P R A S I C ' 02. Simpozionul na.ional cu participare interna.ional/ PRoiectarea ASIstat/ de Calculator

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1 UNIVERSITTE TRNSILVNI DIN R0OV tedr Design de Produs i Robotic Simpozionu n.ion cu prticipre intern.ion/ PRoiectre SIstt/ de cutor P R S I ' 0 Vo. I Mecnisme i Triboogie 7-8 Noiembrie rov Români ISN RITIL POSITIONS ND MEHNISM SELF-LOKING ( II ) ezr DU Forentin UIUM Gbrie PÂR$ORU Technic University Gh. schi Ii bstrct: In the second prt of the pper is treted the proem of the mechnism sef-ocking. The sefocking positions re consequence of sef-ocking configurtions t the structur groups eve. t their turn the sef-ocking configurtions re noticed when sttic proem with friction is ffected by singurities. To determine sef-ocking configurtions we propose sttic nysis method using friction circes nd friction nges. The nysis of the group is presented t ength nd for the other spects of the 0// group the resuts re given in Te. We indicte the ccuus expression of the ocking prmeter nd the running conditions into n dmissie domin defined by certin dmissie vues of the configurtion prmeter. In concusions we show the utiity of the obtined resuts nd we so give six exmpes of compex mechnisms indicting the configurtion prmeters which must check up in order to ssure the mechnism running into the dmissie domin without the dnger of sef-ocking. Keywords: sef-ocking positions sef-ocking configurtions structur group sef-ocking prmeters.. Sef-ocking of the Structur Groups The sef-ocking phenomenon occurs in working domin of the mechnism imited by the ocking positions. In these positions the mthemtic mode of the sttic proem with friction hs singurities. Otherwise the rections in joints tend to infinitum when the mechnism position tends to the ocking position. Like the critic position proem the sef-ocking proem cn be fvoury pproched by id of the structur groups. Thus for ech structur group we estish the sef-ocking configurtions nd domin. Of course mechnism is sef-ocking if to t est one of its component groups sefocking configurtion occurs. To determine the ocking configurtions we wi do the sttic nysis with friction using the method of the friction circes nd nges. So the resutnt rection R r of revoute joint (Fig. is tngent to the friction circe with rdius r f = µ.r where µ is the friction coefficient nd r is the spinde rdius of the joint. f r R r Fig. R r In the siding joint cse the resutnt rection is tited from the perpendicur to the joint xis with the nge (Fig.. The ccuus of the nge- impies the existence of the two distinct situtions: If the norm rectionr r cts inside the contct zone becuse of the cernces in joint the retive position between inks is s shown in v

2 Fig. nd the nge- resuts from the retion tn =µ. If the norm rection R cts outside the contct zone the retive rrngement of the inks is s shown in Fig. b nd nge- is obtined from the eqution: b tn =µ (+ ) where b nd re the engths indicted on the R b drwing. We notice tht the sitution is more unfvoure thn the one becuse it eds to the greter friction forces. We consider tht the ppernce of this sitution is consequence of some design mistkes nd so we wi ony tke into ccount the sitution. We mention tht one of the mesures to void the sitution is the use of the degenerted forms of the structur groups. Let us consider the structur group (Fig.) the sme for the study of the critic configurtions nd et us do the sttic nysis with friction forces using the effects overp principe [9]. We consider t the beginningf = 0. We write the force eqution for the ink : F + Rr + Rr = 0 nd we determine grphicy the rections R // f nd Rr = R4r // cb. In simir wy we consider F =0 we write the force eqution for the ink : F + Rr + R4r = 0 nd we determine grphicy Rr = Rr // b nd R4 r // c f. R f r f r f ' " D F b' b" D F f ' " 4 R r R r 'f R r b'c' R r F R 4r R 4r c"f R r "b" Fig. F Fig. y grphic composition we ccute R r = Rr + Rr nd then R nd R 4 r from the force equtions written for ech ink in the hypothesis of the simutneous ction

3 of the ppied forces F nd F. nyzing the force poygon (Fig. we notice tht the rections tend to infinitum when the common tngent to the friction circes b tends to become coiner to ine b c which forms the friction nge c with the perpendicur to the siding xis. This is the ocking configurtion of the structur group (Fig. 4. The pproprite configurtion nge is the ocking nge. If the mechnism cnnot work. The domin where the ocking occurs is evidenty into critic configurtion proximity (when /) nd it my be interpreted s dittion of the configurtion due to the ction of the friction forces. For ech critic configurtion more ocking configurtion my exist ccording to the common tngent position (extern or intern) nd the sense of the nge c (Fig. 4). c) d) Fig. 4 r f In turn these eements depend on the distribution of the veocities nd ppied forces. Thus for the 4 possie ocking configurtions in this structur group (Fig. 4) the ocking nge expressions deduced from geometric considertions re s foows: r f r f + rf In Fig. 4: = rccos( ) c 0 4 r f + rf In Fig. 4b: = rccos( ) c rf rf In Fig. 4c: = rccos( ) c rf rf In Fig. 4d: = rccos( ) c. Of course it is recommended to tke into ccount the smest vue of the ocking nge which corresponds to the configurtion in Fig. 4 (for this group). ecuse running cose by the ocking configurtion is unfvoure with gret norm rections nd friction forces it is recommended tht the configurtion nge observes the condition:

4 () where is n dmissie vue much smer thn. The condition () extended to the whoe domin 0[ 0min 0mx ] eds to the retions: + sin sin 0mx 0min () In the degenerted form cse ( = 0 ) the formus () re prticurized ccordingy. In Te we present syntheticy the sefocking proem for the 5 spects of the 0// structur group.. oncusions nd Exempifiction. The critic configurtions of the structur groups re chrcterized by the fct tht in the mthemtic mode of the kinemtic nd sttic nysis without friction singurities intervene. y configurtion we men the structur group position reported to proper ink. In the cse of the 0//- group the configurtion depends on ony one prmeter suity chosen. This is n nge dopted so tht it hs the vue = when the configurtion is critic. The degenerted group-rtr is excepted from this rue. For the RTR degenerted group the configurtion prmeter is ength which hs the vue =0 when the configurtion is critic. t the sme time the critic configurtions ie t the imit of the domin in which the position proem hs re soutions. s foows the existence conditions of the structur group my be formuted thus: respectivey 0. In Te we hve presented for ech spect of the 0// group the ccuus prmeter of configurtion the critic configurtion schemes their geometric chrcteristics nd so the existence conditions of the group in the re domin.. ocking (sef-ocking) configurtions re chrcterized by the fct tht the mthemtic mode of sttic nysis with friction is ffected by singurities. The ocking configurtions re symmetric reported to the critic configurtions nd they imit the sef-ocking domin which is s proximity of ech critic configurtion. In the pper the sef-ocking configurtions re indicted nd the ccuus formus re presented for the ocking prmeters ( ). The determintion of the sef-ocking configurtions hs been ccompished bsed on the sttic nysis with friction using the method of the friction circes nd nges nd so the procedure of the effects overp. Tking into ccount tht running cose by the sef-ocking configurtions is unfvoure becuse the gret rections nd friction forces we recommend the imittion of the configurtion prmeters to certin dmissie vues bsed on the conditions: << >>.. The stte of mechnism from the point of view of the critic nd sef-ocking positions is refection of the component group sitution. If t est one group in mechnism ies into critic configurtion the whoe mechnism is in critic position. The sme observtion cn be formuted bout sef-ocking. The contro of the Mechnism Stte cn be done using the configurtion prmeters of the component groups. These prmeters intervene into the existence conditions of the mechnism in the re domin (Tb. -coumn.5). These conditions re usefu for both the mechnism nysis nd the dimension synthesis. In Fig.5 we present for exmpe some compex mechnisms used in vrious industri brnches nd we indicte for ech exmpe the configurtion prmeters of the component structur groups. We consider tht the bove-presented pproch soves cery nd systemticy the proems of the critic positions nd sef-ocking. Tht is usefu especiy for the compex mechnisms (contining more structur groups) which hve not hd n pproprite soution unti now. Fig. 5

5 RTR e) f) Fig. 5 b-f TRT References c) d). Kovcs Fr. O nou metod de verificre evitrii ocrii dtorite dimensiunior eementeor uetinu Gtii.ific i Tehnic Inst. Poitehnic Timior Tom 9() Voum Speci 964 pp.7-6. Kovcs Fr. O nou metod de evitre ocrii dtorite for-eor de frecre uetinu Gtii.ific i Tehnic Inst. Poitehnic Timior Tom 0(4) Fsc. 965 pp.-4. Drng M. supr fenomenuui de utoocre mecnismeor dtorit frecrii în cupee de trns-ie Simpozionu de Mecnisme i Trnsmisii Mecnice Timior 984 pp Drng M. Umer D. Determintion of Shutting off Zones Due to the Friction in Trnstion oupings of the Pne Mechnisms Eighth Word ongress on TMM Prgue zechosovki 99 pp.94-94

6 5. Drng M. Moise V. On the ocking of the Mechnisms Due to the Friction in the Trnstion Pirs Nineth Word ongress on TMM Mino Ity 995 pp Drng M. Evution of ritic Zones of R Dyd The Eighth IFToMM Interntion Symposium uchrest 00 Vo.I pp.9-7. Hong-Sen Yn Long-Iong Wu On the Ded Positions of Pnr Linkge Mechnisms Journ of Mechnisms Trnsmissions nd utomtion in Design Nr. 989 pp40 8. Ztnov D. Fenton R.G. enhbib. Identifiction nd ssifiction of the Singur onfigurtions of Mechnisms Mechnism nd Mchine Theory Nr pp Mnoescu N.I. Mro D. Teori Mecnismeor 7i M7inior inemtic 7i Dinmic Ed. Tehnic/ ucureti Duc. Why the Structur Group? (I) uetinu Institutuui Poitehnic Isi Tom. XLII (XLVI) Fsc pp.7-4.

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