Gipki Poluzni Cetvorouglovi Za Pravolinijsko Vodjenje

7/29/2019 Gipki Poluzni Cetvorouglovi Za Pravolinijsko Vodjenje

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JuDEKO KoncrpyacarseMaIIIHHa

Jurnal ofMechanicalEngineering Design

Vo1.6 No 1,2003.pp 1- 40I HayqHlI pa,LJ;KAPAKTEPIICTIIKE KPETAIbA rIIIIKIIX

IIOJIY)KHIIXQETBOPOYrJIOBA 3A PEAJIII3AIJ;IIJYIIPABOJIIIHIIJCKOrBOnEIbAMOTION CHARACTERISTICS OF THE COMPLIANTFOUR-BAR LINKAGES FOR RECTILINEAR GUIDINGNenad T. Pavlovic, Nenad D. PavlovicFnnxa MexaHII3MII cy 1l0KpeTJMIBII aaxsarsyjyha penarasnoj enaCTIl'IHOCTII CBOjllX srnofioaa. Pa,LJ; ce 6aBII HeKIlMKpYTo1J:naHlIM 1l0JIYlKHlIM 1J:eTBOpoymoBllMa II lbllXOBIlM eKBIIBaJIeHTHIlM rlIlIKIlM xonnjaaa, KO,LJ; xojax Il3BeCHaTa1J:Ka cnojxe MO:>Ke 6IITII npasonaaajcxa soheaa, Y pazry lie 61lT1I aHaJIII31lpaHa Ta1J:HOCT npaaorraaajcsor BoljelbarHIIKIlX MexaHll3aMa na noxeparsy O,LJ; 5 mm II yrropeheaa ca rasnourhy Boljelba eKBIIBaJIeHTHIlX KpYT01J:JIaHlIXMeXaHll3aMa. Billie onpeheae OITTIIMaJIHe ,L(IlMeH3lIje rHIIKllX MeXaHII3aMa ca acnexra Ta1J:HOCTII Boljelba IIMaKCllMaJIHlIX Bpe,LJ;HOCTII narronaaa casajarse.

Compliant mechanisms gain their mobility due to the relative flexibilityof their joints. Thepaper deals with somerigid-body four-bar linkages and their equivalent compliant counterparts, which a couplerpoint is capable to berectilinearly guided The rectilinear guiding accuracyofthe compliant mechanisms on the displacement of 5 mmwill be analyzed and compared with the guiding accuracy of the equivalent rigid-body mechanism. The optimaldimensions of the compliant mechanisms will be determined regarding guidingaccuracyand maximal values ofbending stresses.

1. YBOA[1lIIKIl MeXaHll3MII cy IIOKpeTJbIIBII saxsarsyjyhapenarnaaoj enaCTIl'IHOCTIl CBOj IlX 3m06oBa [1].Kopamhea,e ranxax MeXaHIl3aMa ,LJ;OHOCII MHorerrpe,L(HOCTII. Je,L(Ha O,LJ; TIlX npenaocra CBaKaKO ne:>K1I yTOMe ll1TO ce MeXaHll3aM MO:>Ke aanpasara Il3 jenaorKOMa,LJ;a aKO ce rrpoasnene on noronnor MaTeplIjaJIa. ToHe CaMO nrro nojenaocrasrsyje 1I3pa,LJ;y MeXaHll3Ma, Ben-raKolje MO:>Ke CMalblITII Te:>KHHY II eJIllMIIHIlCaTIIxaoaa,e, 3a30p, rperse, 6yKY II norpefiy saIIO,I(Ma3IIBalbeM. C npyre crpane, nojasa IIoTeHIUijaJIHeeaepraje y enaCTIl'IHlIM cersrearaxa II lbllXOBenenaaeapae ,LJ;eopMaIUije 1J:IIHe aHaJIII3Y OBIlXMeXaHll3aMa KOMIIJIIlKOBaHOM. [IIIIKIl MeXaHIl3MII MOry,LJ;a peanasyjy CaMO MaJIa noxeparsa II OBa 1J:lIlbeHllllaraxohe npencraarsa lbllXOB nenocrarax.Pa,LJ; ce 6aBII 06nlIKOBalbeM II ra-rsomhy nohea,a HeKIlXrHIIKIlX IIOJIYlKHIlX 1J:eTBOpoymoBa.

1. Introduction

Compliant mechanisms gain some or all of theirmobility from the relative flexibility of their joints [1].There are many advantages of using compliantmechanisms. One such advantage is that a mechanismcan be built in one piece, if manufactured from anextrudable or injection-moldablematerial. This not onlysimplifiesmanufacturing but can also reduce weight andeliminate wear, clearance, friction, noise and need forlubrication. On the other hand, energy storage in theflexible members and nonlinearities introduced by largedeflection of flexing members complicate the analysis.The compliant mechanisms can realize only smalldisplacementsand it is also their disadvantage.The paper deals with the design and guiding accuracy ofsome compliant four-bar linkages.

20Anpece ayropa (Contact addresses):dr Nenad T. Pavlovic, MasinskifakultetNis, A. Medvedeva 14, 18000 Nis, [email protected] dr NenadD. Pavlovic, Masinski fakultet Nis, A. Medvedeva14, 18000 Nii, [email protected]


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2. KpyTOqJIaHH nOJlYiKHH xeraopoyrnoeasa npaao.naaajcxo noherse

Taxxa cnojxe Hoecken-osor (cJI.Ia), Robertsqe6bIIlleB-JheBOr (cJI.l6), Watt-osor (CJI.I n) HEvansosor (CJILn) nonyscaor xeraopoyrna MO)Ke 6HTHsohena no npH6JIIDKHO npaBOJIHHHjcKoj rryrarsa [2].Bohena TaqKa ce HaJIa3H na xpajy cnojxe (KO,nHoecken-osor H Evans-osor nonyzcaor xersopoyrna),y TeMeHY cnojxe y 06JIHK)' repaapaor xnaaa (KO,nRoberts- qe6blIlleB-JheBOr nOJIY)KHor seraopoyrna),O,nHOCHO y cpezrann cnojxe (KO,n Watt-osor nOJIY)KHorxeraopoyrna).Y Ta6eJIH 1 cy nare Jl:Y)KHHe qJIaHOBa OBHXMexaHH3aMa, xao HnOJIO)KajH xpasaje, xojasra ce MO)KepeaJIH30BaTH XOpH30HTaJIHO nouepaa,e AXe = 5mm,MaJIHM yraonaa rroxreparsexr xpnsaje (L1q> 5) HMHHHMaJIHHM oncrynaa.ea OCTBapeHe nyrarse yoztaocyaa npasy JIHHHjy AYe [5,13].

2. Rigid-body four-bar linkages forrectilinear guiding

The coupler point C of the Hoecken (Fig. la), Robertsqe6bIIlleB (Fig. lb), Watt (Fig. lc) and Evans (Fig.1d) four-bar linkage can be guided on an approximaterectilinear path [2]. The coupler point is located at theend of the coupler (Hoecken, Evans four-bar linkage),in the comer of the coupler as a ternary link (Robertsqe6bIIlleB four-bar linkage) and in the middle of thecoupler (Watt four-bar linkage).The link lengths of these mechanisms, as well as thepositions of the input crank, that enable realizing ofhorizontal displacement of AXe = 5mm, with the smallangular displacement of the input crank (L1q> 5) andminimal difference between realized and exactrectilinear path AYe, havebeen shown inTable 1 [5,13].

6)

U;) ,n)CJIHKa 1.KpYToqJIaHH IIOJIY)KHH xeraopoyrnoaa sa peamrsauajy npaBOJIHHHjcKor aohen,aa) Hoecken-os; 6) Roberts - qe6bIIlleB-JheB; n) Watt-oa; ,n) Evans-on

Figure 1. Rigid-body four-bar linkages fo r rectilinear guidinga) Hoecken; b) Roberts - lfe6blUle8; c) Watt; d) Evans

Ta6eJIa 1. ):t!)KHHe 'lJIaHOBa KpYT0'lJIaHHX IIOJIY)KHHX qeTBOpoymoBa aa peanasanajy npasonanajcxor sohenaTable 1 The link lengths of the rigid-bodyfour-bar linkages fo r rectilinear guiding-n a=AoA b =BoB c=AB d = AoBo AC AYe[}.lm]Hoecken 177 42.195mm 2.5a 2.5a 2a 5a 3.3Roberts 35 66.585mm a 0.85a 2.44a 1.l05a 0.8Watt 311 61.406mm a 1.04a 2.1a 0.52a 1.8Evans 80 60mm 5.75a a 6.09a a 1.6

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3. Tamca nOJIyiKHu xernopoyrnoea aapeanasamrjy npaaonaaajcxor nohersa

Y pazry heMo ce 6aBHTH amlJIH30M rHnKHX MexaHH3aMaxoje CMO


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a)

c Fc

6)

B

B

The calculation of the "coupler"point displacement andmaximal bending stresses have been performed usingANSYS Software for material piacryl [4] (modulus ofelasticity E = 3700 N/mm2 and bending strength ab s =90 N/mm2) , for material thickness of 0= 4mm. Thecalculation has been performed for the elements withrectangular cross-sectional area using Two-dimensionaleight-node Structural Solid [5] as a characteristicANSYS element type. The results of the displacementand stress analysis have been shown in Table 2.Hoecken, Roberts-Hetisnnea and Watt compliantmechanism produce the best guiding accuracy (minimaldifference between realized and exact rectilinear pathAyc) for great values of rigidity ratio wR/wE. Evanscompliant mechanism produces the best guidingaccuracy for smaller value of rigidity ratio wR/wE.

u) ,lI;)Crraxa 3. [HIIKH nonyacaaxeraopoyrnoaa sa peanasanajy npaBOJIHHHjcKor Bofjelhaa) Hoecken-os; 6) Roberts-Hefisnuea-rsea; n)Watt-os; ,lI;) Evans-ovFigure 3. Compliantfour-bar linkages for rectilinear guidinga) Hoecken; b) Roberts -lle6",lUe6; c) Watt; d) Evans

3.1 Ilonepaa,e Ta'1Ke cnojxe MMaKCHMaJIHH HanOHH 3.1Displacement of Coupler Point and Maximalcanajaisa Bending StressesIlpopaxya noxepaaa ra-nee "cnojxe" C MMaKCMMaJIHMX aanona casajaaa M3BpmeH je Y3 nosrohnporpasrcxor naxera ANSYS sa MaTepMjaJI piacryl [4](MO)J;)'JI eJIaCTMllHOCTM E = 3700 N/mm2 M casojaaxapcroha ab s = 90 N/mm2) , aa ,lI;e6JI,MHY MaTepMjaJIa ono = 4mm. Ilpopaxya je M3BpmeH sa eJIeMeHTenpaaoyraonor nonpesnor npecexa, xopacreha,L(BO,ll;MMeH3MOHaJIHO CTpYKTYPHO TeJIO ca 8 llBopoBa [5]xao KapaKTepMCTM'lHH TMTI ANSYS-eJIeMeHTa.Pe3YJITaTM noxepaaa MHanOHCKe aHaJIM3e npMKaJaHMcy y Ta6eJIM 2. Hoecken-os, Roberts-Hetisnnen-rsea MWatt-on rMnKM MeXaHH3aM pearrasyjyHaj60JI,y TallHOCTsoheaa (HajMalhe oncrynarse OCTBapeHe y O,ll;HOCY aarasay npaBOJIMHHjCKY nyrarsy Ayc) sa BeJIMKeBpe,ll;HOCTM O,ll;HOCa KPYTOCTM wR/wE. Evans-os rMIIKHMeXaHM3aM peanasyje Haj60JI,y TallHOCT Bofjelha saHeIIITO Malhe Bpe,ll;HOCTM O,ll;HOCa KpYTOCTM wR/wE.Ta6.2. Oncrynarse peaJIM30BaHe on npaBOJIMHMjcKe nyran,e rMnKMX MexaHH3aMa sa npaBOJIMHMjcKo soheae (Axc=5mm)Table 2. Guiding inaccuracy ofthe compliantfour-bar linkages for rectilinear guiding (AXe = 5 mm)

WR WE Ayc am[mm] [mm] [11m] [N/mm2]Hoecken 10 0.75 18.5 58.46Roberts 10 0.75 8.1 57.53

Watt 10 0.75 3.1 85.99Evans 6 1 0.26 78.46 23


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3.2 Koel(>HUHjeHT xopucuor )J,ejCTBaYnaaaa pan MOiKe na ce )J,eHIJ;HjeHTa xopncaor nejcrsaaa rHIIKe MeXaHM3Me ca OIITHMaJIHHM )J,HMeH3HjaMa ynorneny TaqHOCTH soheaa (Ta6eJIa 2). Bpe)J,HOCTHKoe 2N because ofappearing great displacement of the acting point ofthe input force Ss; it causes decreasing of 11according to (1). Compliant mechanisms with guided point located

at the end of the coupler are not suitable forrectilinear guiding, in the case of acting of theforce resisting the motion, because of smallguiding accuracy (Hoecken compliantmechanism), that is, the small values of theresisting force that they can stand (Evanscompliant mechanism).


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Ta6erra3. Koedrannjear xopncaor nejcrsa mIIKI1X IIorrY)KHI1X xeraopoyrnoaa aa peanasanajy npasonaaajcxorsohersaTable 3. Mechanical efficiency of the compliantfour-bar linkages for rectilinear guidingFe Fs 11 Cfmax AYe[N] [N] [%] [N/mm2] [urn]0 1.453 - 58.5 18.5= 0.5 2.824 44.9 60.7 1581 4.1897 58.6 62.7 298uQ,l 2 6.92 66.5 67.0 576

== 5 15.08 64.32 79.5 140710 28.57 53.96 100.7 27730 3.71 - 57.5 8.1'" 0.5 6.14 35.67 57.9 10.1-"',l 1 8.57 50.11 58.3 12.0.c0 2 13.42 61.71 58.9 15.85 28.06 66.47 61.1 26.70 2.70 - 85.3 3.100.5 3.64 25.07 85.9 2.85- 1 4.56 39.93 85.9 2.55-:; 2 6.43 56.39 86.0 2.05 12.02 74.35 86.0 0.3610 21.35 81.93 86.0 2.20 4.92 - 78.46 0.26'" 0.2 5.77 12.2 79.07 9.32;;- 0.4 6.62 20.8 79.62 15.20.6 7.47 27.0 80.17 18.7

3.3 CJIO)KeHe cTpYKTYpe rHnKHX MexaHH3aMaY narsy IIo6oJbIIIaIha TalJHOCTH BotjeIha epOPMHpaJIMCMO CnO)KeHe cTpYKTYPe rHIIKI1X MexaHM3aMa [5,10].)];O)];aJIH CMO nocrojehesr eneaearapaoa rHIIKOMMeXa.HH3MY jom jenaa MCTM TaKaB MeXaHH3aM, TaKO najenan .D.PyrOM npezrcrasrsajy rrHK y ornezrany (crrA).OBM eneuetrrapaa MeXaHH3MM MOry 6HTH: KpyTO IIOBe3aHH y soheao] TatIKH C [5,10]; IIOBe3aHH IIOMOliy HOBoYBe.D.eHOr enaCTHtIHOr3rn06a (cn.4a); oce CHMeTpMje TOr arnofia cexy cey soheaoj TalJKH C; IIOBe3aHH IIOMOliy HOBoYBe)];eHOr 1JJIaHa ca naaenacnraaa srnofia, KojHMa ce HOBoyBe)];eHH 1JJIaH

rrosesyje ca cnojxaaa (en, 46); oce CHMeTpMje Tor1JJIaHa cexy ceYsoheao] TalJKM C.CnO)KeHM rHIIKH MeXaHH3aM noxpehy nse CHMynTaHeIIorOHCKe CMJIe Fs MF's (err. 4). HeTatIHOCTH BotjeIhacsaxor 0)]; eneMeHTapHI1X rMIIKI1X MeXaHH3aMa ceMetjyco6HO I


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a) 6)CJIlIKa 4. CJIO)KeHH rHTIKH MexaHH3MH: a) Roberts-Hetismrea-rseaH6)Watt- OBFigure 4. The compound compliant mechanisms: a) Roberts-Hetisuuee and b) Watt

Ta6eJIa4. Oncrynarse peaJIH30BaHe 0)]; rrpaBOJIHHHjcKe nyraa,e Ayc [1JlIl] Roberts-Hetisrurea-neeor HWattosor xpyronnaaor, eJIeMeHTapHOr ranxor HCJIO)KeHOr rHTIKor MeXaHH3MaTable 4. Guiding inaccuracy AYe [um] ofthe Roberts-Heeutue and Watt rigid-body, single compliant and

compoundcompliant mechanismKpyrO'lJIaHH eJIeMeHTapHH CJIO)KeHHMeXaHH3aM rHTIKH rHIIKHMeXaHH3aM MeXaHH3aM

Roberts 0.8 8.1 0.009Watt 1.8 3.1 0.039OBH CJIO)KeHH rHIIKH MeXaHH3MH MOry na 06e36e)];esaasajao 60Jby Ta'lHOCT BoljelDa 0)]; onrosapajyhaxeJIeMeHTapHHX rHTIKHX MeXaHH3aMa (Ta6eJIa 4).Tasnocr BoljelDa CJIO)KeHOr Roberts-Hefisnnes-neaorHWatt-osor rHTIKor MeXaHH3Ma je 3Ha'lajHo seha H 0)];Ta'lHOCTH BoljelDa onrosapajyher xpyrounanorMeXaHH3Ma, qaK H KMa ce He Y3MY Y 063HpHeTaQHOCTH BoljelDa xoje rrorasy 0)]; TOJIepaHUHje)J;y)KHHa xpyrax 'lJIaHOBa H nojasy sasopa y3rJI06oBHMa.Watt OB CJIO)KeHH rHIIKH MeXaHH3aM (CJI. 46) peanasyjeyjezrao HTpaHCJIaTOpHO noaepaa,e xnaaa y paBHH, jepCBe rasse aosoyseneaor snaaa HMajy HCTa noxepaaa ypaBHH.

4.3aKJbyQaKY OBOM parrycy aHaJIH3HpaHe KapaKTepHCTHKe xperarsaHeKHX rHTIKHX rroJIY)KHHX xeraopoyrnoaa, ca3rn060BHMay 06JIHKY sapesa, sa peanasauajynpaaonamsjcsor BoljelDa. Tanxa norryscaaqeTBOpoyrJIOBH pa3BHjeHH cy xao aHaJIOrHe xormjerr03HaTHX pemetsa xpyrosnaaax rroJIY)KHHXxeraopoyrnosa.Hajrrpe CMO H3BpmHJIH npopasya nouepaaa soheaera-ise H aHaJIH3Y aanoncxor craaa xopacrehanporpaxcxn naxer ANSYS. O)];pe)];HJIH CMO OIITHMaJIHe

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rigid-body single compoundmechanism compliant compliantmechanism mechanismRoberts 0.8 8.1 0.009Watt 1.8 3.1 0.039

These compound compliant mechanisms can provideconsiderably better guiding accuracy than respectivesingle compliant mechanisms (Table 4). The guidingaccuracy of the compound compliant RobertsQe6bImeB and Watt compliant mechanism is alsoconsiderably greater than guiding accuracy of respectiverigid-body mechanism, even if the guiding inaccuracy,caused by the influence of the rigid link lengthtolerances and clearance in the joints, has not been takeninto consideration.The compound compliant Watt mechanism (Fig. 4b)realizes at the same time translating planar displacementof the new link because all the points of the introducedlink have equal planar displacements.

4. ConclusionIn this paper we have analyzed the motioncharacteristics of some compliant four-bar linkageswithnotch joints for rectilinear guiding. The compliant fourbar linkages have been developed as the counterparts ofwell-known rigid-body four-bar linkages.Firstly, we have calculated the guided pointdisplacement and stress analysis using ANSYSSoftware. We have determined optimal dimensionsof


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,1lJIMeH3Hje rHIIKl1X MeXaHH3aMa y l.\HJbY )],06HjalhaHaj60Jbe Moryne TaqHOCTH sobea,a (MHHHMarIHOroncrynan,a OCTBapeHe 0)], rasae npaBOJIHHHjcKenyraise), a na MaKCHMaJIHH HanOHH casajaa,a 6y)l,yMalhH 0)], casojae xspcrohe.EKCIIepHMeHTaJIHa nposepa rroscepan,a soheae rasxenspahennx rHTIKl1X MexaHH3aMa [5,12] onroaapana jepe3yJITaTHMa )],o6HjeHHM nosrohy nporpasrcsor naxeraANSYS UITO 3HaqH zra ce osaj rrporpaxcxa naxer MO)l(eKOpHCTHTH sa npopasya nosrepan,a rmrxnxMexaHH3aMa.HaKoH rora CMO H3BPIIIHJIH npopaxya noxeparsasohene ra-rxe, MaKCHMaJIHHX aanoaa casajaa,a HKoe

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Gipki Poluzni Cetvorouglovi Za Pravolinijsko Vodjenje