Dynamic Modeling of a Generalized Stewart Platform by Bond Graph Method Utilizing a Novel Spatial Visualization Technique

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1 eol eew of ehl ee... ol.. D oel of eele Sew Plfo Bo ph eho Ul Noel Spl slo ehqe Đh Yılı sf. Öülü Ahe Sğılı As hs ppe epeses oel of eele sew plfo plo Bo ph eho wh ew spl slo eho he se-spe epeseo of he eqos of he sse. D oel les ll he s effes le oo s s well s he sos fo he jos. ollow oel of o sse of se fo of hese wo s oplshe. e DC oos e le e oele s he o sse. Se oell sse osss of hh ole oe fo eoe ole osop foes esl ee sl pole se l ople e elees s esse oseqel sse se-spe eqos e pesee. A spl slo eho s eelope se o lss eo Bo ph eho e o he lk of epese oell ke os of he sew plfo ehs s lss eo o-ph slo. Coph 8 Pse Woh Pe S..l. - All hs esee. ewos: Sew Plfo Bo ph Sse Ds Spl es Se-Spe { P} & & & p B λ Λ S.... [ ] [ ] Noele Uppe plfo ooe sse Uppe plfo le eloes Uppe plfo l eloes e eloes of he le os Al eloes of he le os s of ppe plfo s of he lowe plfo Ale ewee ppe oeo pos s of ppe plfo s ooe sse Ale ewee lowe oeo pos s of lowe plfo s ooe sse elo of ppe oeo pos ffes of l elo of ppe plfo o he le eloes ffes of le elo of ppe plfo o he le eloes l el so elee oes eee os oes eee os eo oe of ppe plfo o les eo foe of ppe plfo o les osopl oes of ppe plfo. oo he oels of pllel ehss e oe ople h sel ehss ese of he lose-fo se. Neeheless oels e po fo he ool of pllel ehss. he sew plfo s s-eee-offeeo ehs wh wo ples oe s lel e les hs fs popose s flh slo 9 D. Sew s []. pplos ele o phsl slo of spl oo hs ee p o elo. Pese s eos o folo of eele sew plfo s Bo ph eho wh spl slo ehqe. Bo-ph eho hs ee eslshe s ew ppoh o oel le ool os l sses Pof. e Pe 9 whh ee os e le o efe he ee flow ewee he phsl elees of sse. Se s phl ppoh esl eqos e se-spe fo he eho s sh fow el fo follow ool es poles. esehes he woke o Bo ph oel of ehl sses. efeee [][] eelope Bo ph ehqes fo hl eho heo sses. efeee [] se opehese eseh o Bo ph ehqes whose esls e pplle o he oos spll o ojes. efeee [] eelope Bo ph ehqe o e lo fos oel sses wh hh eee of ole. he eho s sp eee J 7 ese J 7 Coph 8 Pse Woh Pe S..l. - All hs esee

2 Đ.Yılı..Öülü A.Sğılı se o ef he epee eloes of he sse wh eel ooes lol ooes. efeee [] se o sse oel eho of spll o ehss wh Bo ph ehqe. efeee [7] woke o oel ehl sses wh eo Bo-ph eho. efeee [8] se e lo eqos fo sol he ee sl pole o eoell ole sses. he ese s of he sew plfo ehs s sole s Newo-le eho efeee [9] whh foe-oe eqles e se o eh he se foes hoh he jos he os ss sel h les foless jos. efeee [] sole he ese s of sse l ll he l ol effes s Newo-le ppoh. efeee [] eelope oo eqos fo sse s eqos whh les ke-poel ee eqos o f he elo eleo hess of sse. A sl eqo sse s eelope s [] fo ool pposes. efeee [] pple ke eo Bo ph eho o elesop o e oe se spe folo of hs ehs sole ee sl pole e he el elees o he epee elo pos s l e so elee. efeee [][] se le ph ehqe o eee he sse eqos of sew plfo fo pee ool e he els of he ppoh he eelope hel oel wee o poe. hs s Bo ph oel of sew plfo ehs s esse l ll l ol effes. he ole oel les le oo s ll jos he sos fo. he ese kes eqos e se fo oel of he ehs.... hel oel of Sew Plfo ehs Asspos Peseo of he Sew Plfo ehs A epeel sep of sew plfo he phsl oel of eele sew plfo ehs s show.. oele ehs hs s le oos s os. h o s he o he ppe plfo he lowe plfo sphel esl jos espeel. Uppe p of he sew plfo ehs pefos follow oos: e oo lo P P P s; espeel. Coph 8 Pse Woh Pe S..l. - All hs esee oo o espeel. P P P P P p p p P P λ {P} P εp P P P B B s; γ ϑυ P B B B B {B} εb Λ B B B B. A peel Sep he Phsl oel of eele sew plfo ehs s sse h Cee of of ppe plfo s loe he o of he ole fe. Cee of of os s loe o se of he / of he ol o leh fo he lowe oeo po. el foe oe effes e elee. Be fos ol foes e pese o he sse. he pllel eo ewee os ses l eloes o eh le... es Poso of ppe lowe oeo pos e epesse wh he follow eqos P P p osλ p s λ B B [ os Λ s Λ ] qo eoes he poso eo of ppe oeo pos wh espe o ole plfo fe {P}. qo epeses he poso eo of lowe plfo oeo pos wh espe o se fe {B}. Uppe oeo pos e epesse wh espe o he se fe lpl wh he oo [ ] υ ϑ υ s ϑ s γ s υ γ s υ s γ γ s ϑ υ s υ ϑ υ γ s υ s ϑ s γ s υ s ϑ γ υ s γ ϑ s γ ϑ γ s ϑ whee os ss e fos. q p o le eos le lehs e epesse he es of ppe plfos poso les. S q S U eos lo he les e epesse le eo he le leh. eol eew of ehl ee ol..

3 Đ.Yılı..Öülü A.Sğılı s S / 7 e elo lo he les e efe s s S 8 whee S q 9 A lso l elo of he os e epesse s s S. e Bo ph oel of Sew Plfo ehs slol ool eloes lo he os e epesse he es of ppe plfo eloes. s s [ sq sq sq sq sq sq s s s ] s q sq sq sq sq sq sq sq [ ].. [ ].. sq sq sq sq s s [.. ].. s s he l elo of ppe plfo lples he fs seo h ols of se s he le elo of ppe plfo lples he foh ffh sh ols of. e eol o ph oel of he ehs fo oe le whh s oe fo s e.. oplee oel eh pllel ee pos he ee os eh le hs ffee slol ool eloes. A ew oel s eelope o es he eloshp ewee he ke se of he sse he phsl oel.. shows wo elo les of eh le whh e epesse wh se ee os s ew ke ppoh. Ass wo s ee pos wo eol effo le e o hese ee pos.. ef se of. epeses oo eo oph of wo s ee os. he h se of. ee os ee pos e ssoe oe ee o ew ople eo o-ph s eslshe. he h se of. epeses wo s ee pos wo epee ee pos.. po shows oe oe s ee pos. he ee ssoe wh flows fo po o po s he ee ele o he flows fo he ohe po o he ohe po.. B wo s ee pos oe po. e eo o-ph oel fo oe le of he sew plfo ehs. B epese wo s ee os oe qos e show s [ ].... [ ]..... Cople ke eo o-ph oel of he sew plfo ehs Coph 8 Pse Woh Pe S..l. - All hs esee eol eew of ehl ee ol..

4 Đ.Yılı..Öülü A.Sğılı f wo s ee pos oe eh ohe oe ee po hs se e show s.. h se of. llses eelope ople eo o-ph oel he oe o he lef se epeses s lssl ppoh. Now s possle o show oell ke oel of he sew plfo ehs s ople ke eo Bo ph eho... D Bo ph oel of Sew Plfo ehs Ah he phsl elees of he sse o he ke oel Bo-ph oel of sew plfo ehs e oe. eol Bo-ph oel of he ehs fo oe le s show.... [ ].... P [ ].. P. eol Bo-ph oel of ehs fo oe le.. Dee Csl Solo Whe wo o oe el elees e he o po sse se les eoe epee hs ses ee sl pole. hs es epee eloes of hese elees eoes epee eloes whe el elees he hs ses ee sl pole o he sse. hs pole esls pl ffeel eqo se el poles solo. hs pole e sole sfo el elees of epee eloes o he pos of epee eloes. heefoe el elees shol e ee o he pos of epee elo pos s l e so elee. Depee eloes epee eloes el eloes of he sse shol e efe efoe e he sse. slol ool elo of les e hose s epee eloes heefoe ppe plfo s slol ool eloes e hose s epee eloes. All epee epee eloes e hose s el eloes. Depee eloes e epesse s q s elee. heefoe q s elee. epee eloes e efe s q el eloes e epesse s q q 7 q he eloshp ewee epee el eloes s e efe s q q 8 All el elees of he sse shol e efe wh sle e efoe o l el so elee. el elees shol e e s el elo. he l el he so elee e epesse s [ ] [ ] [ ] [ ] 9 [ ] [ ] he ee of elo s eee o lle he so elee. s sefl w o ee hs slo of oplee oel of he sse. Afe e he el elees o wo pos o ph of he sse s show [.. ].. [ ] JS : J Bo-ph oel of sew plfo ehs fe e he el elees J J J s. 8 Dele ew of oe ole o elee Coph 8 Pse Woh Pe S..l. - All hs esee eol eew of ehl ee ol..

5 Đ.Yılı..Öülü A.Sğılı. 7 shows he oplee o-ph oel of ehl p of he sse. he oso foes o he plfo s epesse oe ole o elee.8. he el elees whh e show. 8 e efe he l el.. 8 flow eqos e epesse s Whee. he o of he sse s se o le DC os whh e hose s les of he sew plfo ehs. h le oo s oe o ole plfo sphel jos s oe o he so plfo esl jos. Coplee o-ph oel of he ehs fo oe le s show. 9 fe he o p. he ol effe o les ppe plfo e oele effo soes he o ps of he les e oele effo soes. 9. h se of he pe shows he le oo he lef se shows l oo of he le... oel he Ao ehs e DC oo JS : J.. [ ].... Sf. os [ ].. s S.s f Y s e S e e S f p. 9. Bo-ph oel of sle le of he sew plfo ehs fe he o p. SYS SA-SPAC QUAONS Se eqos e epesse s [ ].. he ose lw of he o elee e epesse s he h se of he eqo s ee wh he es of epee les whh s e epesse wh he es of se les o f se-spe Coph 8 Pse Woh Pe S..l. - All hs esee eqos. o he pllel jos of he ehl p of he o-ph oel. 9 e eqos e oe s 7 eqo 7 es e effo les of he o elee whh e llse. 8. Ope fo of eqo e epesse s.. eol eew of ehl ee ol.. p 8

6 Đ.Yılı..Öülü A.Sğılı Coph 8 Pse Woh Pe S..l. - All hs esee eol eew of ehl ee ol ope fo of eqo 7 lso epesse s.... p.. he.. e eqo 8 shows he fs ow of o. e foes le oes e kow les of hese eqos. hese kow les e fo w he ose lw fo ee pos. All kow les shol e epesse he es of se les. e oes e e s os os.. e foes lso e e s.s s 7 A foe of he le s s lso kow le eqo 7 e epesse s he o-ph oel s e 8 whee s s. B w he s s eqo 8 foes e epesse s.. e 9 o eqos 7 8 es e epesse he es of se les. p

7 Đ.Yılı..Öülü A.Sğılı Coph 8 Pse Woh Pe S..l. - All hs esee eol eew of ehl ee ol.... e qos shol e pl o eqo. hese eqo sees e epesse o s U D C B A 7 qo 7 epeses he se-spe eqo fo sew plfo ehs.. Colso D hess of ehl sses ke po ple fo effe ool. Pllel ehss espell sew plfo ehss he ople sse s e opleel ole. heefoe he pese s kes s of eel sew plfo ehs e oe Bo ph eho s oel slo ehqe ole se-spe epeseo of he sse s s eelope. A po pole po of o eqos s he possle ee sl pole. f hee s see ee sl pole llos el poles eos o whe sl he sse. hs sfo el elees of epee eloes o he pos of epee eloes ee sl pole s sole. A he e of he s se-spe oel of he ehs s poe. Appe A B C ]... P P

8 Đ.Yılı..Öülü A.Sğılı Coph 8 Pse Woh Pe S..l. - All hs esee eol eew of ehl ee ol.. D [ ] e e e e e e U

9 Đ.Yılı..Öülü A.Sğılı Coph 8 Pse Woh Pe S..l. - All hs esee eol eew of ehl ee ol.. p

10 Đ.Yılı..Öülü A.Sğılı Coph 8 Pse Woh Pe S..l. - All hs esee eol eew of ehl ee ol.. s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s os os os os os os os os os os os os os os os os os os os os os os

11 Đ.Yılı..Öülü A.Sğılı os os os os os os os os os os os os os p e p os.. e Akowleee hs wok s sppoe he Sef eholol eseh Col of ke UBA -9. efeees [] Sew D.A Plfo wh S Deees-of-feeo Poees of ehl ee P ol.8 pp [] opp D.C. osee.c. oo o Phsl Sse Ds w ll. New Yok 98. [] ho J.U. Slo Bo phs: oo o phl eho Spe-el Bel 99. [] ols D. A Sh. A Bo ph oel opo Sesos Aos A ehle Ds o Deelop Coolles o ehle Sfe Jol of he kl se ol [] Alle.. Dowsk S. ehss s Copoes of D Sses: A Bo ph Appoh AS Jol of ee fo s ol. 99 No. pp: [] Bos A.. eeo.j.. ol pl he Bo ph oel Slo of e ehl Sses Jol of kl se ol. 9. / pp [7] hehol.p. Woo J.D. eo Bo ph Alss of ehl Sses sos of AS ol. pp [8] opp D. Appoh o Dee Csl Bo ph oels of ehl Sses Jol of he kl se ol [9] Do W. Q. D. Y D. C.. ese D Alss Slo of Plfo pe of oo Jol of oo Sses ol.. pp [] Dsp B. hj.s. Close-fo eqos of he eel Sew Plfo hoh he Newo- le ppoh. ehs he heo ol.. 7 pp [] e Z. es. S. ee J. D. Coll.. O he D oel e Alss of Clss of Sew Plfos oos Aooos Sses ol. 9 pp []. el. Dwso D. W. ews.. oel ool of Sew plfo plo AS DSC ol. Cool of Sses wh e D oels 99 pp [] Sl A. Bool.. Ol.. oel o Ce Bo-ph eho Alss of Dl Beho o Spe Alss P Nole Ds ol. pp. 7-. []. Dlkos P. Chkos. Ppopolos Deelope of oel-se pee Coolle fo leohl Seos.A. eh. oos Applos ACA Pess 98-. []. Dlkos. Ppopolos A oel-bse pee Cool of -of leohl Sew Plfo Poees of he ope Cool Cofeee eee 7 pp. 7-. Ahos foo Yılı ehl Ues ehl ee Depe 9 Besks sl/ke : 9--9 e-l: Coph 8 Pse Woh Pe S..l. - All hs esee eol eew of ehl ee ol..

12 Đ.Yılı..Öülü A.Sğılı Yılı ehl Ues eho ee Depe 9 Besks sl/ke : 9--9 e-l: Yılı ehl Ues ehl ee Depe 9 Besks sl/ke : 9--9 e-l: Đh Yılı ws o o/ke o h of As. e eee hs.s. eee Yl ehl Ues of sl/ke o he op of s of sew plfo ehss o e 7. e s el wok o pllel ehss oehs el ehles.. Yl s el he eseh/eh sss Yl ehl Ues s wok ows hs Ph.D. eee. sf. Öülü ws o sl/ke o h of J 99. e eee hs.s. eee Yılı ehl Ues of sl/ke o ehle s o e 99 oplee hs Ph.D. ses o sl oos Oho Se Ues of Cols Oho/USA o e. e plshe seel ppes o he ops of ehle s ool s of oo e sses sl oos. e s el wok o pllel oo plos ooos el ehles oo sses. D. Öülü s el he e h of eel eslshe eho ee Depe of Yılı ehl Ues. Ahe Sğılı ws o /ke o 8h of Noee 9. e eee hs.s. eee Yılı ehl Ues of sl/ke o he es o e 988 oplee hs Ph.D. ses o he s of elesop o es Yılı ehl Ues of sl/ke o e99. e plshe seel ppes o he ops of o e s s el wok o pllel oo plos w ffes o seel osos s of eleo sses. D. Sğılı s el he fl of ehl ee Depe of Yılı ehl Ues. Coph 8 Pse Woh Pe S..l. - All hs esee eol eew of ehl ee ol..

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