Stffne An of ow-do e Mnto ndng the Et Defoton of Both ont nd nk IAS Hn Sng K,* hng-rok Shn,* n-ho Kng, ** Yong-Ho H, *** Hn-Sk Y, **** nd oong-soo Sh ***** * Shoo of Mehn nd Atoton Engneeng, Kngn nvet, Mn, Koe e : +8--49-67; E-: hk@kngn..k ** Robot & onto Go, Koe Inttte of Mhne & Mte, Dejeon, Koe e : +8-4-868-788; E-: jhkng@k.e.k *** Geongn Regon Innovton Agen, hngwon, Koe e : +8--64-78; E-: ong@k.og **** Eetve Deto, EM Koe o., D ***** Gene Mnge, R&D Sot ente, Wod Indte Ae Abtt: h e eent tffne n ethod fo ow-do e nto, whh tke nto ont of et defoton of jont nd nk. A ow-do e nto defned t e nto whh h e thn degee of feedo. Dffeent fo the e of 6-DO e nto, the e hn n ow-do e nto e bjet to ontnt foe we tton foe. he eton foe de to tton nd ontnt n eh b n be detened b kng e of the theo of eo ew. It hown tht the tffne ode of n -DO e nto ont of ng eted to the eo ew of tton nd 6- ng eted to the eo ew of ontnt, whh onnet the ovng tfo to the fed be n e. he 6 6 tffne t deved, whh the of the tffne te of tton nd ontnt. he ng ontnt n be ee detened b odeng the one of jont nd nk n e hn foow; the nk n be ondeed n Ee be nd the tffne t of otton o t jont n be odeed 6 6 dgon t, whee one dgon eeent bot the otton o ong the dng deton eo. B ng the et defoton n jont nd nk, the one t of e hn obtned. n, ng the eo ew to the one t of e hn, the one ve of ng n be detened. A n ee of enng the oede, the tffne of the et e nto h been ned. Kewod: tffne n, ow-do e nto, jont nd nk tffne, eo ew, tt eton. INRODION A e nto t ont of ovng tfo tht onneted to fed be b eve e hn, ed b. In gene, e nto hve oe dvntge of hgh eed, od, nd tffne ove e nto. Aong vo e nto, the 6-DO Stewt-Gogh tfo h ttted the ot nteet of eehe nd ndte, ne the ne tto e nde on tenon/oeve foe. [,] Howeve, the nto h oe ddvntge h oe fowd knet, woke, nd eqng n t. o oveoe the bove hotong, e nto wth fewe thn degee of feedo hve been nvetgted. [~] ow-do e nto hve the dvntge of etve e fowd-knet, ge woke, owe net, nd eqng e t ove 6-DO ontet. A ow-do e nto ot e thn 6-DO ontet nd, hene, t be oe eono to eo h nto fo ton fo whh 6-DO not nee. Aong ow-do e nto, -DO tnton e nto [6~9] nd -DO otton e nto [,] hve been foed. In the ft degn tge of nto eqng hgh eed,, nd tffne, the tffne n be ve eent nd the ot otnt te. o 6-DO e nto, vo ethod of the tffne n hve been bhed. [~4] Howeve, the tffne n fo ow-do e nto h been tte nvetgted. Aong the eeh et, Zhng nd Goen [~8] ned ow-do e nto wth ve ontnng b. Howeve, the ethod of ng vt jont not tet. It we known tht the obn nd tffne te of 6-DO e nto e 6 6 te. Howeve, t not e to wht the bet w to ee the obn nd tffne te of ow-do e nto. o the obn t, oh nd [9] eented tht 6 6 obn t ndng tton nd ontnt hod be ed n ode to ne the ngte nd to event n eoneo degn. [,] Sne the tffne t b bed on the obn t, the tffne t hod ontn the nfoton on the tffne de to tton nd ontnt nd hod be 6 6 t even n ow-do e nto. In th wok, the eo ew of tton nd ontnt e detened b ng the theo of eo ew. he eo ew e the eton foe de to tton nd ontnt, whh event et n the nfnte defeton of jont nd nk n e hn. ng the 6 6 obn t fo the tt eton, the tffne t beoe the of the tffne te of tton nd ontnt. he jont tffne ve n be ee detened b odeng the one of jont nd nk n eh e hn. he tffne ve of jont n be ee detened b ng the nt o eeent dt of beng, nd the tffne t fo evote nd t jont beoe 6 6 dgon t, whee one dgon eeent bot the otton o ong the dng deton eo. he nk n e hn e odeed Ee-Beno be. Sng the et defoton n the t, the tot one t of e hn n be obtned. Sne the tot one t gene ng, t obe to get the nvee t. Inted, tng the tot one t b the eo ew ed fnte defeton bot o ong the eo ew. o the fnte defeton, the one ve of ng n be obtned.
. SAIS ANAYSIS In th wok, ow-do t e nto wth -DO < 6 ondeed. A hown n g., t ed tht the ovng tfo ontned b nbe of e-knet hn nd eh b hve t ot one tto. he b hvng n tto e ndeed ft h,, K,, nd the othe b wthot tto e ndeed +, +, K,. et the degee-of-feedo oted wth the jont of the th b be defned the onnetvt,, of tht b. [,] Eh b ontn the ovng tfo b 6 nbe of ontnt, nd the tot nbe of the ndeendent ontnt hod be. o the tt n, et onde the e tht n eten wenh ed on the ovng tfo. o ow-do e nto, the wenh eqbted wth the eton foe b nbe of tto nd 6- nbe of ontnt. In ode to detene the eton foe b tto nd ontnt, we w e the theo of eo ew. [,4,] t, the ntntneo twt of the ovng tfo need to be eeed ne obnton of the nt twt of -DO jont ontng of eh b b, [6] & θ S fo,, K, j j, j, whee nd Ŝ denote the twt of the ovng tfo nd the nt twt eeed n the oodnte, [4] nd & θ j, denote the jont te. he bt, nd j denote the b nbe nd the jont nbe n the th b, eetve. A the foow, the eo ew n the th b n be detened. [9] t, thoe ew tht e eo to the jont ew fo 6 eo ew te, defned the eo ew of ontnt. et ŝ, k, denote the kth eo ew of ontnt of the th b. kng the othogon odt of both de of Eq. wth eh of the 6 eo ew of ontnt, 6 eo ew of ontnt n be dentfed b ne -, KINEX, Geongg-Do, Koe fo k,, K,6, k, whee ŝ denote the nt ew eeed n the oodnte. [4] Seond, when the tto of the th b e oked, the denon of the eo ew te nee b n n o. hoe ew tht e eo to the ve jont ew fo 6 + n eo ew te. e, th 6 + n eo ew te nde the 6 eo ew te dentfed ee bet. Hene, ddton eo b ew tht e eo to the ve jont ew nd don t beong to the 6 te e defned eo ew of tton, ŝ,, nd n be detened b, whee ne obnton of the nt twt of ve jont. o the oede, we n detene ndeendent eo ew. Ignong the gvt, n eten wenh eqbted wth the eton foe b tto nd ontnt ong the eo ew gven b w [ + [ +,,,,,,,, + +,,, + + + +, ],6,,6,,6,,6, + ] whee the wenh eeed n the oodnte w [ f, ] when f nd denote the foe nd oent veto t the end-effeto. nd denote the gntde of the eton foe b tto nd ontnt, eetve. Eq. 4 be ewtten n the fo of te nd veto b 4 w + whee the obn t of tton nd the obn t of ontnt e gven b [9] Movng tfo 6 [ ] R nd 6,, 6 [ ] 6 R. 7,,,6,,,,6, he ove obn t obtned b eg eg eg eg + + g. Stte of n -DO e nto. Note: : tve jont, : ve jont 6 6 [ ] R. 8 In Eq., [,, ] R denote the tto veto,,, 6 [,,,,,, ] R denote,,,6,,,,6, 6 the eton veto b ontnt, nd [, ] R the ove jont veto.. SINESS ANAYSIS In th e, t ed tht the ovng tfo gd nd the jo oe of one oe fo the febt of the beng, nk, ehn tnon ehn nd onto te. [] he eo ew be fed nto thee tegoe; eo-th eo
ew, nfnte-th eo ew, nd fnte-th eo ew eeed eetve b ŝ, ŝ,. 9 + h whee the nt deton veto of ew, the oton veto fo the efeene fe to ew, nd h the th of ew. he h enng of eo- nd nfnte-th eo ew e e foe nd e oe. Athogh the eo ew be noneo fnte-th ew n e e, t not ondeed n th wok. When e foe eeted on b wth oe one, t genete nfnte tnton oton ong the ne of the foe. On the othe hnd, when e oe ed to b, t genete nfnte otton oton bot the of the oe. Hene, the nfnte tnton nd otton oton n be odeed the defeton of ne ng ed ong the ne of the foe, nd the defeton of otton ng wth the of the oe, eetve. A een n the evo eton, t n be odeed tht the ovng tfo oted b ndeendent ng, ne thee et eo ew n gene e. Aong the ng, ng e eted to the tton nd 6- ng e eted to the ontnt. et k,,,, be defned the ng ontnt of tton, nd k, +,,6 be defned tht of ontnt. he eton between the foe nd defeton of ng n be eeed b [ ] δ, nd [ ] k δq k q whee [ k ] nd [ ] k denote the dgon te wth the dgon eeent of k, nd k,, eetve, nd δ q nd δ q e the nfnte deent veto of tton nd ontnt. B ng the ne of vt wok, the foowng eqton n be obtned b δ D δq + δq w whee δ D [ δ, δθ ] denote the nfnte twt eeed n the oodnte, when δ nd δ θ e the nfnte tnton nd otton deent t the end-effeto. Sbtttng Eq. nto Eq. ed δ D + δd δq + δq Sne Eq. vd fo n ve of wte nd, one n δq δd, nd δq δd. Sbtttng Eq. nto Eq. gve w δ δq [ k ] δq. 4 D δq [ k] δq + ng Eq., Eq. 4 n be ewtten b w D D [ ] D D δ δ k δ + δ [ k ] δd. Sne Eq. o vd fo n ve of δ D, the tffne ne -, KINEX, Geongg-Do, Koe ng between ed wenh nd nfnte twt t the end-effeto obtned n te of the tffne t, K w K δd 6 whee the ove tffne t obtned wth the of the tffne te of tton nd ontnt gven b K [ k ] + [ k ] 7 ng the ove obn t, the ove tffne t be fed b K k] [ 8 [ k ] whee [ ] nd [ k ]. [ k] It noted tht the tffne t fo ow-do e nto h fo wth f-do e nto. [-] he tffne t of f-do e nto eeed on wth the tffne t of tton, ne n ontnt do not et. On the othe hnd, the tffne t of ow-do e nto hod be eeed wth the tffne te of tton nd ontnt. Hene, the nttve oh of ng t tffne t ed to eoneo et. 4. OMAINE MODEING O SERIA HAINS In th eton, we eent ethod to detene the ng ontnt eted to tton nd ontnt n e hn. In devng the one ode of e hn, the febt n jont nd nk ondeed. t, wthot o of genet, on evote nd t jont e ondeed, ne he jont eqvent to thee nteetng non-on evote jont, nve jont eqvent to two nteetng evote jont, nd jont eqvent to the of evote jont nd t jont ong the evote jont, nd o on. he one t of -DO jont gven b,,, θ, θ, θ, 9 whee the of jont gned wth the - of o fe, nd the d deton of jont ed on the ne of o fe hown n g.. he bt, nd θ denote the ne nd otton tffnee, nd the foowng bt, nd denote the nd d θ, deton. It noted tht, fo evote jont, nd,, fo t jont. Seond, the nk n e hn e ondeed Ee-Beno be, ng tht the he effet nd net of otton of the be eton e gnoed, nd be eton t ne nd eend to the net. oe nd oent et defo the t of eh nk.
he et defoton t the t of nk e wtten foow: δ EI + EI M δ M, EI EI AE θ + M, EI EI δ, θ + M, θ M EI EI GI whee A nd e the e nd ength of nk, E the od of the ongtdn ett, G the od of the tnvee ett. I, I nd I e the oent of net bot the,, nd e, eetve. I the o oent of net. hen, the one t of nk gven b EI EI EI EI AE EI EI EI EI GI. ne -, KINEX, Geongg-Do, Koe he nfnte twt t the th jont o the th nk eeed n the th o fe n be eeed b δ D w whee denote the one t of the th t eeed n the th o fe nd ŵ denote the wenh ed on the th t eeed n the th o fe. Eeng the nfnte twt nd wenh wth eet to the ovng fe gve δ D δd nd w w whee the tnfoton t of ew fo the th fe to the ovng fe gven b R R R 4 whee R denote the otton t fo the th fe to the ovng fe nd denote the kew-et t eeentng the veto fo the ogn of the ovng fe to tht of the th o fe eeed n the ovng fe. he tot defeton of e hn n be ted b the of the defeton n jont nd nk gven b n δ D w. heefoe, the one of e hn eeed n the ovng fe n be wtten b n. 6 he jont one ve eted to the eo ew of tton nd ontnt e ted b δ f nd δθ 7 θ, whee f nd.. EXAME g. one ode of -DO jont. nk + θ + θ θ + + δ δ δ + g. one ode of nk. + In th eton, the tffne of the et nto ned, n ode to en the ggeted ethod. A hown n g. 4, the et nto h thee tted SS She-t-She b nd one ve nve-t b. [,7] he b wth tto e nbeed ft nd the ve b ndeed 4. Sne the onnetvt of the thee tted SS b, thee et no eo ew of ontnt n the thee tted b. Ao, thee et no eo ew of tton n the ve b. he eo ew of tton of the th b fo,, eo-th ew ng thogh the two ente of he jont,, fo,, 8 b
whee nt veto ong the t jont nd b B. Sne the onnetvt of the ve b 4, the nfnte twt of the end-effeto n be eeed ne obnton of thee ntntneo twt: & θ S + & θ S + d& S 9,4,4,4 whee,4 S,4,,4 S,4, S,4,4,,4,4 nd O. he eo ew of ontnt n be obtned foow:,4 4,,,,, 4 6 whee 4,4,, 4,, nd 4 6,4., 4 heefoe, the obn te of tton nd ontnt n be obtned b, b b b 4 b4 4 b 6 whee b 4 b. A hown n g., eh tted b n be odeed ne ng ong the t jont, ne the eo ew of tton e foe. S, fo the two eton foe nd one eton oent, the ve b n be odeed two ne ng nd one otton ng. ng Eq. 8, the tffne t of the et nto n be obtned b K b [ k ] [ k ],4,4 [ k ] b b [ k ] b + k 6 6 ne -, KINEX, Geongg-Do, Koe dg,,,,, ]. [,,, θ, θ, θ, whee, the one of ne tto, nd the othe dgon eeent e the one of t jont. he fed nk ength nd e e defned nd A, the ovng nk ength nd e e defned nd A, nd the tot b ength. he tot one of n SS e hn the of one of the owe nd e he jont, ne tto, nd fed nd ovng nk. he one ong the ne, A B, n be e ted b S, k,, + + +, fo,,. 6 A E A E Seond, the tot one of the e hn the of one of the nve jont, t jont nd the fed nd ovng nk. Eeng the one of the nve jont n the O ed dg,,,,, ] 7 [,,, θ, whee, nd, e the ne one of the ne nd the -, nd θ, the otton one bot the -. he - of the o fe of the t jont ong the b, O. he one of the t jont gven b dg,,,,, ]. 8 [,, θ, θ, θ, ng Eq. 6 nd 7, the one eted to the eo ew of ontnt,.e.,,, nd,,, n be obtned b efe to g. B B Movng tfo w b v,4 B S - jont - jont whee [ k ] dg[ k, k, k, k, k ] nd k,,,,4, denote the otton ng ontnt. he net te to fnd the ng ontnt fo the nfoton on the one of the jont nd nk ontng e hn. t, the one of n SS hn odeed. It noted tht the hn et bot the ne, A B. So, t onvenent to gn the e of the fe ong the ne. he ovng oodnte fe ote t the ente of the e he jont. Sne the he jont n be ondeed thee nteetng non-on evote jont, the one t of he jont eeed n the oeondng o fe n be odeed A - jont,4,4 O - jont A S - jont S S S dg[,,,,, ]. 4 S In nne, the one t of ne tto eeed n the oeondng o fe gven b A g. 4 Knet ode of et e nto.
, B k, Movng tfo f,,, k, B ne -, KINEX, Geongg-Do, Koe eo ew eted to tton nd 6- nbe of eo ew eted to ontnt. he tffne t fo ow-do e nto beoe the of the tffne te of tton nd ontnt. he t ve of ng ontnt e obtned b odeng the one of jont nd nk n eh e hn. n, the ethodoog ed to the -DO et e nto. In the fthe wok, th nt ethod w be ed n the degn otton of e-knet hne too nd the effetvene of the ggeted tffne n ethod w be vefed thogh eeent. B k AKNOWEDGMENS k,,, O k, k,4 h wok w oted b MOIEMnt of oee, Indt nd Eneg Reb of Koe nd Geongngn-do. REERENES g. Stffne ode of et e nto. θ θ g. 6 Defnton of the o fe of n e hn. + [, O θ k + +, 4,4, θ,,,,, k,, +,, θ + [ k + +, 6 θ, θ, θ, θ, θ, oθ ] oθ ] 9 It noted tht n Eq. 9, on jont one e ondeed. 6. ONSION In th e, the tffne n fo ow-do e nto ng the theo of eo ew nd ondeng the et defoton n jont nd nk b the eo ew eented. o n -DO e nto, t deved tht thee et nbe of [] Stewt, D., 96, A tfo wth S Degee of eedo, o. Inttte of Mehn Eng., ondon, Engnd, Vo. 8,. 7~86. [] Gogh V. E., nd Whteh S. G.., 96, nve e et Mhne, oeedng 9th Int. ehn onge.i.s.i..a., Vo. 7,.7~. [] ve, R. 988, Det, t Robot wth e Geoet, 8th Intenton So on Indt Robot, Sdne, At,. 9-. [4] eot,., Rend,., nd one, A., 99, DEA: A Se nd Effent e Robot, Robot, Vo. 8,. ~9. [] Sno, B., 999, he et Robot: Invee Knet, Mnbt An nd oed-oo Det Knet Agoth, Robot, Vo. 7,. 47~44. [6],. W. nd oh, S.,, Knet nd Otton of St - e Mnto, ASME on of Mehn Degn, Vo., No. 4,. 49~446. [7] Wenge,., nd hbt, D.,, Knet An of New e Mhne oo: he Othogde, Advne n Robot Knet, Edted b. en nd M.. Stn, Kwe Ade bhe, ondon,. ~4. [8] K, H. S., nd,. W.,, Degn Otton of ten e Mnto, on of Mehn Degn, Vo., No.,. 4~. [9] K, H. S., nd,. W.,, Evton of ten e Mnto, 8th Intenton So on Advne n Robot Knet, 4~8 ne, de de Mve, Sn,. ~8. [] Goen,. M., nd Angee,., 989, he Ot Knet Degn of She hee-degee-of- eedo e Mnto, ASME on of Mehn, non, nd Atoton n Degn, Vo., No.,. ~7. [] ng, Y.., nd,. W., 4, Stte Snthe of of -DO Rotton e Mnto, IEEE n. on Robot Atoton, Vo., No.,. 7~. [] Goen,., 99, Stffne Mng of e Mnto, IEEE nton on Robot nd Atoton, Vo. 6,. 77~8.
[] Gff, M., nd Dff,., 99, Gob Stffne Modeng of of Se ont ong, Mehn nd Mhne heo, Vo. 8, No.,. 7~4. [4] heb,. nd,. W., 99, On the Stffne of Nove S-Degee-of-eedo e Mnto, on of Robot Ste, Vo., No.,. 84~86. [] Zhng, D., nd Goen,. M.,, Knetott Modeng of N-DO e Mehn wth ve ontnng eg nd t Atto, ASME on of Mehn Degn, Vo.,. 7~8. [6] Zhng, D., nd Goen,. M.,, Knetott Modeng of e Mehn wth ve ontnng eg nd Revote Atto, Mehn nd Mhne heo, Vo. 7,. 99~67. [7] Zhng, D., nd Goen,. M.,, Knetott An nd Degn Otton of the et Mhne oo, ASME on of Mnftng Sene nd Engneeng, Vo. 4,. 7~7. [8] Zhng, D., nd Goen,. M.,, e Knet Mhne Degn wth Knetott Mode, Robot, Vo.,. 49~48 [9] oh, S. A., nd,. W.,, obn An of ted-do e Mnto, on of Mehn Degn, Vo. 4,. 4~8. [] Ztnove, D., Bonev, I., nd Goen,.,, ontnt Sngte -Se Sngte, oeedng of the 8th Advne n Robot Knet, edted b. en nd. ho, Kwe Ade bhe,. 8~9. [] Hn,., K,., K., nd k,..,, Knet Sentvt An of the - e Mehn, Mehn nd Mhne heo, Vo. 7,. 787~798. [],. W., 999, Robot An: he Mehn of Se nd e Mnto, ohn We & Son, New Yok, NY. [],. W.,, Mehn Degn: Eneton of Knet Stte Aodng to nton, R e,. ~47. [4] Dff,., 996, Stt nd Knet wth ton to Robot, bdge nvet e. [] B, R. S., 99, A ete on the heo of Sew, bdge nvet e, bdge. [6] Mohed, M. G., nd Dff,., 98, A Det Detenton of the Intntneo Knet of e Robot Mnto, ASME. Meh., n., Ato. De., Vo. 7,. 6~9. [7] Yoon, W.K., Seho,., nd k, Y., 4, Stffne An nd Degn of ot Modfed Det e Mehn, Robot, Vo.,. 46-47. ne -, KINEX, Geongg-Do, Koe