions n eommentions pplition of the softwe s Mth o Mtlb we he ehe to out the full nlsis of this ppe. In this ppe e me the lultions of ll positions isplement fo the whole mehnism n lso e etemine the plns fo eloities n eletions fo eh point. Howee in this ppe e shown the outline plnes of the mehnism sme s the igms fo eh linkge though Mth n Woking Moel softwe Si-b linkge mehnism igms whih e eie b Woking Moel e lmost simil to the igms eie b Mth sme s the eie esults Though Woking Moel softwe e eie the esults of etions fom the equilibium onitions of si b linkge mehnism ngul eloities n eletions fo the points n 5 fo the ngles n 5 in time omin though the ommn Run s the genel onlusion; the esults eie b both softwe sme s fo thei igms fo ll points of the si b linkge mehnism e within the esonble bounies. Ou epettions e tht simil esults will be eie b pplition of Mtlb softwe. 6 YR I VOLUM VI P.P

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