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97 8 1 4244 8452 2 11 26 0 0 20 11 IEEE FPM 20 11 Experimental Res earc h of the Infl uenc e of Cons traint for Pneumatic Artific ial Mus c l e Charac teris tic Zang Kejiang Ma Yan Col l ege of el ec tromec hanic al engineering Northeas t Fores try Univers ity Harbin China kjzang 163 c om Sun Ning Li Xiuc hen Zhang Lan Col l ege of mec hanic al engineering Jiamus i Univers ity Jiamus i China Abstract Pn e u ma t ic a r t ificia l mu scle PAM is a n e w p n e u ma t ic a ct u a t o r A lo t o f wo r k h a v e b e e n co mp le t e d a b o u t t h e p r in cip le t h e o r e t ica l e x p e r ime n t a l mo d e lin g a n d a p p lica t io n s o f p n e u ma t ic a r t ificia l mu scle Re se a r ch e r s h a v e fo u n d t h a t PAMs e x h ib it n o n lin e a r ch a r a ct e r ist ic Ba se o n t h e p u b lish e d lit e r a t u r e s n o n lin e a r ch a r a ct e r ist ic r e la t e d t o e la st icit y fr ict io n b e t we e n r u b b e r a n d b r a id a n d t h e co n st r a in t r in g Th e fo r me r t wo a sp e ct s h a v e b e e n ma in ly st u d ie d in t h e p u b lish e d p a p e r s Ho we v e r st u d y o n t h e in flu e n ce o f co n st r a in s o n t h e e n d o f p n e u ma t ic a r t ificia l mu scle is st ill r a r e Th is st u d y e st a b lish e s t h e PAM st a t ic ch a r a ct e r ist ic e x p e r ime n t a l syst e m a n d t h e PAM ch a r a ct e r ist ics a b o u t mu lt ip le co n st r a in t s a r e t e st e d Th r o u g h t h e a n a lysis o f e x p e r ime n t a l r e su lt s t h e in flu e n ce is o b t a in e d wh ich co n st r a in t s t h e wo r k fo r p n e u ma t ic a r t ificia l mu scle wo r k in g ch a r a ct e r ist ics Keywords p n e u ma t ic a r t ificia l mu scle PAM co n st r a in t s st a t ic ch a r a ct e r ist ics e x p e r ime n t a l r e se a r ch I INTRODUCTION Pneumatic artific ial mus c l e is a new kind of pneumatic ac tuator with the ad vantages of c l eannes s l ightweight l ow c os t eas y maintenanc e c ompac t s truc ture and high power vol ume ratio For this reas on they are wid el y c onc erned by ac ad emic s tud y and engineering appl ic ation The pneumatic mus c l e was invented in 195 0 s in ord er to provid e d rivers for pros thes is or rehabil itation mec hanic al However for the prac tic al probl ems s uc h as pneumatic power s torage avail abil ity and poor q ual ity val ve tec hnol ogy at that time pneumatic artific ial mus c l e have not been d evel oped and appl ied In the 1988s engineers of the Japanes e type manufac ture Brid ges tone propos ed more powerful vers ion of the red es igned pneumatic artific ial mus c l e c al l ed Rubbertuator intend ed to motoris e though s oft yet powerful robot arms They were c al l ed Soft Arms and were c ommerc ial ized as s ervic e robots whic h have al s o been s tud ied The artific ial mus c l e whic h is s impl e in d es ign is mad e of rubber inner tube c overed with a s hel l braid ed ac c ord ing to hel ic al weaving The mus c l e is c l os ed by two end s one being the air input and the other being forc e attac hment point The braid fibers run hel ic al l y about the mus c l e s l ong axis at an angl e c al l ed interweave angl e When pres s ure is s uppl ied the inner tube trans formed together with s ets of rad ial movement d riving weaving interweave angl e inc reas ing the axial braid s l eeve s horting whic h pul l ing the end of the l oad and weaving s ets of fil aments prod uc ed tens ion at the s ame time then the tens ion and internal pres s ure eq uil ibrium Bec aus e of PAM s working c harac teris tic s s imil ar to animal mus c l e it is c al l ed pneumatic ac tuator pneumatic artific ial mus c l e 1 2 Pneumatic artific ial mus c l e is a new pneumatic ac tuator A l ot of work have been c ompl eted about the princ ipl e theoretic al experimental mod el ing and appl ic ations of pneumatic artific ial mus c l e Res earc hers have found that PAMs exhibit non l inear c harac teris tic Bas e on the publ is hed l iteratures 3 4 non l inear c harac teris tic rel ated to el as tic ity fric tion between rubber and braid and the end c ons traints The former two as pec ts have been mainl y s tud ied in the publ is hed papers However s tud y on the infl uenc e of the c ons traints on the end of pneumatic artific ial mus c l e is s til l rare This s tud y es tabl is hes the PAM s tatic c harac teris tic experimental s ys tem and the PAM c harac teris tic s about mul tipl e c ons traints are tes ted Through the anal ys is of experimental res ul ts the infl uenc e that c ons traints work for pneumatic artific ial mus c l e working c harac teris tic is obtained II EXPERIMENTAL PNEUMATIC SYSTEM A Ex p e r i me n t a l r i g This pneumatic experimental s ys tem Fig 1 is d es igned to s tud y the rel ations hips of the pres s ure c ontrac tion and forc e of PAMs with d ifferent c ons traints The experimental s ys tem c ontains el ements s hown in the fol l owing tabl e TABLE I DETAIL SHEET Co mp o n e n t n a me Co mp o n e n t t yp e Co mp o n e n t t e ch n ica l d a t a air s ourc e Fuma CEBM power 11KW maximum pres s ure 0 8MPa gas hol d er 2L s ol enoid val ves FESTO R10 7 s uppl y vol tage DC24V out pres s 0 0 6MPa pres s ure s ens or SMC PSE5 40 A R0 6 s uppl y vol tage DC 12 24V pres s ure range 0 1MPa ac c urac y 0 5 l oad s ens or CZL 3 s uppl y vol tage DC 12 24V l oad range 0 5 0 Kg ac c urac y 0 0 3 PAM Home mad e initial l ength 17 6mm initial d iameter 8mm 132 pres s ure range 0 0 3 MPa s tepper motor 86BYGH45 0 B 113 s tep angl e ac c urac y 2 s tep angl e 1 8 max torq ue 6 7 Nm guid e s c rew SFU160 5 nominal d iameter 16mm l ead 5 mm rated l oad 7 65 KN d is pl ac ement s ens or KTC 5 0 0 l in 0 0 5 8 R 5 3K c omputer LEGEND 1 1 CPU Pentium III 45 0 RAM 25 6M d ata c ol l ec tor WS USB res ol ution 8 ac c urac y 0 0 0 3 FS 1LSB d river CW25 0 AC s uppl y Vol tage DC12 24V mod e of operation 1 5 1 10 1 25 1 40 1 5 0 1 10 0 1 20 0 pul s er MPTG s uppl y Vol tage DC10 0 25 0 V output Freq uenc y 6 9999Hz weight c omponents of national s tand ard s 2Kg red uc ing val ve IR20 20 0 2G R max s up pres s 1MPa out pres s 0 0 1 0 8MPa Figure 1 Pneumatic experimental s ys tem The feed eq uipment is c ompos ed of four parts s tepper motor pul s er d river and guid e The pul s er outputs pul s es to s tepper motors d rivers to d rive the s tepper motors forward or bac kward The pul s er c an be meas ured in 1 4998 The s tepper motor turns a ful l c irc l e by 20 0 s teps The l ead of s c rew is 5 mm r The pos ition error is l ittl e about 5 e 6mm r Straight l ine l ead rail s are ad opted in the experimental s ys tem with good ac c urac y and s tabil ization Fig 1 s hows an ord inary pneumatic experimental s ys tem The c omputer c ontrol l ed s ol enoid val ves c an output a pred etermined gas pres s ure When c ompres s ed gas enters PAM it c ontrac ts and prod uc es a pul l ing forc e The gas s ourc e is us ual l y a c ompres s or Cl earl y the experiment s houl d inc l ud e both a s ol enoid val ves and PAM Firs t we d is c us s the s ol enoid val ves This is a c omputer c ontrol l ed s ys tem outputs a pred etermined gas pres s ure within a d efinite fiel d whic h is proportional to the vol tage whic h as a s ol enoid val ves input whos e q uantity c an be c ontrol l ed by the c omputer The pneumatic experimental s ys tem c ons is ts of a pres s ure s ens or a l oad s ens or and a d is pl ac ement s ens or The pres s ure s ens or meas ures the output gas pres s ure the l oad s ens or meas ures the output l oad and feed thes e bac k to the c ontrol c irc uit The magnitud e of the gas pres s ure output from the c ompres s or s houl d be l arger than the maximal gas pres s ure output from the s ol enoid val ves B Muscl e The artific ial mus c l e c ons is ts of the inner rubber tube where the natural rubber l atex through the vul c anizing proc es s has been us ed as s hown in Fig 2 In ord er to red uc e the infl uenc e of the rubber el as tic the rubber us ed in the experimental is very thin The outer s hel l is the braid ed s l eeve s ee Fig 2 Figure 2 Rubber tube and braid ed s l eeve The as s embl y of the artific ial mus c l e is s hown in Fig 3 one s id e of whic h is the air inl et and the other s id e is the c l os ed end In this experiment four types of the number of the c ons traint rings 0 1 2 4 have been tes ted 5 Figure 3 Pneumatic artific ial mus c l e with c ons traint rings III ISOMETRIC LOAD EXPERIMENT The experiment s etup is s hown in Fig 4 One end of PAM 5 is mounted tightl y to a metal frame The other end of the mus c l e is tied by wire rope with d ifferent l oad s s us pend ed to it Dis pl ac ement s ens or 8 is fixed to the metal frame s l id e rod is c onnec ted to removabl e end of the mus c l e s o that a prec is e meas urement is mad e The pos ition d ata obtained from d is pl ac ement s ens or is s ent bac k to the PC through the A D c onverter To provid e the power for the mus c l e air c ompres s or 1 c an s uppl y 0 8MPa c ompres s ed air The c omputer c ontrol l ed s ol enoid val ves 2 c an output a pred etermined gas pres s ure In this tes t weights 7 are 4Kg and 6Kg Compres s ed gas enters mus c l e PAM c ontrac ts whil e the weight is abl e to maintain c ons tant pul l ing forc e The real time d ata through the s ens ors are l ogged to the PC The experiment is repeated s everal times und er d ifferent c ons traints Then we c an s tatis tic al l y anal yze rubber tube braid ed s l eeve 133 the res ul ts to find out the rel ations hip between the c ontrac tion ratio and pres s ure of the mus c l e for d ifferent l oad 6 7 8 9 Figure 4 Princ ipl e bl oc k d iagram of is ometric l oad experimental s ys tem The l ength of mus c l e is meas ured by d is pl ac ement s ens or 0 l is initial l ength lis real time l ength then c ontrac tion ratio is c al c ul ated as 00 l l l 1 Fig 5 s hows the rel ation between c ontrac tion ratio and pres s ure From this figure we c an obvious l y c onc l ud e that the experimental c urve is a hys teres is c urve this is bec aus e of a c hange in d irec tion of fric tion when the PAM working d uring a tes t period And at l ow pres s ure the experimental c urve s hows more hys teres is than at high pres s ure This kind of phenomenon is referred to the internal fric tion c oeffic ient of PAM and fil l ing pres s ure 10 Figure 5 Pres s ure vers us c ontrac tion ratio In ord er to highl ight the infl uenc e of c ons traints c ons traint ring d iameter s l ightl y l arger than the initial d iameter of PAM When the c ontrac tion ratio reac hes a c ertain val ue the c ons traint rings begin to work on the PAM When c ons traint rings d on t work the experiment c urves are s uperpos ition when c ons traint rings und er working the c ontrac tion is obvious l y s mal l er when inc reas ing the c ons traint rings in the s ame pres s ure Cons traints red uc e the PAM c ontrac tion abil ity IV ISOMETRIC PRESSURE EXPERIMENT Is ometric pres s ure experiment s tud ies the rel ations hip between the c ontrac tion ratio and forc e und er c ertain c ons tant pres s ure One end of PAM 5 is mounted tightl y to a metal frame through l oad s ens or 4 The other end of the mus c l e is attac hed on a s l id e pl ate s l id ing al ong l inear guid es and the s l id e pl ate empl oys guid e s c rew 7 c ontrol l ed by a s tepper motor 6 thes e trans mis s ion c omponents are abl e to s imul taneous l y obtain high c ontrol ac c urac y and operating effic ienc y In this tes t Pres s ure val ve s et pres s ure at 0 1MPa 0 15 MPa 0 2Mpa and 0 25 MPa Then by us ing the motor to c hange the l ength of the mus c l e und er the c orres pond ing pres s ures mentioned above The d ata of pul l ing forc e and d is pl ac ement through the s ens ors 4 6 are s ent to the PC The experiment is repeated s everal times und er d ifferent c ons traints We c an c arry out d ifferent c ons traint is ometric pres s ure experiments und er the d ifferent pres s ure 11 Figure 6 Princ ipl e bl oc k d iagram of Is ometric pres s ure experimental s ys tem Fig 7 s hows the rel ation between c ontrac tion ratio and forc e The output forc e of PAM is rel ated to c ontrac tion ratio the greater the c ontrac tion ratio the greater the output forc e As mentioned above the PAM is ometric pres s ure c urve is a hys teres is c urve d ue to the infl uenc e of fric tion With the inc reas e in the number of c ons traints there exis ts s ignific ant hys teres is phenomenon the experimental c urves d rop as a whol e the l inearity d egree bec ome poor but the trend d o not c hange whic h c l earl y ind ic ate that c ons traints are s ignific antl y impac ts the s tatic c harac teris tic s of PAM Figure 7 Contrac tion ratio vers us forc e V ISOMETRIC LENGTH EXPERIMENT The experiment rig is s hown in Fig 8 One end of PAM 5 is fixed on frame The other end of the mus c l e c onnec ts a s l id e pl ate s l id ing al ong l inear guid es whic h is the s ame s truc ture as Is ometric pres s ure experiment s ys tem The s ys tem is c ompos ed of a s l id e pl ate a guid e s c rew 7 and a s tepper motor 6 s el f l oc k d evic e whic h is us ed to ac c uratel y c hange the l ength of mus c l e The c omputer c ontrol l ed s ol enoid val ves 2 c an make gas pres s ure c hange regul arl y When c ompres s ed gas enters the mus c l e a pul l ing forc e is prod uc ed and working on the l oad s ens or 4 The l oad d ata obtained from l oad s ens or is s ent bac k to the PC through the A D c onverter The guid e s c rew is c aus ed to rotate by means of s tepper motor to c hange l ength of the mus c l e The experiment is repeated s everal times us ing d ifferent c ons traints 0 1 2 4 n t scon st r a i 44 t scon st r a i n 23 sn tcon st r a i 12 tcon st r a i n 01 n t scon st r a i 44 t scon st r a i n 23 sn tcon st r a i 12 tcon st r a i n 01 134 Fig 9 s hows the rel ation between pres s ure and forc e The res ul t is a l oad c yc l e of ac tuator forc e in the range of operational pres s ure Fig 9 s hows that forc e d ec reas es with ac tuator c ons traint Tiny forc e is al mos t al ways meas ured d uring the d ec reas ing pres s ure phas e of the tes t 12 Figure 8 Princ ipl e bl oc k d iagram of is ometric l ength experimental s ys tem Figure 9 Pres s ure vers us forc e Fig 9 al s o s hows that the output forc e of pneumatic artific ial mus c l e is proportional to infl ation pres s ure However d uring this tes t fric tion between rubber tube and braid ed s l eeve is very s mal l the hys teretic behavior appears to d ec reas e The rubber thic knes s whic h is us ed in this experimental is s mal l The rubber el as tic forc e is s mal l The graph c l earl y s hows that the s ys tem mentioned above have a l ittl e infl uenc e to this experiment The l inear rel ations hip between pres s ure and output forc e d o not c hange when the number of c ons traints inc reas ing However there is a c hange in their s l ope Without the infl uenc e of the rubber el as tic forc e and fric tion between rubber tube and braid ed s l eeve the c ons traint infl uenc e is obvious VI COMPARISON OF MODEL TO EXPERIMENT In ord er to verify whether the res ul ts are reas onabl e a theoretic al approac h is introd uc ed without c ons id ering the d etail ed geometric s truc ture mod ified from the work reported in To find the eq uation of the mus c l e forc e by us ing the princ ipl e of virtual work there mus t be an eq uil ibrium between the virtual work i n d W d one in the mus c l e by the pres s ure and the virtual work d one by the d is pl ac ement of the mus c l e out d W 11 s ee Fig 10 Figure 10 Sc hematic d iagram of the two interac ting virtual work c omponents i n d Wc an be c al c ul ated with the hel p of the rel ative pres s ure p the s urfac e of the pres s ure attac k i S the normal vec tor on i d s the working d irec tion of the res ul ting forc e i d land the c hange of the mus c l e vol umed V i i i nii S ii S d Wp d s d l pd s d l p d V 2 The axial forc e Fand the mus c l e axial d is pl ac ement d l prod uc e the outer virtual work d lFd Wout 3 By eq uating both the virtual work c omponents and us ing 2 and 3 the eq uation for the mus c l e forc e is d erived outi n d Wd W 4 d l d V PF 5 By as s uming that the c ontrac ting mus c l e s urfac e ac ts the s imil ar as a c yl ind er i n d Wc an be d ivid ed into an axial and a rad ial c omponents The axial c omponent has the oppos ite working d irec tion to the rad ial c omponent s ee Fig 10 The forc e eq uation is found 2 2 d r Fr r l prp d l 6 A PAM is mod el ed as a c yl ind er and the wal l thic knes s is as s umed to be zero The d imens ions of this c yl ind er are the l ength l and d iameter2Dr As s uming inextens ibil ity of the mes h material the geometric c ons tants of the s ys tem are the thread l ength b and the number of turns for a s ingl e threadn The final d imens ion us ed for this formul ation is the interweave angl e whic h is the angl e between the thread and the l ong axis of the c yl ind er The interweave angl e c hanges as the l ength of the ac tuator c hanges The rel ations hip between thes e parameters is s hown in Fig 11 13 With the hel p of Fig 11 the c orrel ation between mus c l e rad iusr mus c l e l ength l and interweave angl e formul ated Due to the fac t that the l ength of the fibers is c ons tant one find s that 00 l l c os c os and 00 r r s in s in 0 l is the initial l ength 0 r is the initial rad ius 0 is the initial interweave angl e This is us ed to c al c ul ate the c orrel ation between randl i p d s i p d s F r d r d l l i d s i d s n t scon st r a i 44 t scon st r a i n 23 sn tcon st r a i 12 tcon st r a i n 01 135 Figure 11 Geometric mod el of PAM 0 2 0 0 0 0 0 2 0 l l 1 r 1 rr s in c os s in c os 7 henc e 2 0 0 0 2 0 0 2 0 l l 1 1 l lr d l d r c os s in c os 8 By us ing 6 7 and 8 the forc e c an be c al c ul ated 2 2 0 222 000 31 tans in l Fr p l 9 The c orrel ation of forc eF pres s ure p