Coordinate System for 3-D Model Used in Robotic End-Effector
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1 AU JT 8(: 8 (Apr Codnate Sytem f D Model Ued n Robot EndEffer ulfqar Al Soomro Shool of Advaned Stude, Aan Inttute of Tehnology Pathum Than, Thaland Abtrat Th paper reve the onept of odnate ytem on new D model ued n robot EndEffer A very bref degn of th model ha been mentoned and hown Th model ued alulate the unnown appled fe, but here t nemat onfguraton explaned through t odnate ytem Frt loal odnate ytem f eah ndvdual leg drawn Then thee loal odnate are mapped n global odnate ytem Thee global odnate are haped n unt ver by onept of rotaton matrx ung ertan trgonometr dentte Th paper refrehe the geometral entaton of odnate ytem through onfguraton reognze the operaton of robot model Keywd: Poton, entaton, loal odnate ytem, global odnate ytem Introduton In der deal wth the omplex geometry of a manpular odnate frame have be affxed varou part of the mehanm and the relaton hp beten thee frame derbe repreent poton and entaton of rgd obet (Crag 989 The followng eton brefly derbed varou onept and onventon that would eventually lead ward fmulaton of odnate ytem Derpton of Poton A pont n pae an be derbed wth Poton er Hover, th eleton mut be defned relatve a odnate ytem Derpton of entaton In der defne the entaton of a body, a odnate ytem attahed the body, and th odnate ytem then derbed relatve a referene odnate ytem (Wolovh 987 Atually by expreng odnate of {B} n {A}, are proetng every unt ver of {B} on eah unt dreton of the referene odnate ytem {A} Thee eld a matrx, eah element of whh dot produt of a par of unt ver Th matrx alled a rotaton matrx Robot are lafed adng the type of ax movement needed omplete the ta The fve lae of ax movement alled odnate ytem n whh arm move through pae aung ertan ax movement Thee movement are dentfed a arm geometry (Dougla 98 Mot preentday robot manpular are uually lafed nematally on the ba of the arm frt three ont wth the wrt beng derbed eparately (Sandler 99 The maty of thee manpular fall n one of fve geometr type artulated (RRR, pheral (RRP, SCARA (RRP, ylndral (RPP, and Cartean gantry (PPP, where R denote revolute ont and P a prmat ont The man onfguraton n whh robot operate (Mau and Allup 98 A bref derpton of eah follow: Cartean (Retangular Codnate: Three dtane, n whh the wpae reemble a retangle, defne t Cylndral Codnate: It defned by two dtane and an angle, n whh wpae reemble a ylnder 8
2 Spheral Codnate: It defned by two angle and a dtane n whh wpae reemble a phere Jonted arm Codnate: It ombne the feature of other ytem A mple odnate ytem ha been appled upon a newly propoed D model ued n robot manpular The nemat of a mple odnate ytem ha been appled upon a newly propoed D model ued n robot manpular The nemat onfguraton, through whh a robot nown and onerned operaton, Cartean Retangular odnate ytem Methodology Adng Cartean odnate ytem, whh appled upon the propoed D robot model, t ha alo apablty move n,, dreton In th proet, t wll determne the odnate ytem at elevaton a ll a at p of the model Here t determne the loal odnate ytem of eah plane along wth t poton and entaton (Soomro Then t an tae odnate of any one leg a referene f global odnate ytem Thu loal odnate ytem onverted n global odnate ytem n ubequent eton Loal Codnate Sytem At Plan ew: the eth of model hown n fga, the omponent of the leg along loal odnate are wed a followng RCo 987 Co R Sn 987 Sn Where R Dfferene of plate radu and 987 mm Inlnaton of leg wth loal xax Where z z y y x x L L L L Length of leg 97 mm π/ π/ Fg Plan eth of odnate At Elevaton: l Sn l Co Sn l Co Co Thu LCoCo(LCoSn(LSn Global Codnate Sytem In th odnate ytem, tae enter a referene and orelate other loal odnate t Thu entaton hange wth repet t gvng great trgonometr analy Hover a new equaton et determne dfferent nemat term f further onveron and analy Tranfmaton of Codnate ytem Here loal odnate of eah leg onverted n global odnate ytem Followng the repreentaton of the odnate relaton through matrx ytem Thu fnally unt ver are extrated n hape of relevant Fg Front vew of odnate 9
3 Above Seth drawn fro [ ( ( [ ( ( [ Thu [ ( ( [ ( ( [ (9 (9 Fg ( ( ( Thu ( ( ( Fg : ( ( ( ( ( Thu ( ( ( Fg [ ( ( [ ( ( [ Thu [ ( ( [ ( ( [ (9 (9 Fg ( (
4 Fg Thu [ ( ( [ Thu [ ( ( [ ( ( [ (9 [ ( ( [ ( ( [ (9 Fg [ ( ( [ (9 (9 [ ( ( ( ( [ ( ( In above analy onverted loal odnate ytem n global odnate ytem f general alulaton of nemat term Here entaton of the loal odnate ytem hanged wth repet global odnate ytem Reult and Duon There are numerou way; one an dfferentate one robot from other Robot dffer due far uh a degreeoffreedom, type of wrt and endeffer, nemat onfguraton, and wng range wpae Eah of thee an be derbed brefly n ueedng paragraph Here have appled the nemat onfguraton dfferentate a robot The propoed D model poee x leg oned by prmat ont n mddle wth prng nde and ftted wth two dfferent dameter platfm by pheral ont Botm plate fxed whle upper plate moveable a hown n Fg The ba purpoe of th model determne the unnown appled fe through nown tffnee and ompreve dplaement Here odnate ytem appled onvert the loal dplaement of ndvdual leg n global odnate ytem a hown n Fg loal odnate ytem a mple geometral entaton ha been appled An gn of plane taen enter f onveron from loal odnate ytem n global ytem Thu unt ver are obtaned by ung the onept of rotaton matrx In th way global odnate ytem ganed n hape of unt ver by puttng the ued trgonometr dentte n loal odnate ytem
5 Conluon In th paper, an attempt ha been appled reognze the type of nemat onfguraton on a new D model, whh ued n robot endeffer f arryng obet by t manpular The truture of the model ha been dued very brefly and t degn hown n Fg A th model ued meaure the appled fe pratally theetally Sne our model belong Cartean odnate ytem, o t loal odnate of eah leg onverted wth repet x, y, z axe Then thee loal odnate trgonometr ymbol are ued f global odnate ytem at enter Thu unt ver are obtaned by rotaton matrx n global nemat odnate ytem Fg Plan vew of Model wth entaton Fg Tranfmaton of loal odnate n global odnate ytem Referene Crag, JJ 989 Introduton Robot, Mehan and Control, nd ed Addon Weley, Bon, MA, USA Dougla, MR 98 Robot: An Introduton Bren, Bon, MA, USA Mau, R; and Allup, R 98 Engg: Foundaton of Robot Wley, New, N, USA Sandler, B 99 Robot: Degnng the Mehanm f Aumated Mahnery Prente Hall, San Dego, CA, USA Soomro, A Degn modelng and mulaton of robot endeffer f ngrap fne manpulaton ung parallel omplant mehanm MS The, Natonal Unv of S and Teh, Rawalpnd, Patan Wolovh, WS 987 Robot: Ba Analy and Degn, t ed Holt, Rhnehart and Wnn, Autn, Texa, USA
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