mchie desig Vo75 No IN 8-59 47-54 ON HE YNHEI OF PAIAL RACK MECHANIM: ON HE MAHEMAICAL MODELING ANALYICAL AND 3D OFWARE CREAING OF HE FACE RACK DRIVE EEH Emii ABADJIEVA * - Vei ABADJIEV Isie o Iomio d Commicio echoogies oi Bgi Isie o Mechics oi Bgi Peimi oe Received 535; Revised 865; Acceed 65 Absc: i hee-ik ck mechisms e ied o eie oio somio o oe o he movbe iks iio io eciie somio o he ohe ik ge ck he hos o his sd e eboed he commo kiemic heo oieed o he shesis o hee es ck dives- coic cidic d ce oes A KOD 94 sd is eseed h es he is e o bove meio ck dives he secod e o ck ses is seci cse o he iodced ed ck dives I is obied eive esi om he show i 4 sd his wok eses heoeic sd o he hid e ck mechisms he eseed hee icie o he shesis o mesh egio is eied b deveoig deqe mhemic mode Hee e show goihms ic descibig cive ooh sces o oig ik d mesh egio he ess which e shesis o si covoe Achimede d ivoe ce ck dives e ised ghic Ke wods: mhemic modeig shesis ck mechisms ce ie heicoid INRODCION he somio o he oio moio io eciie sios is dme e moio somio i he echiqes his c deemies he eseches iees i diee e mechic ssems which desigio is o ese he e meioed moio somio s i qiive d qiive ems i ck mechisms occ seci ce mog hese mechisms [] hese dive ssem es c be cosideed s seci cse o si hee-ik mechisms somig oios bewee ied sed es whe: he mbe o he eeh o oe o he movbe ik is icesed d iiiim wiho iceg he mbe o he meshed ooh sces bewee he med iks; he is o oio o he e meioed ik is disces i iii d is moio is somed io eciie sio; mbe o he eeh d he e o moio o he secod movbe ik emi chged; oig ik wih iie mbe o eeh wi c iio d he ik wih edess mbe o eeh eiig eciie sio wi c i ge ck his sd eses mhemic mode o shesis o mesh egio [ ] o si ck ge se i which he cive ooh sces o he iio e s o ce ie heicoids ooh sces o ge ck e heoeic coged wih he hose o he iio he oio is o he iio is o-ohogo sed wih he diecio o he eciie sio o he ge ck YNHEI OF PAIAL RACK DRIVE WHICH ROAING LINK HA FACE LINEAR HELICOID Whe shesiig si ck mechisms wih ie coc i is evide he ecessi o coo hei qi i he whoe mesh egio ch oches o shesis obems eqie deqe mhemic mode he kiemic scheme o sch mechism is show i Fig [ 3] he eso is h he seciic geomeic d kiemic chceisics o he mesh egio deed o is osiio i sce d he geomeic chceisics o he oo sce J geeig he ks i i = his mhemic mode is bsed o he secod Oivie s icie d he ik eomig oio d hvig sces is chose s geeig ik Geeed sces beog o ik which eies eciie sio he shesis o si ck dives bsed o he secod Oivie s icie ivoves sovig o wo mi sks: hesis o he ooh sces o he oig movbe ik which e ideic o he isme sces J ovig his mhemic obem ovides he echoog o mcig he oig ik o he ck dive hesis o he mesh egio d deiiio o he dimesios d ocio o he mesh egio o he sce o cio his sk eies he geeio o *Coesodece Aho s Addess: Isie o Iomio d Commicio echoogies Acd G Bochev bock 574 oi Bgi bdiev@gmicom
Ceig o he Fce Rck Dive eeh; Mchie Desig Vo75 No IN 8-59; 47-54 cive ooh sces o he movbe ik o ck mechisms which eom moio sio he shesis o hese es o mechic smissios i ccodce wih he secod Oivie s icie eds o sovig wo mi sks: shesis o he cive ooh sces o he bse isme movig ik - ce wom d shesis o sce o cio/mesh egio o he sdied mechism he cive ooh sces o he bsic ik e ce ie heicoids Fig Kiemic scheme o si ck dive wih ie coc bewee oohed sces d shesied g mesh egio MR: i -iio ge is he oig ik; i -ck ge is he ik o sioeciie; i - sce o k o iks i ; - oio veoci o ik i ; V - veoci o eciie sio o ik i ; V cos -veoci io o moio somio; V - sidig veoci; A - cio sce; D - coc ie; L - ogidi ie o Geeig o cive ooh sces o he bsic movbe ik he ocess o ce covoe heicoid 48 = geeio is sdied i coodie ssem O I is ised i Fig whee he geeio o he ce heicoids wih cos ich is show [ 4] he geei ie L does o s he is O d cocdes wih i ge O d he smes disce bewee he L is he is he dis-veco o he dieced cide o which he codiio cos is ied o he eie ocess o ce covoe heicoid geeio he geeio o he is i es o he sed gei eed o he dieced cide C heic moio o he ie L wih heic mee cos he geei L ies i e gei o he dieced cide C sed hee d beow ide obis ves = : is eeed o he mees eed o he ce ie heicoids geeio o he mees eeed o he ce heicoid Ps o sces d c be sed s cive ooh sces o he ce wom ce hob esecive he cive ooh sces e e o he O hа he cive ooh sces I his sd i he ocess o = geeio o simici s we s om echoogic cosideios eed o he e ge cig is cceed C C ie d cos Le oi N beogs o he ie L h geees b is heic moio he heicoid he o he veco eqio o is wie: whee is he ve o he sed gei heic moio o he ie L ; e ideede coodies o he eqi is wie i he coodie ssem d i is obied: bsiig i R co he eqios ssem c be wie s: R R R 3 he eqiies 4 c be cosideed s ssem o eqios descibig cidic heicoids wih i heic mee cos 4
Ceig o he Fce Rck Dive eeh; Mchie Desig Vo75 No IN 8-59; 47-54 49 Fig Geomeic scheme o ce heicoids geeio Fce ivoe heicoids geeio As i hs bee meioed he mi chceisic o he sces whose geei is sigh-ie is hei mee o disibio he mee o disibio is deemied whe we ese 4 s oows: R 5 Hee } { c be cosideed s eqio o he dieced heic ie sied o he dieced cide C d } { is dieced veco o he geei ie L I is obvios h: 6 I is kow [5] h he mee o disibio o he ce ie heicoids is deemied b g he oowig eio: 3 3 3 3 d d d d d d d d d h 7 he o he cocee cse e sime somios om 6 d 7 we obi: co h 8 Fce heicoid descibed b eqios is deveobe sce whe he oowig codiio is ied: = co h 9 Obvios he codiio 9 is sisied i Hece o he eqio o he ce ivoe heicoids we c wie he oowig: Fce Achimede heicoids geeio he ce Achimede heicoids e obied whe he geei ie L ses he is o he hei O ie I his cse o he eqios descibig his heicoid e g we c wie: Hee he mee o disibio is co h I he eqios ssem is ge which he om veco o he i e O L cocdes wih he is O I we oe he ge omed bewee e O L d he e O wih he he eqios ssem is wie s: ] [ ] [
Ceig o he Fce Rck Dive eeh; Mchie Desig Vo75 No IN 8-59; 47-54 Eimiio o he decig ois om he ce heic sces 5 I he ssem descibig ce covoe heicoid is eseed s: 5 o he cive sces d he om veco o hem wie i hei coodie ssems s oows: O 3 he o he om veco o his sce bi oi N we c wie: Hee 4 d gei o he oi N e ve Whe we se he eqio se he oecios o i coodie ssem e eceived s: 8 A [ [ A A] A] 5 he mgide o he veco is esecive: A 6 I d e sbsied i 5 d 6 he he eseio o he om veco o he oi N is ic obied whe is ce ivoe heicoid d ce Achimede heicoid Fom 5 d 6 i is obvios h he ce covoe d ce Achimede heicoid e cosised o b ois o gei coc N ce he codiio is ws ied I he ce heicoid is ivoe oe d coseqe o is oi he oowig codiio is eied: 5 7 he i hese ois o I cod be esi esbish h his codiio is ied o commo ois o he geei L d he bsic cide C 3 hesis o he sce o cio/mesh egio o he si ck dives Fce covoe ck mechism he shesis o he sdied e ck dive is eied i ccodce wih he secod Oivie s icie wih esec o he give smbos i Fig 3 [] Le ese he eqiies d Fig 3 Geomeic-kiemic scheme o ce ckmechism: - ce heicoid; - cive ooh sces o he ooh ck; - veoci veco o he oig ik i ce wom; V - veoci veco o he eciie sio o he ik i ooh ck; O - sic coodie ssem; O - coodie ssem im coeced wih he ik i ; O - coodie ssem im coeced wih he ik i ; - meshig mee whee whee K K K d 9
Ceig o he Fce Rck Dive eeh; Mchie Desig Vo75 No IN 8-59; 47-54 he eqios 8 d 9 e wie i he ied coodie ssem O ie: M L K 6 he cio sce o he sdied ck mechism see Fig 4 hs he oowig ic e which is cosised o he eqios d 6: Hee M L K 7 Whece whee K K 3 Fo he sdied cse he eqio o meshig is wie s [ 6]: V V V V 4 he sidig veoci veco bi coc oi o he coc ie D bewee d is V i k 5 whee i k e ge ve o he coodie es o O ; is he veoci io o he sdied ck mechism he om 3 4 d 5 we obi he eqio o meshig s: Fig 4 i ce covoe ck dive wih veoci io 73 ; mbe o he eeh : а ce covoe igh-hded heicoid 5 mm; [ 6] [48 8 ] ; b ce covoe igh-hded heicoid mm; [ 6] [48 8 ] ; c egio o mesh egio MR MR ; d mesh he ooh sces o he ooh ck e deemied b he eqio ssems: M L V V V L V V V V whece V V 8 5
Ceig o he Fce Rck Dive eeh; Mchie Desig Vo75 No IN 8-59; 47-54 M L E 33 he eqios o cive ooh sces e obied om 8: K 9 Fce Achimede ck mechism Aic desciio o he cio sce see Fig 5 o he ce Achimede ck mechism is obied b ssem 7 sbsiig whece K i e: Fom 9 wih simi sbsiio he ic desciio o he ooh sces o he ooh ck coged wih ce Achimede heicoids is obied 3 Fce ivoe ck mechism he eqios o cio sces d he cive ooh sces see Fig 6 o he ooh ck o ce ivoe ck mechism e obied om ssems 7 d 9 b kig io cco he codiio o deveome o he ce ivoe heicoid K ie: Fig 5 i ce Achimede ck mechism wih veoci io 73 ; mbe o he eeh : а ce Achimede igh-hded heicoid 5 mm; [ 6] [48 8 ] ; б ce Achimede igh-hded heicoid mm; [ 6] [48 8 ] ; c mesh egio MR ; d mesh egio MR Fig 6 i ce ivoe ck mechism wih veoci io 73 ; mbe o he eeh : ce ivoe igh-hded heicoid mm; 5 73 [ 6] [48 8 ] ; b ce ivoe igh-hded heicoid 73 mm; [ 6] [48 8 ] ; c mesh egio egio MR MR ; d mesh 3 3 5
Ceig o he Fce Rck Dive eeh; Mchie Desig Vo75 No IN 8-59; 47-54 33 Fo he cse o ce Achimede ck dive he eqio 37 is o he om: P P P P 38 34 Asis o he geome o he cive sce o he ce ie ck mechisms o sd ic he geomeic chce o he cio sce/mesh egio o he ce covoe ck mechism he eqio 7 is eseed i coodie om Fhe he e idees wi be omied i he sd Fom he hid eqio o 7 we obi []: ie: Le s sove he is wo eqios o 7 ogehe wih he eqio o meshig: K K 34 Le we sbsie d i he secod eqio o 34 d sove he obied qdic eqio he B K 35 B 4 K K o moe P P 36 whee P K P K K We mi he is eqio o 34 wih d he secod - wih d e smmiig we obi: P P P P 37 Eqio 37 descibes cidic sce wih geeices e o he is O d i is he cio sce o he ce covoe ck mechism whee P P he eqi 38 descibes ic cidic cio sce o ce Achimede ck mechism wih geeices e o he is O Aogic he cio sce o he ce ivoe mechism is obied b eqio 39 whe i eqi 36 is ke io cco he codiio o deveome o he cive ooh sces o he ce ivoe wom 39 his is he eqio o e e o he is O 3 CONCLION he ese sd gives bie sve o he och o sed desig mesh egio mhemic mode o ce si ck smissios shesis he eseed hee mhemic mode is oieed o he shesis: o he ce ie heicoids he cive ooh sces o he oig ik sce o cio d he cive ooh sces o he secod ik eiig eciie sio goihms d come ghics o shesis d desig o he ce si ck mechisms e eboed he discssed bove mechisms e sibe o imemeio s cos i vios ieds o echiqes O ic iees is hei icooio io he coscios o bio-obos [7] s eive o si hebooid ges [8] ACKNOWLEDGMEN he hos ge ckowedge he dig b oec AComI: Advced Comig o Iovio o he FP7 Cci Pogmme Resech Poei o Covegece Regios FP7-REGPO--3- REFERENCE [] Abdiev E i Rck Dives Mhemic Modeig o hesis VDM Veg D Miie GmbH&Co KG IBN: 978-3-639-445- [] Abdiev V 7 Geig heo d echic Aicios o Hebooid Mechisms D c hesis Bgi Acdem o cieces Isie o Mechics i Bgi 53
Ceig o he Fce Rck Dive eeh; Mchie Desig Vo75 No IN 8-59; 47-54 [3] Abdiev E V Abdiev H Kwski4 O he hesis o i Rck Mechisms: Mhemic Modeig d owe eeh Geeig o he Movig Liks eeh Poceedigs o he Eigh Ieio mosim KOD 4 Mchie d Idsi Desig i Mechic Egieeig -5 Je 4 Boed Hg Fc o echic cieces Novi d Fc o Mechic Egieeig Bisv 63-7 IBN: 978-86-789-65- [4] Abdiev E V Abdiev 3 Geomeic hesis o Fce Heicoids Nio Coeece Wih Ieio Piciio Egieeig Mechics -5 M 3 vk Cesk Rebik e No 77 bished o CD [5] Rshevsk P 956 Cose o Dieei Geome Ed e Pbishig Hose o echic d heoeic Liee Moscow i Rssi { [6] Livi F F Fees 4 Ge Geome d Aied heo Gmbidge ivesi Pess New Yok A IBN 978-5-857-7 [7] Weeg Zhg Demeg Che Hogbi Li Xide M Qig Che Dog D &Zhego 9 e de-aced Mi-Figeed Mechic Hd wih Mod e-adive Ge- Rck Mechism Idsi Robo: A Ieio Jo Vo 36 Iss: 3 55 6 [8] Abdiev E Abdiev V Kwski H & Moi 3 O he hesis o Hebooid Ges d echic Aicios Poceedigs o AME 3 Ieio Powe smissios d Geig Coeece IDEC/CIE 3 Pod Oego A bished o CD 54