Using Computer-aided Techniques in the Dynamic Modeling of the Human Upper Limb

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1 Usin oute-aie Teniues in te Dynai Moelin of te Huan Ue Lib ANTOANLA NAAI, Faulty of oute Siene Vasile Golis Westen Univesity Aa 00, B. Revolutiei n ROMANIA tt:// Abstat: - Te wie obility of uan boy leas to te neessity of oelin te osteoatiula syste as a eanis wit a lae nube of eees of feeo. Dynai oelin of osteoatiula syste is neessay beause te exetion of vaious ations an natual ysioloial oveents ae essentially ynai. Vey often we use a silifie oel beause te enoena oue ae so olex tat auate ateatial eoution is atially iossible. A ynai oel ust ovie a oo estiate of total weit an ass istibution as well as tansissibility an aotization oieties fo bones, usles, joints, bloo an skin. Te ae esents a ynai funtional oel onsiein te uan ue lib as a eani syste wit eees of feeo in te ase te seents ae ove by tei own weit foes. Te bones an te usles wee oele in Soli Woks, te oel of te ue lib obtaine bein vey lose as fo to te eal one. Base on tis oel, te alulus of ass oieties was ae. Te iffeential euations of otion obtaine wee solve usin Laane foalis. Key-Wos: - Moelin, Huan ue lib, Dynai oel, Osteoatiula syste Intoution Te esea eain te eanial aset of te uan boy s osteoatiula syste an be suessfully ae tou lassial an oen alulus an exeiental enineein etos. Tus, te osteoatiula syste an be seen by te eninee as bein a efoable seial stutue, wit a onsieable olexity eain its eoety, elasti oeties an its funtions. Altou te bioeanial oelin of te osteoatiula syste is subjet to te sae eneal laws an iniles wi ae use in enineein, we still ave to onsie te fat tat tee ae soe iffeenes wi liit te ossibilities of tis esea eto. As a onseuene a oel ust be oneive an investiate as to eteine witin etain vey auate liits, te beavio of te oiinal syste. Te inbe vaiability of eoety an of te eanial oeties of te osteoatiula syste, fo eson to eson, is one of te asets tat eneate onsieable suleentay iffiulties eain te aolisent of bioeanial eseaes an wi always ust be taken into onsieation. Te ynai oelin of te osteoatiula syste is neessay beause te efoane of soe ations an oon ysioloial otions is in its essene ynai. Te i obility of te uan boy leas to te neessity of te oelin of te osteoatiula syste as a eanis wit a i eee of flexibility. Te iffeential euation syste wi is obtaine is olex an it ilies nueial inteation. In ost ases, we use a silifie oel beause te ouin enoena ae so olex tat a eise ateatial elia is vitually iossible. Te D oel eteination of soe funaental sizes in te stuy of ynais is neessay fo: iovin te ostesis an te etalli ilants of te ue lib an tei akin in aoane wit te atiulaities of ea ase, te assessent in wi bone fatues ae ae in ost of te ases ynai: falls, slis, iats, wit iliations in foensi eiine; knowin te iustanes in wi te fatues ou tou sok et. In oe to ay out a funtional ynai oel of te uan ue lib as losely as ossible to te eal one, it is neessay to stuy te oieties of te bioloial ateials tat ake u te uan boy, so tat te easues involve in te iffeential euations ae as oet as ossible [], [0], [6]. ISSN: Issue 7, Volue 7, uly 008

2 Te stuies aie out by iffeent eseaes ae base eseially on oels ae in FM oas. Bone Stutue an Poieties In oe to efo te loootion funtion an to aintain its sae, te uan boy ust ossess a bone stutue wit etain eanial oeties wi woul aat to extenal fatos an envionental onitions. Te bones of te uan skeleton ae of iffeent saes an sizes. Tey fit into fou ateoies: lon, sot, flat, an ieula. Fo a iosoi oint of view, bones onsist 0-0% of oani ateial, of wi alost 9% ae oesse ollaen fibes, an 60-70% of inoani ateial, of wi aoxiately 8% is ae u of aliu osate, 6-0% of aliu abonate, an te est of alkaline salts. Tis oosition leas to te esevation of bone iiity an esistane to seveal stesses []. In fiue, te stutue of a lon bone is eesente [], [7], [], []. iisis Diaysis iysis Atiula atilae Line of te eiyseal atilae Tabeula of te sonious bone Meulla avity Boy of te otial bone nosteu Peiosteu atilaj atiula Fi.. Stutue of a lon bone Fo a aosoi oint of view, bones ae of two tyes: otial oat an sonious tabeula. Te otial bone is vey ense, intensely alifie, eate to esist oession. It an also esist tosion an benin, but to a u lesse extent. Te otial bone is usually foun in te iayses of lon bones. Tey featue a ental avity eulla anal o eulla avity. At te en of te lon bones an suounin tenons an attae liaents, te bone stutue is oe oous an beas te nae of sonious bone []. Te assae fo te otial bone to te sonious one is aual. Te otial an sonious bone ensities o not iffe eatly beause bot bone tyes onsist of bone laellas. Knowin te bone ensity is iotant fo aeiatin te sizes aateizin te istibution of asses in te osteoatiula syste of te ue lib, witout wi te ynai stuy of latte annot be aie out []. Te alulation of te ente of avity an of te oents of inetia on te D oel of te uan ue lib Deteinin funaental easueents in te stuy of ynais on D oels is neessay fo: efetin osteses an etalli ilants of te ue lib an tei ealization aoin to te atiulaities of ea ase, establisin te iustanes in wi bone fatues ae oue in tei vast ajoity ynai ases: fallin, sliin, iat, wit iliations in foensi eiine; knowin te onitions une wi fatues ae oue in stesses by sok, et. [], [], [8], [8], [9], [0], []. In oe to eteine te ente of avity of a oonent of te bony skeleton of te uan ue lib an te oents of inetia, one an eloy te oe oan of te oas Soli Woks [6], Mass Poety, o ote oas an be use, into wi tese files ae iote, su as Po ninee, Autoa, et. In fiues -, exales of alulation in Soli Woks ae esente fo te vaious oonents of te uan ue lib skeleton, as well as te uan ue lib as a wole. Fo te alulation of te oents of inetia, te efeene fae was lae in te oonent s ente of avity. ven tou bones o not onsist of a ooenous stutue, te value of te ass is te one alulate wit te aveae ensity: ρ, /. Aoxiation leas to esults tat ae oatible to tose in liteatue [], [9], [0], [], [], [7]. ISSN: Issue 7, Volue 7, uly 008

3 takin into aount te fat tat esultin syste is no lone ooenous fiue. Fi.. alulation of ass oieties fo te ueus Fi.. alulation of ass oieties fo te fo te skeleton of te uan ue lib wit usles Fi.. alulation of ass oieties fo te ulna Te Dynai Moel of te Huan Ue Lib It is onsie te ue lib s stutue as a eanial syste wit eees of feeo, subjet only to its own fition foes, so tat te iffeential euations of otion will be eteine by usin Laane s euations [], [6], [7], [8] [6], [], []: t Q i, i i i wee: total kineti eney, i - enealize vaiables oesonin to oules i, Q i enealize foes. Takin into onsieation te silifie eoetial oel an te satial stutue wi ysially oels ols te ue uan lib, te total kineti eney is obtaine: Fi.. alulation of ass oieties fo te fo te skeleton of te uan ue lib Fo te a wit usles, te usula ensity ρ, / was onsiee. Te alulation of ass oeties fo tis ase is aie out wile s s s wee z0, z, z eesent te otation axis ISSN: Issue 7, Volue 7, uly 008

4 oesonin to te tee otions at level of te soule flexion-extension, abution-aution, otation, z te axis oesonin to te flexionextension otion at te elbow level, z te otation axis oesonin to te flexion-extension otion at te level of te wist, an z0, z, z, z, z, te inetia oents in onnetion to tese axis. Te followin notes ave been ae: s ue lib, aius, al, fines, also stanin fo te lents of te affeent ats. Te inetia oents in onnetion wit te axis z0, z, z, z an z ae alulate by alyin Steine s foulas []:,,,,,, sin sin s,,, os os s 6 0, 0, 0, 0 s 7 Altou te bones o not sow any ooeneous stutue, te value of te wei is tat alulate base on te aveae ensity: ρ, /. Aoxiation leas to esults oatible wit tose fo liteatue [9], [9], []. Fo te a wit usles te usula ensity ρ, / as been taken into onsieation. Wit te el of te Soli Woks oa [6], knowin te bone iensions an te usle an bone ensities, tese teoay fiues ae ietly alulate by uttin te efeene systes ietly into oules wit te z axis oientate alon te axis of tose esetive oules. Fiue 6 sows te uan ue lib oel fo wi te inetia oent alulus is ae, te axis in onnetion to wi tis alulus is ae, as well as te esults obtaine [0], [], [9], [0], [], []. Fi.6. Te alulus fo te inetia oents fo te wole a ue lib Te kineti eney eivates oae to enealize veloities an tei eivates oae to tie, as well as te eivates of te kineti eney oae to te enealize ooinates beoe: s 8 t t s s s s sin sin t s 0 s ISSN: Issue 7, Volue 7, uly 008

5 sin sin t s t 8 sin 9 0 t sin By elain te euations 8- in, takin into aount te exessions of enealize foes fo i,, we obtain te followin euations: os os os os os os s os os os os os os os os os os os os sin sin s 0 sin sin s os os os sin 6 os sin 7 By elain te euations -7 te values fo te inetia oents: I z0 s I xx 0,7909 k* I z s I yy 0,8009 k* I z s I zz 0,007 k* 8 I z I xx 0,007 k* I z I xx 0,00066 k*, weits: 0,66 k an, 0,86 k foea,,078 k ue at of te uan ue lib, s,06 k ue lib an te bone sizes 0,9, 0,, 0,6, te followin iffeential euations syste is obtaine [], []: os 0,6 7, os,78os 9 os 0,6 os os 7,8os os,60 os sin 0, sin 0,06 0 sin 7,8 sin,6 8,78os,os sin,09 sin,09 86,66 os sin 8, sin 8, Solvin te Diffeential uation Syste fo te Silifie Moel of te Huan Ue Lib Te inteation of te iffeential euations syste tat eesents te eue oel of te ue lib as been ae in MatLab 7.0, usin te followin notations [], [9], [], [7], [8], []: ISSN: Issue 7, Volue 7, uly 008

6 y, y, y, y, y y6, y7, y8, y9, y0 Te oe use fo alulus is: funtion yantoanela_t,y yzeos0,; y y6; y y7; y y8; y y9; y y0; y6 -.78*osy- 7.*osy-0.6*osy; y7 0.06*y7*y0*sin*y0.*y7 *y9*sin*y-.60*osy*osy- 7.8*osy*osy- 0.6*osy*osy; y8-8.6*y8*y0*sin*y- 7.8*y8*y9*sin*y; y9.09*y8*y8*sin*y-.09*y7*y7*sin*y-.*osy-.78*osy; y0 8.*y8*y8*sin*y- 8.*y7*y7*sin*y *osy; Fi.7. Gai iaa of te otion laws an veloities, t [0,0.] As solvin of te iffeential euation syste is nueial, te statistial oessin of te ata sybolize in fiue 6 is atiulaly iotant fo te vaiation of te atiulato vaiables i witten own as y_i in te MatLab oa. Te ain statistial estiates ae eesente in fiue 8 fo wi esults: te ean values uin te seifie tie, te eian values an te lobal vaiation inteval iniate as su tou te esetive extee values. Te syste inteation was aieve tou te seuene of lines: >> tsan[0 0.]; y0[ ]; [t,ysol]oe'antoanela_',tsan, y0; ysol:,:0 lott, ysol:,:0 leen'y_','y_', 'y_','y_','y_','y_6','y_7', 'y_8','y_9','y_0' On te basis of te nueial values an te atiulato vaiables an te atiulato veloities obtaine as a esult of inteatin fo t [0,0.] an te initial onitions iffeent fo zeo, te ai eesentations of te otion laws an veloities oesonin to tese esults ave been obtaine fiue 7. Fi.8. Statisti estiato fo vaiation o atiula vaiables i, t [0,0.] In oe fo te esults of te ynai oelin to be usable also fo te ealization of ue-lib osteses, on te basis of te solutions obtaine by inteatin iffeential euations, one also efoe te aoxiation of funtions y _ i f t tou te eto of otoonal olynoials. As soon as tey ae obtaine, one an aly te evese eto in te iffeential euations of otion 9-, wit a view to alulatin enealize foes wi an be onetize by usin ativation enines fo oulins tat ae oin to evelo ative oents in aoane to wat esults fo te aboveentione euations. ISSN: Issue 7, Volue 7, uly 008

7 Tus, also in MatLab te olynoial funtions aoxiatin te laws of otion wee obtaine, avin in view tat te eee of te aoxiation olynoial soul oeson to as little eviations as ossible. One an obseve in fiues 9 tat a olynoial funtion ensuin an aeuate aoxiation oul not be obtaine fo all of te atiula vaiables. Fi.. Te olynoial funtion fo atiula vaiable Fi.9. Te olynoial funtion fo atiula vaiable Fi.. Te olynoial funtion fo atiula vaiable Fi.0. Te olynoial funtion fo atiula vaiable Fi.. Te olynoial funtion fo atiula vaiable ISSN: Issue 7, Volue 7, uly 008

8 On te basis of te nueial values an te atiulato vaiables an te atiulato veloities obtaine as a esult of inteatin fo t [0,0.] an te initial onitions eual to zeo, te ai eesentations of te otion laws an veloities oesonin to tese esults ave been obtaine fiue. Te syste inteation was aieve tou te seuene of lines: >> tsan[0 0.]; y0[ ]; [t,ysol]oe'antoanela_',tsan, y0; ysol:,:0 lott, ysol:,: leen'y_','y_', 'y_','y_','y_' Fi.. Gai iaa of te otion laws, t [0,] Fo tis ase, te olynoial funtions wee obtaine, an exale fo atiula vaiable bein illustate in fiue 6. Fi.. Gai iaa of te otion laws fo null initial onitions, t [0,0.] anin te initial onitions an te eio of tie, te esults ae: >> tsan[0 ]; y0[ ]; [t,ysol]oe'antoanela_',tsan, y0; ysol:,:0 lott, ysol:,: leen'y_', 'y_', 'y_', 'y_', 'y_' Fi.6. Te olynoial funtion fo atiula vaiable fo t [0,] Te sae eto an be use fo stuyin te olete oel an fo obtainin all laws of otions an veloities in joints tou nueial inteation of te iffeential euations esultin fo te n -tye Laane euations. onlusion In oe fo te esults of te ynai oelin an to oess a ostetis fo te ue lib base on outoe obtaine by inteatin te iffeential euations, te aoxiation of te ISSN: Issue 7, Volue 7, uly 008

9 funtions y _ i f t an be ae tou te otoonal olynoial eto. Afte obtainin te, te oose eto an be alie in te iffeential euations of otion 9- to alulate te enealize foes tat an be ut in effet wit te el of oule enines wi will evelo ative oents in aoane wit te esults fo te entione euations. Te vaiant stuie in te ae an be extene to ote ases in wi te initial onitions ae iffeent an te tie eio is lae. Bot te obtaine eesentations as well as te ossible ue to te anin of te initial onitions o te eio of tie, allow ultile subseuent uses. Te futue wok an be eesente by ealizin a ynai oel of uan ue lib base on a eanial syste wit oe tan eees of feeo. Refeenes: [] Abaas P.H., Hutins R.T., Maks S..., MMinns olou Atlas of Huan Anatoy, Mosby, Lonon, -t e., 998 [] Abualla H., Tay., Abeai M, Teaeuti Robot fo te Ue Lib Reabilitation, Wseas Tansation on Systes, Issue, Vol. 6, 007, , [] Baiu., Anatoia funńională şi bioeania aaatului loooto, itua Meială, Buueşti, 98 [] Boja N., Touzu., Miut I., Petiso., Kle F., Reni B., Aleba, eoety, iffeential euations, Tenial Univesity Tiisoaa, 99 [] Bikan P., Fobin W. Leivset G., Musuloskeletal Bioeanis, Tiee Stuttat New Yok, 000 [6] olas F., Dieulot., Bae P.., Bone P., Dynais oelin an ausal Oein Ga eesentation of a Non Miniu Pase Flexible A Fixe on a at, Wseas Tansation on Systes, Issue, Vol., 006,. -, [7] Denisi A., Main G., Antonesu D., Bioeania, itua Aaeiei, Buueşti, 989 [8] Daulesu D., Roboti ynais, itua Diatiă şi eaoiă Publisin House Buuesti, 997 [9] Dăulesu D., Rusu, L., Moovesu V., Peu., oaative stuy of eanial stesses in uan libs bones, Alie Bioni an Bioeanis, vol., no., 00,.-9 [0] Daulesu, D., Tot-Tasau M., Staniulesu, V., oute-aie exloation insie uan oans, Te st National onfeene on Meial Infoatis MDINF 99 Sibiu, 999 [] Daulesu D., Staniulesu V., Tot-Tasau M., Deuean M, Moellin an Rebuilin te olex Anatoial Stutues, Poeeins of Mateatial Bioloy an oloy, 00, Wseas Intenational onfeene Gee,. 66-0, [] Fazekaş D., Pliuta., Stuiul inaiii aaatului loooto, Politenia Univesity of Tiisoaa, 999 [] Fun Y.., Bioeanis: Meanial Poieties of Livin Tissues, Sine Vela, Belin, 99 [] Ginea M., Fieteanu V., MatLab, alul nuei, afiă, aliańii, itua Teoa, 00 [] Goss., Fetto,., Rosen., Musuloskeletal exaination, Blakwell Siene In., USA, 00 [6] Hana-Lua V., Maties V., Bisan., Tiua T., RoboŃi. Stutuă, ineatiă şi aateistii, itua Daia, luj-naoa, 996 [7] Haa K., Haai L, Te Fatal Diension oelate to te Bone Mineal Density, Wseas Tansations on Sinal Poessin, Issue, Vol., 008,.0-, [8] Luin M., Moelaea şi siulaea sisteelo eanie, Tiişoaa, 999 [9] Mauste St., Nueial etos in solvin unlinia euation, Teni Publisin House Buueşti, 98 [0] Náaji A., Moelin Teniues, Univesity Hoizons Tiisoaa, 00 [] Náaji A. Metos of Desinin D Moels in Bioeanis, Sientifi Bulletin of Politenia Univesity of Tiişoaa, Tansations on Autoati ontol an oute Siene, Vol. 9 6 No., Tiişoaa Politenia Publisin House, 00,. 9- [] Naaji, Antoanela, Wokin Sae Reezentation fo te Huan Ue Lib in Motion, Poeeins of te 7t WSAS Intenational onfeene on Alie oute an Alie outational Siene, Hanzou, 008,.9-00, [] Naslau, Pavel. Nuei Metos, Politenia Publisin House Tiişoaa, 999 [] Nette F.H., Atlas of Huan Anatoy, Seon ition, Novatis, New esey, 990 [] Pailian V., Anatoia oului, vol. I Aaatul loooto, itua ALL, Buuesti, 998 [6] Panjabi M., Wite III, A. Bioeanis in te uskuloskeletal syste, uill Livinstone New Yok, 00 [7] Petila T. An olab., Stiinte ale natuii ISSN: Issue 7, Volue 7, uly 008

10 outationale si stuii inteisilinae, Diital Data luj-naoa, 00 [8] Peu T., Hana-Lua V., Peu D., Sios D.,. Robot siulation usin objet-oiente oain, Po.Intenational onfeene on Tenial Infoatis, Tiişoaa, Vol., 99 [9] Savii G., Bazele oietăii asistate e alulato. AD, itua Miton, Tiişoaa, 997 [0] Taylo L.D., oute Aie Desin, Aison Wesley, nlan, 99 [] Tot-Tasau, M., Daulesu D., Results an objetives in bioeanis stuies at Polytenial Univesity Tiişoaa, Ti-atite bies: uatos, Povies an Uses, B.Rias., M 0-96, 998,.77-8 [] Watt A., D oute Gais, Aison WesleyPublisin Lt, nlan, 99 [] Wloka, D.W., Robotesystee, Sine-Vela, Belin, 99 [] ei I., AD/AM Teoy an Patie, MGaw-Hill, 99 [] *** - MatLab 7.0 Use Guie, Te MatWoks, In. [6] *** - Soli Woks 00-00, uational ition [7] *** - entu e oelae a otezăii şi intevenńiilo iuiale asua seletului uan M-PISU, Gant NSIS, Poiet BUM inińiee, n./999 [8]*** - entu e oelae a otezăii şi intevenńiilo iuiale asua seletului uan M-PISU, Gant NSIS Poiet BUM, o NSIS, [9]*** - ontibuńii la aelioaea stăii e sănătate a oulańiei in ealizaea e aaate otetie, instuenta iuial şi tuse e ilante entu eeieea efetelo e selet, Gant PNDI/BIOTH, ontat n.0-6-pa- 6, [0]*** - Moelaea, oietaea şi ealizaea atiă a unui siste e ilantui eiale estinat iuiei axilo-faiale şi otoeie, Gant NSIS, ontat 0/ , Tea, o NSIS 69, ontat 0/ , Tea, o NSIS, ontat n. 90/.06.00, Tea 7, o NSIS []*** - Aeieea in etoe oaative a efaeii aaetilo bioeanii ai subieńilo u efiienńe otie, Gant e ti, ontat n. 90/.06.00, Tea, o NSIS ISSN: Issue 7, Volue 7, uly 008