Compliant Mechanisms by Larry L. Howell

8/4/2019 Compliant Mechanisms by Larry L. Howell

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. u c . , 3 &!.K~l..~!nk o c i J a n u l r s . m s . * . ~ ., . ., . 8".. ;0 , 3 5 '9 .1 11.3 1 i Ene t gy 1!;q lllJ ialions .. , ,. ,. , . , ,,' .... , 300111 .3 ,2 'Requ i l r ; ememsfo r B istat:'He IB eh~r " , ., , . , 3621 1 .3 .S Y O un g [B istab le MeehMisms ..... , ., " . " , ....... " .. , . , 3 6 7


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Cn m pnW iiltme chan l i~m so f fe r great prora ise ia pmv. i o i ng DC'''' a n d be t t e r ! ! :o I : u t . i : o m s tomanJIIJ1,ed l :a :DI 'ca~.~deslgn problcili l lS. S ince m aeh r e . c ; e a l f c h In : th e t l leory o il c nmpUan itrn ech an lsms h as been don e in th e ~a:,n few years,! it is im po rtan t th at: th e a b u n d a l J ! [b lfo rm atb .ln 1 00 presen~ed to the enginecr lng t ' ( lmmu l1 l i t . y~n a oonc iS ie ,~ ,u_ j]de : :rstan:d !~a b ~ ~ . and usc,fu ' l , forml. The . pUrpO'!iieof~h~sbook !s to f f u . l l f i U thisneed .fur sl\uj~nJt5"p r a C : t i : c ~ I 1 i S , e : n g ; i n ~ r . s . and r e s e ' a r o J : J , ~ r 8 .

The: boot presents Dileduxls for fh e un aJys i:s . an d! de s ign o f oompUutn l c c h a n i . s m s a n d ! i U U s t r n t e s d I J C : Mw i t h cl,amp]cs. Th e m alerials in dJcboo Ic . p: :oovideideas far e ng in ee rn to employ the advaln:tages of cmnplia1l l t l iJIoch:ali lul, l):ruusn way~ thatothe:n .v~:se . m a y n o t b e p ossU ') :le . T ile : analysls 'O f sm.aU d e : E 1 e c l t ~ o l l l devk 'es i saddrc~ssed. but: emp,'asi:s isgivcn Co c-omp! l ia :n tmec~al l l~sruru; t ba t: u o :d eqn ~argc.n o nUQ ear def Je c'J lo n s. ' T h e p scudo ..r i g t d O O : b o d y I m o d e l i ! s b:uroduc:~d, a s a .me thOOwlti .cb, :s~m plif f ie s (h e an ally sls o f cOn lp ,u an t: ! rI leChart is li ls th a t, u n d e tg !o la rg ed " ' ~ e . . , 9 : ' " " - I T I I ' " b '\If - m ' . . 4 e J l n 0- l '1 . , ., . W . w t i l ~ ' I" " m -e ~ t '~ . . , c -,,-m ~ n ~ O " 'iI'c~~!;'.m , ' a 1 ' I ~ ~ " ' ' ' ' ' ~ ' ' ' m ' :- c~U .. d ......I."'J .L",\JU "~'!C u,....."... 1L e , ~L.u~s COnLL.1 ,0." I~. l~rn!:JiII~J,lcO. __ J , " . . .. . . ,U...'l"_'" .s,'c n d ~ 8 : h : n .p U f : i : c : a t i : o n ~ : a k e ~ , i l t p o s , i d b l , e to dccsign c { ' l ~ l : 1 J p U a n ~ m e c h a : n ~ S : I i T I ~ so r ma~ytypes o f tasks, T he ad ....I!rn mge.'l:o f cQmpUanl m~c: ,hani smIS in th~ l B : r E I . e : r g i ; n g aJ'ea o ff 1i.If lcro e~ ec~ rom ecb aR l caly stems (M EM S )are also addre ss ed" an d se ve ra~ M EM S' c c ~ a m p . I , c ; s a r e p r o r v i d ! c d t b r o u g b o u t , tb e b o ok .

TIlle , chap~ :e rnfC u rg ard ~ e d to now fhHI!lI si.ru.pJe~ om o r e eomplcx iConc~pl '8~. lhebo Ilk then eon elades w ith the a;ppl i:ca i jor li o f m e I P : r e ; v i i o U i s m a t . e r i : a l : s to S : p e c : i l f i . , e t . Y 1 J X : - s,o f de vic ,c :s. T Il is IS done ~y {) irg ,a niz in g t he c ha pte rs in toma jo .r :se c tio rm& f iJ ltro d iu e ~t-> ' ~ ' ,, d ' - , - "~ , , , ]- ,, :, -, - [. ,- , ' : " 4'1--. - - ., - d ' '- - ' '' i I- I~ - " " .i ,,-, e c h : ' - '" ' -' , . ' - " J ' ' 1 . , : ' - , " 1 ., . .JQn~d l f L amen 'm .S . ; : u n . L y~~~~i.!e5Ign~.an_specaa . -puq>osemc c.a nU !im s, .. n a Sllmhali_ .. '_ "'-Wily~ s;i~npleexa~:p~es~ad1iune u n d e r s m m : J i ; f i l g ~ . f oUowed by n u ) : 1 ' e , c o m p ] l i c c a r e de:xal l lp~e,Sl th.a~,de1lionstr~te.how lhe mater ia l : can tle : used b l app; l~cat ion$ .

xv


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PrefaceR e"Jiew o f e~seAda~ .UP lCS .~ n s l r c c o g l h o .f : m a t c i T ' i a h ~ t machine d ( . , g . ~ g ; n . an d k in e-

m : a : t : i : e s i : s , :~)fmi"idedmc;liCa(e a s e l f . .. c .o f : l ! t a i n e d book. i lhm does nos ' l I e q u i . r e a : Io t .o: faddi~n O D a L :refe:remt'esi ln 'so~.V 'eom,pHant -mer ihatdsm p rob fems" The ,s ewv~mv$ ~n heJpem:phai t .~ ~ m p < n t a _ n t ~ O p , t C S th e JCadcr.ha.5stutHc,dpr~viQu~s:ly~o r th e y ,c un b e used asa. Fe,solllfCe f 'o r lh oseFmm ! o th e,r dtS 'C ipH n e;s w h o m e' 'W O l'ki.ll,gin r h ea r ea o fM EM S o r~~~teiar:eas . , The a p p e n d i : < e ,s p l ' o " i l i d e a . [eSOlJJ!CC fo r q uick fC 'J t : re lce~oi lmPOl1Wl teq ,H a:l 'i .Or t lSPW sen 'l ed i :n lhebook : .T he a re a o f o o : m p l ia i l i U , m . e c . b a H l i : s m J ~ ex is ts tibanbw 't h e v isio n : a m d . ~ n s j g 1 : n o f,Professor A s ~ b o l k Mldba , M a n y have cOltributed. to t h . e : Jcnow. l~edgeof oomp ]~a l 1 tl n ~ ha n j ~m5 . b"!ltPJlaJi;$SOf M id h~ m ay 'be ,conside red ti le fntii lc"t ,o f m o o e rn ,c ow ;p~ i~0011 .me eh an is :ms. H l s iin si gj b,t and . vii t!i!i io:~a.ve bad a [pro fo uud. effecj1 o n th e : fleld and00 t hose 'w i tb w~Gmtte nao ;es 'oc "a ted I II \! I- e :'r re - dlt ! beJ -e f i t oo fro,e- bo t ' hh " - ,w r l .__ .~,~"~w,~~~ ,Sj,L_" ~a.gi!i . . i ! " 11 ..' _ ,.. m .. 1.18 .~O,h t l c o m : p ' J 1 i a n t I J O O c h a n t s m s : 3nd h l s C 'J : a m p l e a n d m i m t n r s h l - p . 3IId. l : l ! 1 i I I 1 g , f 3 i t e ~ u ~ f u l i ' h i s ,i r n l D q e , n . c e . .

TIte , ea rUe rvcem im l , so f this book w ere use das noses IIom;pUain t mec!hanisms,courses . ( J f t l ~ o m d .at :B r i gham Y o u l 1 j g Unj :ycrn . i .~ .y~urdue U n t i \ 1 e r s : l t y . and t !h c Un ilv e rnh .yo f :M j i 500U< f~~ : 9 : n m a . StOOe ' I l L " ' Imade . l i l l !a . m y h e l p f u 1 oommen t . , t o j , l i I lprorve th e q u a : ~ i i t yo f t h e : no t e s ,S e v em l m U c a g - - '- 'I le s lU1V ' t : grac iQus: iy ' V O t IJ : U l t c e : re d ~ b e i , r t lm .e a n d e xpe rtlse by cea-m h u t l l i l g , pam of fhebook. Professor O . K. Ananthasuresb a;[ Ihe~U l i~ersi~y IO fP e n t L cS , IV ; 3 ;n l a a n d PmfeSSQf Mal) I. : F ~ ~ e : r a i p,'en;l lsy I v a H : i : a . S r n t e UIDI l \ i~ rs i ty w r o t e'Chapter 9. Dr:. MorgaJl D. .M urphy of . 1 D e J i p h i Autnmotiv~ Sy'St'em..s'cor r u r . ~ b u ' : e dAppe .nd~x( i . Obaprer ] 1 re lies h eavn yo n g,rru:I:U tat,e \~ 'O Fknm:p~eted b y Br ianJensen\\\h~n h e , was at ~B rigflam Yo un g Un iv ersclty.

$-O~Qf :tbe.lext ad ti.gure-s in Ibis book.aro summarized from.prey~~us. \!!i'riil~in,gs. .lncludl!l lg a .. num lb e r o fp apern ,c oo uth :o re d. w ith gradiU!iEI! te ; tm d e n r c 's a n d . eo~~b,~a:!ues,andpubUshed by dJe Ameri can Socie ty o f M echan ,c a~ E;ng ineeB(ASMB. )ln va:_rio us ,c~n feren cepro ceedin gs an d in th e J ( } ! U f 1 : l ( l , I . o i Mechanic,, ] l D ~ s i g n . "Workf rom an :u rn ib er o : f g : r : a d i u l l l e t S ~ U 'd e , ; n tt he se -s h as als o been lne luded, O r a t c ; [b l t h M l k -s w sex ten dedl 'O all th use w llIo havepal1 ie ipated. in Ilh is \V{)~~,: J ame s D e rd eri an .P a iric kO p dah l, :B i rlianEdw,a:ms" J ohn Parise, and.Brlsn Jensen h:3! . \ l 'ege:nerouslyco(IDri .buleds~tlO:M o :f th :irs b oOk,. The cOI i l t r l~Jt ' io :ns 'o f Swl:Ly,o;il.Bre~tWe;igbt". and, GregR oa~ h are : o l ;sogmat ly apl;llecialed.,,$ 31 iCd lle 'e ff i: .r r t \, o f m a n y o il le r s~udents t ha th av e made Ib is, p o ssIb le . T h e valuab le as.i;i~ '5 uln o e (Jf' M e S la n Popp i b ; is a:~~mgrate-fu U y .a c kn .0 w le d g ~ .,

1 ' 1 1 : 1 1 : 1 M 'ecb a~icalH n ,gj n :e .e '.ri in gD e pmtm cm t at B r igh am Yo u n g U n ~ver :s i ty basb e e l ! ! l . \ i \ ~ r y s :uppordve at t lds pmjed . an d. h as p.ro vided m an y resourees toas:sis~ ie n .its,eomple . t io l ! ] . 'The, CoUeg ;e o f E ng inee ring and t l1ead:l ]1j l i l~:stmt: io.n. o f Brigham Y i:m n,gUn ivN 'S tt yt il a;v c; al so suppo rt ed t he nu~ tmr~ scf f'o rt s i A many " " ' a y s .' I : n l addiJtio.n. to th e manysl l l loonts wli1lobav~ p1(fvjdedreooflllmeAdalions ande nco umg~m elilt fo r (b is wum,. o th ers are tban J.ed fur the l r he lpfu l rev iew s and com-m.~nlS:t. o i l m , p r o v e : t l l 1emanusc: r ip l . SpecIal thanks l ( ! lPro" fesso( n..K ..Anan~has.u: r:e .: sh"D r ; M . o .r g a n . D . .M1Urphy~Pro f eS5QrKenn , e~bW. C h a s e , 3 !o dP ro fe sro .rD o nNQ i1 o :n o fBd~:hamYoung Uldve.rsiity":s 1Engmsh 'De,partUleill t , a !l ld lhe l !l~ive :r~J lY ed idngse . rv ioef 'o r",~duabh~\rov 't ews , a!OOC() :mm.en t 'S ' o n t he . nl '~nu~rip t-


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m e m"Ow .D e s e ; e n e :r : g y s ,l o m , g ;e c:hamCiler ist ics : m a y a~so b e used 1 0 des igE lmecb i l i , ~ 'l 1 i ~ S : 1 l . I 5th a.t h av e s : p e c : : l t l l" c " ' o r , [. e - d e f : l ! e c U O i ll ,p r o p e r t ~ i , c s : . o r to e au s ea l n ~ c . C ' h 3 u i , s , r 1 l i lto

~II" 'II . 'I:' . m . : 1 . . ~"h . '['.,"'. 'J '7 .ilCinU!Epartlclh!af po~mt j o l s " I , 'or e~am:pwe.uie meC~!:iJjl:lsm ,s.ow n ,II .~-I\g,w:rtl:". 153,:ro bo t en d effecw li' th at 'WM d~s, i ;~ned O C I have a c o n : S l 3 : n t , o ! J m : p u n fOJr :cer e g ,a r d W e ' .s s o ft h e i n ! ; l ! ! ! l t rd i s p , 1 a c e m e m l t .n: i s , p o 5 s i b ~ e t 'O rea~i~e a . s : ' , g n i t f i ! c a D i t r e d l ! lC l i, O I m n w , e , i \ g h ~ , by usin ,g ( l omp i l ~ a J 1 ! t :ln~h~fIji~m~raidie~tiIl~theifri.gid-~y IC i .} lU ~ l e ~ ~ \ , Thb;m~Jbe,a sig~lUj.c:arnf a e -t o r il a e m s l P i a c : e - 3 J l l I D d , o the r ' a p p U c a U O ! J l s . CompUo o l t mech .m i sms i h a . v e a I D S I O o o r : o : e l 1 l i e dI c o l D p a t l i i e s , by re d i! c j,mg : t b e \ ~g t 1 i t ood s l! 1 I i . p p i i n g e o s s s o f c o n s u m e r p r - o c ' J l l J c : t s .

Fig) l l ieI ,~6. C o m lP ~ ~ a J lI [ . w e g r i r p p e rn 1 ! . ! J ~ d ~ , bo ld a d J ! 1 , i( ! h U : i ~ g , p f O O C ' S ~ i n S ' e v ,e r ald i f lF~ 'r en~harnh 'chem ic -D I~ ,


12/45

A .L ~.~I' 'f - IU" '1:."" .,1. ". -0 'I..: ' I:.. JI..__IDO lll.! er ( l,Uva rn_g, e: 0 . com ,pw lant meCuaJl~Sim:1) ~s h ie ease ' \V, l: ! i i l . i l\ ' \ i ' , I : i l l ICLiiu])ey are:mJ~tllllurized [I 0 -1 9 1 ID . S imp]e nrrl lcros t ll lc tiUfCS. acmat ;oH ~ and se lo om ;afe S i e e : i ~ : ! i ! ,l y i : o i e lJ1:sa:g:e~a~dmany o th er 1l l l1croeleGtromei;harruical sys te :ms ' (MEM's, ) i Sba" 8M'at,pMlmlse.. T he Jie du cu :o !D in Ib e ' to~3iln[Jmlhe:r of pans an d ,j,oinlS o : . f 1 e w d bycompUan:t: m e c .l i w a u i5 , l 1 Is i s a . 5lg!l l i :f icamt a t i ' Y . 8 J n : t a g e I n t : h e f : a : b r h . : :3 i H o : n o f micmmecha:n isms"Comp~h~[ltm~c:ro!ll~echmismsm3iybe fabFi,cated us:ing ' t e c l 1 J m l c d o g y a[lOI!lllllleii;als,s imU a:r to dio se used , J n d le f ab r ic 3 ! t i: o u o : f ~Di[e1lrnted e lre ults, M BM S 3 liC ~ discU5S1~dII more detaU in Sec t i !D1 1 .a 6 .The >oompUan~f ishhook, p lj, cr n , ~C omp : l, ie r n ) ,m~ws tTa~ed ijn ,f igu.re :~.8~emOJl8tta~iC;se vt';m~ ,o f th e a.d,vafilllia,le:s d~:sct ! lgsed aboVie; . P a r t . ~ C O U I T I I ~ reduct ion is ; l e ; v b : I J e n t ill! malt h e y are i n u e c t : i, Q ! t i . n :~ old ed as a silngle: piece, T h , e y are in afald:y hamh ell\"lmmment


13/45

6

whe re [l i~njDihlts nmym:s t ,andreq!uire n : uD ema~n te u ll ce ..T h e)' are , 1 1 : S C I ' ~ i g h l \ v e : i g h 1 ~and Me IIU)~o [ J . ~ ye,u,y[O Cor.ry1 bill w i n n O O l ~ : i i f the ;alg l lcr dmps Il~!ilm.lmlwate:r..

1Ihe~hi~h'~!lped'On'i!l~IQeb E c y d ~ , '~s~h(llw~ i n :FtGto: reL S I ' ru'e m~ttI~t' ' i; :x a m : p f e :'o f a ,on tmp~i.3 Jm~I l~ e c f l !. i , !U J l UlI3i t d e n l 0 l 1 S u a ~ e s seveRd ad'l3Jmlt~:ge;s o f oompHmr .r :J l :e c i h ! 3 l m i is m s . U I r n I U i l i e ~ . m d ~ t m Q n i J J l l, c M l it L l e v e r ; . : t y p e btilkes. I the,-si3: l !Jrampad:5 do nllllr o l a ~ l 2 l : i l m l m : tu ~ : i r m a tio n. 'T 1h ef i r n t b(r:Ii l te:sthat bad S U i C l i : Im o U o tll u se d i l i J I t [f :ad1:t i ,onB~ porn . l l~le~ogram :rolr,;baf ' t bmikageu l acbie!l le~b:e d!e idred mot io in~ :ad. a re turn S P . I ? i . F l I ~ , w asw~.sary I to le n5~ r e :t J 1 J ; 1 I I 1 t h e : b r n l k ~ \ ! ! ! ,( ) i U i l d rlisc~~~ge''\I'hem ~ h : e l 1 ' . i d e r~e ' tgo( ) l f [ ihe1iD ia:[Jd ~e .hil l ! compU8!l t t . b ra ke s sl:i;o w ,n h3 !w ; 1 l I Imdl l ! !ood. ~~ncoum~ooc . : n . ! l se n~o phl lj~m:ts a n : c ! l t h : c . r e r u m : s : p r i m g : a r e : i l ]~ :egm:too into a : s in g l e l l J e l ' l : : i : b le s ~ r , jp , , o f 1[l i taniium. o rs ltU l le ss s t:e et Thellnll!~!!l:fatfWreli 'c: lalms lh iam the : m a n ; u f o t : ll lu i l i l .g , cos~i s . apil l rol l l l -m a r n e I , ! o n . e - l h i : l i d . o f t l r r l a ~ . fo r tm l e ( l t h : e r s /l y le e l f , a ndBe l m.ot i , t11bmkes" TIle r e U a b U . i ~ yi ;S ,~ IDCf i f'Med ' Ii leC S! I lS 'C~f ' l l f ; ~ m d l l J c ~ d . I n I ~ m J O O : I i o f pu ts lo ' f ru .~.M ld t h e spri:n g lIiiIa t w as,~W!;i!~gi'.:~~S!'U:lille!i'c ~ i l f i : p ~ ! ! ! ' i n t s ! \YM e l i m _ i : ! i 1 l a ~ d . The~dt!!~~d joiiw~a1.~otlake i , t mOrer eUaJb .~e: in d~n :y l e n \ l : i r o n l l1 e : I i II I: S ~ sichas m o u D ~ a i l : 1 i bjS i ; , i lg ! . be~all ie fOilieigr.! maferi:lllIi.. ]-. ;,., ..... iI" ' f - ' " I:.~ f - . . . . " . .. . .~~M ,0 .:oiit;\lyeli"mulJ!ulLwlly 0 " gettl:lllg 10 jG~nts:.11o.1!lmuc;f ,0: oomm.ol ' u e I V l c e - S h i J a m ; 1Ue! c o m i P ~ : i l 3 ! m w ~ e c h a ! l ! w i s m s a f e : :shO'\:v'li.1 F i g )I J J 'p e I " M l

A I : I 1 J G U l g h . ' o l i e d n i C ; : a . l i I u m lb e li ' o f ,adW lJlla,ges~ , c o m p l l i ia m ~ m e . e l \ la n ~ s l l l! l : S l ! l re s e n t se,rera~,chaUe ,ui es : ;mli ldd 1 i : 5 a ( h \l m l ~ l : e s i J n ! i O i f l l i l . e3 J P ' P ~ 1 c a t i . o . l l I I s : . P0[h3 IP iS~he : Iuges !l i ch : :J i~.~er tg 'e .ist 1 . " , - _ . '~~'a~'"c.,~ ,A:"I I , I , ~ ' i l ',c - '- " I ' U ' 7 " - -. - ' . ~ . , -.l d - : - ' " ~ ! - ~ - --.C , - - . - n l " - '0 ' - c , ' c _ I I I , . . , : " . _ . c 1l"_ .. I ~ .!l-[~e rell ...~"!\'ew~W.I~ '~ ' . . I ' In _lit ' .i ! . . . Ilng an!.!! . e 5,lg lm lm g . o ompw .1 all....m~Cli.IU.I:sms\..wu.OW ..'ed lge ' o l f : l l l e ' d i i l a n i s J f l I Q I J ! B ' I. y 5 : i l s a n d s y n t l l . W l i s meU t od s a (1 ;d ~ be de;Hec~h:m o f n e :: d b l i el I t e l m O O : l i 1 : is mq i il~md . T h e o o m b i : lJ i l } t i o [ J J 'o f :t t .e : 1 . " ' \ 1 0 'b O O . i ie s ,o f ' k m o l ! ! ' ~ I ' ~ e d , s e ~mcom:pU-ant m e c h i 2 l m 1 l i s m s l icquires. 1 ] , 0 1 .o \ l 1 i ~ Y_ l iJ ! i i l d l u s l : 9 i m : d i : l il g , O I f b o t h . l i n J ! ~ : 3 ! l I s o n n u lde 'n tan d ...h ~ . g ; O I f l b e ! i l ' i ! ~ ~ : e r a . c U C l l n s .in a. CO .W i IP ~~ X .iUl.3itiiCi~'!. S b : 1 ; c e : n ' i l : ; r n y o :f Ith e f 1 , e x i b i l e r : n t ~ m o o r : s ,I l l I n d e r , g o ~a!I!~ i f l 'H ! .l c t , i o n s : , l i : n e i iJ l r i im t iJ . b e a m . ' e q l : J ia ~ i i o r n saJJe I tC l , I !ongel ivaHd. N ( ) i n ~ . i . m 1 e a J l i


14/45

'~

r 1 g ) l l N : 1. :11 . IComrno~ compl i lU i l i l d l.w i!e ~ .. A. b i il fl d ie : r d l~p. . .p a p e w c liiP b i lc l l : lp~ck ~rnitc\b.l i : [ Ie: l ! 'em~sibc 1 I I Ir l e i l : . r r m ; [ J !l!~ii~>eHpper s ~ re 1 lihO \!o fn .c q u , e J t i l o : n s that OOOO i l l l U fo.r UU~~g.e'01i11elt ic~on~il$ear,i t i !es,c,l lsed b r y lallUe de'llect~oiJl:S1 I 1 I 1 U S ~ :be ! :1 lwdLB . ec : ll .1 I s. eo f t hese d i . M ,cmlt ie5 t n H ! lm y c o l ii fl p ~ i ;. ~ liifI.oohanl~8I1lS in I tbe [ p 9 J S [ .\ v e N cl )e~dgned b y ~ r i i a J Jand. l e r r o r , S,lch m .et lh ,ods app:ly oM l ) ' 1 0 v e r y s ~ m p l e s y : s t e I i i 1 1 5[ ] J U l t . ,p!l ll " .tbml. ,r :e I .a~iV 'e ly~i :m lJ l, le~:ask:sand are oRen not o O ! S : I- e f f i :c j le n l [ : fornul l l fY pCi le i l l i -tlal ~ l p p : l i i c a t i l o n ~ . Theory h a s b e e n de;ve lo~d [ 0 s i : ~ n p U i f ) i the ,ana~.ysisa liWd c I D e ~ i g ; no rcD lmpUa l l l ~ . r r o e c h a n i is m s . : 3 ! l J 1 i dU \ l e ~ , i .l l li : t a ! t: i .o n ~ are no t as g re B l~ . 3 I ! i , t h e y ! In , ~ e ; I; ~ e r re ;. . I 3 ; '~ 1 i 1 Ic o n s ~ d e l i ' . i , l , g : t ihese~d:val1iOe~. h G w , e v ' e r ~ , al:1ia:iys~sil' l1d d C c S i g f l i ( } i f o D l D n p ~ i il l n t ,W : le c i 1 H t -n ism s are t y p i I C 8 U y l i tu.ne di f f f icu I[ U : II 3 ' n [or r dgi.d~bod)' l m . e c i la n i s J l1 s .

E- !ne~ :y s ' I ( ) : r ~ d ifl!ne:db~e c ;~ e :m e : l : D J t : $a : b e e n d'~S(i iJs!Sled, a s : l ! i lWadvant :a.~e", : ! i l i~~ce~C i l I m : l 0 0 : used to si .l :n IP ,I~ i. fymechaa isms ~ha: t , in : c o l l J l o i m ~ : c .s , .r ings. obln in spec-madf O ! l'o e e = d e f l: e c t i: O l 1 1 1 r e ~ a : t : i : o m ' : h ~ p s : " a ' l l d : s t ~ 1 ' i e , j 2 i : l ' 1 e r g y : r i h : a J t h : ~:rnl f ' i 'e : ! i ' r e d l o r I tm~s : ~bma1b y [ f r ID e 'm o c ~ a : n I ~ s ; Im . f 1 ] ' D ' . i V e l i l c r , . i n ' c r . m e , a p p . l l i c a : [ ] o l s : " ba\! lrn.~. e m : e : r g y stD! r ,ed~n . f i e ' x l b l em e m o o r n i J j j , a . d i ~ s 9 J d v D i n l : J i , g , e .F i a r , e 'x a m 1 p h ' l: . I r D ! . :mned\lim~sm.'S.rll:n:c~,~on: s ~ C lII[Jr.SJe'.r'e ' l ID ie~g, f ro lJ l ,~ h e wnpUl . k) 1 M O ItW ~ : PlD l~ :.UO [ I Idi l ! ; ) f th e e ne rg y ~ tmnsfeDied, b l!!l~ om : !: iss;[O:redin Ilh em .e c h!a nh ;:Il:l .

.RmHg!ueailla~ysi:s ~:St . , :p icaUy n 1 i W I ,( ! Ir ev~tal ! t i s s u e : : fQl iool1f !p~. ioo[ m 'e c h i J I l lj s m s , U ! w a n:(61l '~beiirrjgid:-booly( ,; IOl l l l l l1terp31ri : . S i l l l l J c e C iom pilbtl:1i~m em be 'lsare IORCl l l ioadled cJ!clil-c ;a illy \V bC i n : 3 1 ' C D l r w p l l, i ,I U W ~ : m eehan lsm is use d . i'L is i l l1 l p o r l l :i l Im i I ~ ' t , ( I i ! d e s , i i i ; l n tio~em e J m o o l f 5 J.s()lilc:yhav;e suf f icEenl f a l i , g l l ! l ! L \ ; .U f e t o perfo!fm the irpJ lescri i lcd [1IJ 'Ilc t i ,Ol lS.

n : t e moHo:nf~( l ' ! l I ' ! the denec~ ;~on Q f C O I :w : lp ~ i , 3 . n ' t . ~ i ' l l 1 lk s i s a~s ,o~ . i~ l i~~ lCdD l y IL~e: s l rr e n g t m l ,c r . ~ h - .~II- ", c -- - ~ , .. -~. - '1.,- P ' " " - I ' . . - . - . - , H ( ' . il;'.-: . u - I.,.c-,- - ~ .-, ,cc~


15/45

8 ,

4 , 3 , , '.. .TIle coooep l o f u si ng :f ie>&lbl e :mem:be rs , to-store e n .e J fg ya nd cre a te m o t~ o ill!h as beenused ~[o;['miUenru'a. A__rcl ae otogjc~ l e vide nce s;u,gge slt$ 'lh at OOW $.h a;V (l:been ,in , mesin ce b efo re :801) ( ) : 8 , . C . , a n d WQre t t " l e ~primary wM p o n and,huDi t ing 1 0 0 : 1 . in m o st cu l ,~(vres, 1 l : 2 O ] 1 . ,: b n t i d e . r m,e~,QD,g ,oow ;UIi lS1tal~, I n F:i, l!llre 'I. l ,I, Saidy [bows were eon-s_trncted ofretatJv,ely : D 'e ~ c i b le D U L l e r i a t s , s'UcJh :U wood an d mdmal tS in ew ~ S t m i l 1 l l~n erg" in t h e ! ' b o w : i s , tnmsf 'GmEd to kinetic e ne rg )! ,o f d te ; arIOW"

Catapults are aAoH mr lexamp~e of dte; , ood } use 'o f ,c omp:Ua n.t members used by' t h e G lie ek s as ,ear ly ' a s : th e fuudhC'entllll1 B .C . (2 1 ]j . :Ear1 I~yca! tapu l ts w e re ,co n~structed o f ' v ooden , me:mbe.rs t l 'm ! w e re de.:l,ected. to stom e n .e rg y an d then re lease i tIOp l~ l , aprojecti l~el , :F i i gum 1 J.2is. a ,skf:t:ch o f a ,oompHan t ,catap ult b , y Leonamod a , 'Vinci.

,R e : d : b lc m e m t l i@ _ f f i halve a l s o been usedro sin ndate me lllotijcm o f tumiDI jOI:ntR' 'I l Ic : f f~ ' I ;l ll ra]1bing,e s 'O f book : c 'Ove rn~ (O ire~a :m .p le ;~a, ' i I ' e , been cons t r uc t ed by , ehWlg , -iD.'glhe: mate,r ia] oo~posJdQ n and I J J i c k n e s s , at th e desired , p 0 J . 1 U o f llex ure 1 : 0 ob la lnd le d e si'm d m o ;tlo J l. IOthc tmctboos we re de~loped ~arly~nlhe: tweD l i e~_hce" ' t1 )J~roo i ) t a ] T i l l t h : i s : ~pe o f m o n o r n fur 0 1 E C l T 'app li ca ti o n s . .T h e s i n g l ! t N l X l : s c o o s 's - : f l c cX U ! F e p i 'o l l o t[ 2 3 , 1 (A l u r e t1 .3 a) l:ln d ~ c nd ~ :x . C


16/45

19

. L

.L3Wtu:n .~sUl:e difference b dw o o n a cnm'p l~an l l i 1 I l : o c h u n i s m : a n d a . cOIJ IP~ian t:s~ructtlre?L 4 C O F !sid e r~he 'Happe l ' rnechardsm shol i l l rn, i,n it s und:efl ' i lcled p z y s l , t i < l m in Fi,gureP l A . H ow Illany nJ lJ~sdo es th ~s,l l i I1e ch iUlITS m~a. e"l[d~ [1I~ it fJth esegm en ts fart h e ' o( )( rn lp .l .i ai iJ~ ~ink.

l . ,S C o n side r t 'b :ec o m ip l . i .a n t . mechan ism sh ( )wn InFlgure:PI .5 .(a) How many l i n k s , docs th~smeehaeism h a " ! - " o ?~b} U , O ' I W m " , ," \ f " " ' m - - '- p - ~ j i~ : : I - n - te a m e 'IlC~''''..~. " I - ! i i l - I - Ih~s me L , " ' n ' ~ " " " ' u .? ' R ; ; f I' " I - ' } ~'''Pl~'''n>t-''~)t. -. ,~,' _. ,'.. L__~~II'.J' '\;IV~ ",,,, I J ~ I I I ! o I ; _ , J '~I~II!.IJ.._'''''I.L 'I,'I.i!' '"'-I,'...... J. ' 1 ,11._, ,IJiIi,. : -,tJII'" , !lr, :1i IUU,. , ', . ,~ ,u , .""""',~.U,IIi""~,.-~,~(Irulc~ude:~rmmd")( ' c ) : r : s t l i l i s a.par t iaUy C ; o n l , p U a n ; t : ,li[Jc'Ctilani:sm. a .~td:lyc~D lpnantmcclnr __i s lr n " O : f

a rigid ..body mec,hani . sm?US , Consider ~be ( :QimiP,~i ~ m e C i h i li .E i j: s m m~str~ted in Fig-l i tre PL 6 .. H QW ma'Il!Jlin ks do es it .have? HO l l y . many dgid . s c ; g m c r n J t s do es th is m e cl~ an ~ s:m ,l I T I a : v r c " : ?

Comp l i a n t segmen~s"? Idcl i l t . i fy and lab e l th e segll1lC~l[~of ; :a r. ~hU~k . b ; th is ~fu U y oom pU anr o r a pania l ly o omp L ia nt m e c h a nism ?

~ ~Ol~ 1 - ' - -11


17/45

Inkoducfton

. 1 ' 2 ;I

I .. Con s'ide__JD 'mechmli:SmI Illustrated in F ilu re P t .1 .. .H ow many ~il i lksdoe. .!. I~have? H ow man;y rigid : s . e g m e : n l s doos t h i s . meCiooni's,m.baveN Comp'l li an ! t s eg~mClt5 .?ldfin t~ry an d lab ell U le :se gnmn ts o f e ach Unlk,

1.:8 Cons id . e r t h e mecbanism i U U 8 tW e d In .PlgurePl . .8. H ow maul'" Hnk:sdoes it:tuwei? H@w many rigid segments does;~hismet'banilsmhae? CompHanl t :seg-ments? lden t l (yand . labe-~ U i t c S6:gtne l1 l ls , o f e ac h . l in k ,


18/45

CHAIPTER2

'T r n d m n : n a J 'k i n e m a U c : ~mal.ys:is,assumes~h i l , tt h e m.echan ism H n k s a re ~nfJJnite, l ly ig idan d dQ n o~ de :f le> ctA h hQ u g n cl l isass lmption, i! iade qu a~ e w 'h en tbe den~donsarev ery sm aU '. real m att!da1 ]:swi l l have s o m e d e f l . e c t i Q f J . when a toad i:sappl1ed" S t n c ec o m , p H a n l t mc~ba :n 's :ri n s : ro ly on d c f: i,e c tlo ll fo r t h e i r I D Q H o : n . t n , C { t r d e O e , c , t i u p s c an o o tbe ignored.

:U : ll e jj jl tand nQ n~ i li l~a rdeJ 1~ U o .n a m a J y s i s , iaW r c v : i . e \ l i 1 e d ~ Int h i . s , c h a p t e r . A basicundc r tand in ,g . iQ f mochsin i :cs o f mal~el i i i31.s is assara ed , a nd 'COI i I~ept ,s particlJJhlf io'C \ Q : m i P ~ i a n r ~l l c c ~ a n ' i : S l i n ; i i i a r e < ! , m p l h a s : i . z e d .

,2 ., ' IJ I!E A1 RV E F lS U S,N ,O iN UN IE AR D EF LE C T lO :N SIn :m .e st de : f ! !~1 . i : on3 ! ,n a : ly s c " Q "h ~ s a~ sum ed , (h at die d e : R e e t i Q : ~ 1 is ~ m a i U c ~ l m : ~ lQth e dim en sio !lils o f dm 'f .i tl fUo tu re . tha t t he meterial is 'cl l ,asdc.and tlnnt s:tJ [ai ini5pmpor '~t i i on311co s tr es s. T I i le :. _~a: S :! il urup~~Qm;rc ; used H) s.lI:nplify th e a l : 1 ! a l y s i . s by U n e a ' r l d n gt!lle equ~llo;[l:s .ln most ! l i : tnu:: tural l a pp ll ca rie as , U t e d e Jh ! ct io n s il ire sm al] , 'th e sitres!!, i : sbe Jo w th e e l a B ! t ~ c i ~,~mi t .an d U n c ar e q aa tie n s prov ide : :U ; : :C U M ! C r e : s w h . s . Howc"e r .t h e l i C , a r e e a s e s fOir wbic !h structural: nnnlincarities l (K':our. and th~as!S 'ump[lo :n 'S a r e :nm\ i fa~ . i r l .lnsudi1l easesa n o nUn e aF a ll al :y si ~mu :~ { beperunmed,

Stru~t ) j ro11 : n ~ . H l t n e a r i ~ ' r , e : . .a o o d i : v i d c d . i : h ! t ' O lW Q 'ca .t e , () rf e$~ m a u : i f J ' a J l lonJj:oearitiesnnd l goon : l I e t r ic o o n I '~neaif~t~.cs, . ,'(; l ' Ierial ' lcmll: ' ltf!tff, it ie:K arise w ! l r t e n . Hoo;ke 's b l ! w .wh. ich s 'l al e s I h : :u sn e s s t i; p ' ro~n.' ;oo- 'Ito:- 'F:- ' ifi . dgeNnO~ -Int" l l !.:! l Ek-,--c:]~ ,~f,c-.t!~_~.. -- , 1._ F"" ,I. a _ ~ rn __~ .- _ ,'- , ''It''lf'' ,J' __A am p",_ (),. m a . r e :r i_a~,O IlI~IiI,e~ lf i l[ ' iesinc lud e pllas,lii,c.ity"n .on l inea r e las t ic i ty" i l.Y lpe r e l: a s[ id ly .and c re e p ..

G,eometr ic UO ~ J ' J f : n e . ( _ " , i r i e s IQCc t l L r w ille n d eflo ct i:o ns arc :su ch :UUU , t ihCJa~ l t :o r ' t~enallUre~f the; iPM b iem .. I! , ; ;anl!ples, of g~meurl:c nm~UnearU:i :~ an : lurge dei lJect ions, !


19/45

: & 8

:2 5

( . ~ - _ . > - _ : _ - - - - - . . . _ _ - _ . _ . ~ . J ( I ~ .

i:......Figp're2.]. Cblll:lg~"in delrn:(:ion due t Q C b O l i n i l ~ i n beam i geome t r y . Tbc S I l i O O i ! : furc~ i s:a ,P p il ie dto e ac h b eam ,

The e ffe ct o f m a:te da~ . p oo :p erti.e s, o n . f le :x lblHty is . : f jupponed by ottf~fIIUldth}ngailne d from e ve ryday e xpe rie aees w ith ~ma:tcd;als ,Fbr c) l ; . l l l l1ple. ,.s,IPPOsc that scv-etal be~l I :usare cons:tructed with the same geometry. have tbesarm.e load. but are:m ade o f dif feN n t materials . A stee l (E= 3 0 Mps ; i , 2GJGPa) b eam w ill h av ead e f i e c , t i o n 3 . t h i r d a s ~ : a : r r g eL O Sd l ] : o d e n e c f k m Qf :m a l lumi l1 lum. (.E.~ 1 . 0 M _ p s J . ,7 0 1 a l P a )beem , w hU .e a. pal .ypropyl :ene (Ii ~ 0 . 2 M 'ps,ii. 1 .4 GPa)ooani l ' s . de ;noo~ : inn wiUbe . : 50t im e s g re at er t b : 9 ! _ ( ! I ih e ' a ~ u m l [ 1 l i I J m beam's deHec l i oA .

~n; tuH:ion also supports tb e fact. t ha t : geQm~l i r y af f~c t5H.GXibmi . ty . : I : t you mat~eoome~ih~ngdl : inneT, l i t becOIlile\ mnre f l le :db l ie . It i i s use fu l ~o qruan.tify 1l~lis~[O. roV: ide ab e tt erum :J .c rs ta :n d ing o f dua se e ff ec ts M df i~d~vh i c h is th em o~t e:t1j:cienitapi ' lroachtoobta: i lmif i lex~biHlY.

C.()ntinUlh:lgwi~bthe example offiglure~ 2,2~ i t : is n,~teddun the . f ! ) e : x : i b i U t y is: b - c , l h - I c. d e o e nde n - ~.":-C.' .. ,.~~ .kn .SC~ H, '1 . : load I. '. i l ie,~al a ,d : em" , tcof thc,1 g ..y J ; ' ! p e : n _ell~.on I ~ r u n . UJJc,~_ne__ J & ~ hJle II_a . ~ , rn a rL ~.n . ll-_W ! ry __. _beam rem ain th e' same . b tu U le lh ic ilrn e ss is , halve d . lb e d e~H e ctio n i f lc;reases b~a fac~to r o f B. .No te also tha t~he length o f t ile b eam is,cub-cd.. If th e lc :ngth : ,o f the ' b e am . ! i sdoub led , the OOAn~d e tlie c tio n i'~ i] 1!c re a


20/45

The l re la t i0~s :h lpbe t .weenH:ex~bi l i ty :alild d i U . c t : i l l . i ~ y Is of t en I l1 i1 i.su :ndeOi lood . . Man iY.peop l .e \ !j ;'Uu ld l cons ide ra brinle l'ilUltenal. silldt M g lass no t lobe f l lex ib ie . However.RC - 'li.t~l an d b .~" tt j1e .'C!.~ '.- . --- ,t,- '. '. -~ .~"Ic' --l- '~'~ d . A : . c 'l - - - Ii..~. - .. . .. , .' "-_. .A. u_JU! : , lh _L y~~_ ._ r ic LD ~Ij. are , U( 'hnecessa rhy r c . .l h : e _0 . "g ass ~am Ina ,y iIlA.; .m1U l i I . e" o ' c r y H . c - x F b l e by J l i I .od i Jy l l i l g thegeomet ry a s ; d,tOCIlS8ed above . ' T h i s , d~st:i.Act.ion is p a r . .ticlJdady : ~ m P Q r t a . n J t J n m i c r o e l e c . t r o l l f . l e : O w n i e a l s y : ! ) l e L r n s ~ where , c o m , p U a n t meeha-n isms; are o ften fabl1 icated o f po lys i~ : l co l i l~ ., very b rUdema t e r i , a L One source of ttiiJe

t;. ..' '. .. f " . .1 : . ._ L_L ... 'r ' d 1',"'.- '1 ' . .;1'_ 'b " 'h '"Qo : n'~U s lo nC oR te s' rom hlK: U !;;iID Y 'lO cT (] , . rl,~~~ren t m~1:1~nas un~1 i , . li t 'S~lie.iiiSes,.,M .bdl tl e mal ec. .ri al ,can f al l c at as tro ph ic aiUy when~ ts f i tUure :swe~sis,mac:boo. Howeve r ";"'...;....ii " ; + 1 ' ~ e m t fe - n < i , I . wnl~lI..~...~- i I w l t A t ' i i , _ ' ;~e : " ,~ . . . . . . " , . "~i'i.A4c, '~"v,... " d l the ' l l I ' . ' ' i" " II - iI t , _. . , .,trtlf-. - n - isi!,!!_~4 __ . .:,_. ,~." --~J!I~"" .. ~1'''4.~i l !l . . . n~ ,~V'V" '-"""..,VIH _ Y;I.... Jh.,n:l, ~ [e[l~,.u.,~.~lll.,y : i . C J l d i : n g pro vid es w am i.lc llg , o f overs~l!eSs; the pan: doc-s nQ ~ frl l i :mre. but h as somepem:Jan.el l ! t : dd 'o f l l l .a f rcm. Sam . e d uc tile rrl'ate :r i;:ll:s ( ! i :nch as poly.p'mp'ylene) Ina.)' be,s tre s_ se db eyo nd t be~r yre' ld st re lg ,th tb o us'u uil;so ftime sw i til o:u tf ractl U ri:i ng , .. In sum.-' - , . ' - I e ' . ' i li:-I ,~i.:-;; .-;'-oc\-J:N- .-:-. ' i ' r - " " , , - . ~ - ( ' , - , L.~ ~--.",~ - _ .... ~,'fJ, will 'f : ' 1 ' I - , ,t , , , 'h , ' , , ] 1a r y ~ u n !LC ma~erl ft.._ m a y II.[IIt: ma e e m 1;11\; ~1 .eX l l . l " e . l . IU , u l e y _ . I,~.,a r ca!las.l O P . . ~ca,.y. ..h en o v erstre sse d ..

One ; Q fttle c ihaU elil,g e s o f comp] j_ :aJ l t . m e c i i l a n i s ; m s is toaHmv defl lc(1lo:n~s largercnou igh fbrtlilemechanism to pcdunn .its :~u ( lodon~ wI IUemaj . ' n la~n i in .g stressesb eJow can al~owable; na:dmum stress, Once th e d ef le cte d po-s : i t ion o f a cem plian tmecJ ;rnn~sm, i s knownt t he. s tre ss nn lili) rs, is i's reJ:uively s tm l ig ,f non : va rd . .Mos t meeba-n i S f l . 1 S i 'opc-.n~ein, [ ; w o d~mefls iorn5. a m d i thcstliCsses a r e modeled a s planar . Bend i n san d ,~ n:iin l stre sse s are tHe p ; r e d o m i F J I 8 ! t e .I. o.a din g .m .o d es In ,comp~i,3iJ l t l } l ec l i lan isms, .'D e D x i a l , :B .~ resS a ss oc ia1 e dw i tb an a Jt: ial .ro ,re e~F, is

where F " is the 3)l;ial : foreeand Ai.s , tile are a , ( ) i f tb e cre ss ge cl~ on ,.' The SUe- i l lS duetoh emUng 1 : 9

(bemdi.og) '(.?7~).~ oi .M , ~B t b e ;mo . l J l eD toad ! . y t h e d i st an e e f r em th e n e u ~ r a~ax i s 'to-the p o ~ nt o f im e re ,st .a...ndI ( . h e , m O l I n C l ] ! t of i n e r t i a . o f to o cro ss seetton , T ile : maxim ,um stre ss o ccu rs at dil le:[ o c ' 8 l i c m far t!best f O O . U ldu.')I O O l U i r , a J ax;is"c and i s

(max i .muml b e n d i n g ) ( 2 . : 1 : 1 : )R e fe r to te x ts o n m ecllan l:ca! l de sign and s t e e s s a n a l y s . . i , : s . f o r d e t a i l ; ! ) o n t b . e effects. o fstft:;..SS,OOAc eliltratio flls. te m pe .ratu re ~.e nryiro nm e n.t. an d. other ~oodirn,cond~~~on~d n nr n a ;. y a l m come : i n : t o p~ay.


21/45

ID iS ip Ia ce rn e nt 'y et1 liu s I Fo r ce ,Loads 27

r i,g li ll f le 2.4 .B xam p le fd ~ < ' I , , c : I [ J m p W ~ a l U m e c h a n :i:s m \\'.U h k l l f ~ i 1 ! l . < n d i~ p lla ce lt le m a nd 1 : 1 1 i l 1 k . n t : 1 1 ! v . 1 : I~~ . .

M :ostti! im ilio r stru cnnes are .I:oaded . by .app~ied fmcc : . " ! . . l ix .amp~es o f st!lcl1 s: t ruc. .tiU""'''' ~ 'n : c l l 1de ',bI'~du.e w'th ~lc-.ffi(,:, , , , , , , ,I . 'w ind ~lf"dl~; a~~.~~"-:,~;-II"lom ..: . : - , \VI.~, I ,, ,, ,, :( j t.,~___l!_,,~ -e . - h_" ' , l I"a.. 1. ~y~,"" ',_, _ L~ _ . '_, ~.I.I:g)! 5 .1''''''''1iJ ~,I'I"__ , l , g \ ' = hu,dml!mks loaA:! l , a-'-'"i'~ r, ' , wjl',\1/t'L., .,' .~"" . ' ,-,." ; 1 . , " " '~ ' ' ' ' ..:iI" , f , '1'11o ,-'1 " t " : - i "_y ,~ __,_'" __ J.!I_ __D 3 , 1 J : : C ra tt ,. .-n g ,',~h~ ae1 . ' uuy rn l lm. l ; co ~ ~ , a n Y ! so l.ortl,~" . a m p , l a n t[ f !~ c b an j;sm 5 . hO lW tlV 'e :r .a re t yp i .caUy ~I ! )aded in a. djfJe.fro'l:It~a:y.Rad!1 :er~h!an ea leu l i lJt-! n . , g th e de ne e~ h:m . aJAd , s tre ss ; f rom 11 known to od!~~h ~ disp lacem en t is ' knowi l l ,~ : a 1 ! 1 l d . th ere.s l .dt ing stress and ro ac:tio n fo rces are ' ca~cUi I ,3 i r :ed, .A simple ex,~p:le, j~ iUust fatedi i t l lF igure 2 ,,4 . T h e. d l e : H c c t i i o n o f th e f ie .:x j .b leb eam I S def ined by th e rest of th e ~ , Y S , l C : m ,and ~he 'h :>ad [~ u nknow n. 'T he approach u~ed to design a s y s l e R l I! i l, . ,i : L h a d . i s p J : a o e m e n l .~O'adis s~ gO ii.6 c an ~ ~ydHJ c Jiem ~ han f or s f r u c tu r es wU h :a.force l oad .

T o il~USrml ! ,e this C'OICC:P l . . eonsider the ~w o beams, sJ!;O~,! : f.nn . !Figtn:e 2:;.:5


22/45


23/45

39

ob tain a defl!ectrun o f . B " , A ssum e ~h aJtI jhe defl.ectioli ls, :are sman enm}ghi lha , t l i l r i J e a r r ~lzed be r rn l l equa t~nnBo f AppeJ.Iild ijx D m ay 10 0used .

Fo r a.btmlill w ith a v e;r(ica~1;0[00 at t f u e ~~ l r o eend ,F- ' ' ' i f : ' / ' ~ .',J:"U

C - " " - b r - I ~ ' - ' . , - . '-i~'"- i- ~. ,., 3 :, o J ' - - , e ll ? '1 9 ". ) , . I ' , d ' . ' . - - , , - i' .G_' ." .,. ~ _(jm ,m~ug e'lu~~UJn~ "...". (I ,all,y .,....11 .' , a n _ ,~nlc_g[(hllng ~p,i'CS

W ' ._ , f , . - ' , ~ . ' 3 E ' " , , 1 1 8 " , - . ! O l, . . _ . , . 3 , E I . , " , a ~- I - . -gO ~,---"(1 L )- 2 I}'Po r ab e am w ith a momen t : (Md ) at th e f re e e ad ,

The wo r k done by [he morneur is

90[ [ ; " ' 1 1 : : ' "W -:.Ci.tJ'.. -'-~' L

Iflhc \V iO irK roq lL dre d 1 '0 obla : i n a.defle&;t~on0 is w f itt e: rl a s :

(2.38)

(2AO)

{2A2)

MA I J I )l~'~""'" ..


24/45

l fl e:vaJ jue of :' , e .may be used to oompare th e requiredwurt f or v arious, Itypes of , ~oad .cond i t i on s . TOOvcah! le5 o f Cfo,f ' I ! h e Inad!ing cond i l t iUAS discussed ao ov e are sum:ma~riK din T alille:;l,.2 . N 'o te tha t .itre qulte '5 fO llJ r times m_newo rk. to deiecla. beam whh~f i~ e d! -g lu [d e db o un da! ry ,c o :n d iH o n s l b an . i~wH . r d . to dcf ie cta.f ix e d.-- fre e b eam wi : t havemcal fume ,at th .e end, . This : aiM ) m e ans, cfiatfour limes as , mue h e ntu:~y is .~ to red l . j jH( 1 m : HIOO-g l l J i ded beam.

Work. i s : done to de: l .oot ,O:rebeam. an d t i le ei l l0Q' :Y is sto redin th e beamas strain. '.'..' '";-"5 ',. 'm"1[ .e t d e ~ 1 . t ' ' i . . ' . , . ' - ' , " w J . - . ' . ~.t... : ,-, ..' :"t - . U , ' s - . ,t- , ~ ' , - ' Iene.(g1 . ,I,d_,IS SI~baJ'() __u e e u lg a . .sp:flD ,g , .. u",Ie ,me t m . e r g ;y IS , s ,o reas po,eOdB.

en erg.y in tie :s:l?D n g.lf := 1sprin g: is tw ice! as ' S t i f f as ,a no th e [;~it~wiUs t o r e twice, asnnlcl1 energ~foF. ' 1 1 m same del.eetion. Th0know'tedgc o.f thee; f6 lcj1cncy o f t h e ' load-'l'o ,g ;may beusedto ~s:~gn :m ech an ism s ttJat , ob tahl tb e desired. def tec t ions w h . i l l . e" '] " I ,S1011~gJtt(c:energy.N ow ron s.jdef a isnC1 l1m w ith an uial. lo ad. 'T he , w Q rkrequ:iredto ob tain a :Radal d e : f! :o o l :k l O , o f : s : is

( : 2 . 46 )whe_t I t , A . i _ 5 m e , C ;O O ;s s .- L S 1 i i :o . n a l , R r e a. ~Ifrthe beamh~ 8 , recf,fu: i8tdar c r e s s s;eci t iol lYi .b o n :h :i sl h e; tM ckne ss ,t he n

( - . ) 2 - . - ' c s ; : 2W ' . ~ . ti '/;.,........El..'v. . _ . . h L~- (2.47)o r C = 6 ( 1 . . 1 .1 1 ) 2 For a t yp ia al .f tl e x i b le beam. k i'5, muo b ..sm aU e r th a~ L , . ,an d C Js' v e ~ ~ 3QC ; , c o : r n p a r e a tD (h e v alu e s fro r o lle r I t) ~ d .jn ,g :oondj~ ' iQn$.~ h o w n in l Ta ,b l e "2.2.F o r the ax ian lo ad ~o b e comparab le ; to a i f i r . l~~uided, beam, the ,mic ,bwss w(m: td'~a-v l " i Abe, ," '' '' . ] .~ .~ a. q ~ 1 . . " " ! " ' Q 1 i h ; . 'n-'is m c ; o ; ' 1 1 ' . , ~ ~ . t a d . . ] ]-J'!i."A~~OS." v , . .. f 7 " ' . . h . ~ f - ~ , , . e , i ' i t _..... Iv __ ~ '~'.~'" 'lin... ~""'~COi~-. 'j_ . ~ __ ~~ ~~~~_ __ ~g~ ."~,o,IM_'~=- L g..... ry ,lin,,",1!!.....u ,W31;f to o b ta ilil d;e ,tlo cd on s:,. W J.d a. lot o f e n erg y is :re qu rre di 1:0 dbta:i~n a relath~~,I ,ysmall. ~ ~ --C~- '.T h , ,. ,. .. .~ ;; .-! c - '- ~ ~ C C n 'w h o '" . - -;~II 1i.;;",_.,I!iii .-,-:-:, -'~,~-.,,-'V. ~:~,,~~,.ll .',- ,~, ~i-,.1Ii,-",t ,;-~.cb-~,:d.,:~~eC,~~,OIiiL.'". JS : IS one _rea:sCL _._y ax~_o;ydJ lW i J_RO O o.~.~.n a _Oh..I!;l.! Ul oomp,~_:aI iL me_~anlsms, ' T e O . 5 . I . o l iI 'c au se s sn e ss sUffenilil!g~,b i r c h c a n be anotllcrprob~cm caused byin ial ~o a.ds (hai t reduce datlectIon. S[! [e-sss l U f c m i l : l ! 8 , i c S , di8CUSsed n e : x L

TABLS1:.l. Values of e c o c various !oadiug;conditions{wol'l, W = CEl.5~1l.J)

cs . s

GtI'idc-dA ~ L a lAlIi,ial (~1alll:g,ular)1

614,0: /216(LlhYl:


25/45

48, FI_lllbtliru. ..d.ft-ft'-""I ,_ .aJO;!!:' L'1 an.,. I.iI'II:ItUn",t ,on

(2.70)

-I" ;;a sa n d

-1 c - _ l 8 ]0 d ,ago. . ~ ' ;; :: : ,...',-,1ds " i s ( a s r' (2.74)

d . c . : ( . t I ' 61

) - . ' . ~. : e (d , C ' ' . '. d , , ' 9 ) - . d,e . .~ ,-1 .~-- '-I'~'ti:'s "ds '.' d'e ,astl

bu t t h i s e q t ! la [ i O A ~m ay a~S Qb e.Y ;;1r i u e n as,~ -,,'2 (l M ' . ~ - ' 2 " )"'....Ig. _ u.....I C . _ . ,- . " ..-:= '~I"II .'2 d i e . ! , ' \ 1u,r ,g',,:;, .. (2. ,17)

Bquatilnn (2.77) I m a y be dliifFim;ntiated ~o show (halil ls eqjui. . .alell l Ito e l : i jl lu u i : O I l(::t16).


26/45

4 9

SubsHt :udng lequa,tion(2.Tl)in~cO' equa t l lQu (2. 'S), sepa:mfing 'variali!l~s.3nd,tnie. , . .g,mt ingyfe lds

o r r

1'''' '1;c~\\"\ . ." '~._';/ '1'

whe r e C~is th e cons , tan t o lf i n t e g r a . t : i Q I l . ,lfwe usc the I candH io~s ,a , t th e beam end, w b e r e 9 '~ IQ I ' ii lW ld del a s :=;. 'I( ~. 0,,. ls fo un ~


27/45

(2 , 88 )

This tq juat ion may be so .~ed usJlng nUflle:rkal , i! n~cg ra t i, on o r ell i p l . l c imeg ll 'a ls .S> [i lr ' ~ t nHnc ' c , ~he f ' se --"'1'" ~~ -::x.i ~~",~,t':-, ' - , ' ' '11: c ~ ,"" - '-~r.~- - ,"c -I' {"- ,- ;- ,,,-:.,~ ~, :ih - , : ,] -W , , ' ,,,__ce== y Q , OO~,ree.,Ii; ,Lor ,1!IlOJ::m~L,"m]:0 numerL a ,mtegrnlJOI]i. t . ,C o C ,dpUC~ D l t e g ; J ; D i 1 : s o l u f i o n i s ; s h m v n i i t e l i C , Us ing t L h e c ; ~ U p t i e hne:gra~ ta ble s o f,B Y l1 d and ,F ri ed, . .m an ~97jw~ii~lhqu8z.iol'll f 2 , .89 ' re . .. sld: l. s in

] 1 - , , , ' ' " ' ' " , , ' ' ,e x ~ iE,'",,[F(,f)'-.F('l, 11]' o J ' i I l (2.'90)

(2 .'9 1 )

( 2 . 9 ' 2 )w b e re a s l ' n , E s th e arcsin o p e _ i I " ! l u n :Equation (1.90~' may be asedm relete the endangle ~othe Forcc.Assumingt.''i:',,"'~ijo beam , ( fj " " " m " - e - " t r nfl" ' a i " f l l , / ,. . , ' V " ~ ' U - , " , 'i ) 1 ' s , - 'f " - " ~ ' I " ] " ' "( r ; ' , a n d th e d l r e c r i n n e f -[,'i.e~_iIHI!Yfl' l._II, 1~IUjt, c~_,f" _..-_YJ.;S \. _ . uU L J!~ '.,y _ ~"~l!i..._ IJIII\_JUJ~, .~~1I1 ' .. : 1 : ; : ' ; J ~ ~.:UJ I",IJ U. 1:11\,,.... ,Juu, 'U" , u . ' I i ; " ,Joo.d( 11),~.lhe ' C o r c e 'may be , c a l c u r n : a t e d for a gIwn b e a m e : n d anlg !lg ( e (I'l . T h i s i5 doneby .su ibs,m li !l .t i'f 1 !, g [hcva~ lil c o f 9. ! " I in . tDequat ton ( 2 . 84 )1 , w hic h. is th en su .bs~ t~ tt:!te d.iln 1ioeqnat : l (U18,(2 . .9 '1 , ) an d (2.,92.). T hese v ah !le .sare used 1 i I , - ! : eql!latioill ( 2 . . 00 )~o ealealatea "'Thefhroo (P) is then , caJcu ta ted f row. equat ian (2,83}.' -T h " ~ . , .~ ~'~'I ' I l " " " f - ' 'i. n d f ' 'I., ... ~ , 'L.~.me cq:uatlon.lof mennatvemea pesitnm .0 , " tne en_ 0', me l f0ammay now t . I Cd~ri~e(t The I CU lNam r c . t it" mav be::rew.dUe;n as- -- _. - - - - r#"" - - . - "

{ 2 . . 9 . 3 )Su .bs, tit tl ti :n ,_gequat iQ" 'd (1~9G) iA~ lQ ' equati .Qf! (2"S:2) . SC:Pi l r~U~gV~diiit;.h:~~, ati:di~~~&

gmriJl ,g; y~el!ds


28/45

57

p oL y ec lh y le :n e (HOPE ) W '. i lh Ii ::::::00~OOO p iS~ : .lim dSy ~~.0 0 0 psi, Ass~me:t!he(:o eff i:c'h ;:n t o f :ifrictt~o nb e~ ,:v ee n th e HD f'E an d th e pane~~ob e a:p pro x i.m ate ~y y; ; ; : :~O.3 .ea) D is cu ss d i: f f ere n t possible des igns and t I le advarnEageal ld dIsadvantage o feach..Choose : 3 . . de~ign: fo r ~hisappUc:at i .on..( b ) D e te :n n~n e:t h e lemugth.!shape, and size o f tbe connec1 torand ~t smembem.( c) C a lc ul at e thevertkal f o ree : reqwi.red 1 [ . 0 ' de ; r 1 e c t t h e be.amand. t l IDe .max Imumb e nd in g s tre ss .{d ) Disc~S8 how th e ernd . shape affects th e ;a ssemb ly fo rc e re qu i:re d to i i f t l~ l~d l

UU~fasteaer, C:;dcula~lf!.~he .assembly fo rce req ui.red to im uaU ~b e fas; lener.2 .6 C o ~side 'J ' th e 6 . n g , e . m a U ,cU ppern sh ow n in F J:gw :e P 2 .6 . M rute tb e f:o .ruln 'v ~[Iga~sump~ i i ons~o : rsl imp:. I .~Clty: .Fin ac ts l i1Io:rI i lUl i~.o ~he.rigid segm.{ ' : !~ t ; ,heHe:db~eb eam deAe cdo n ls smal l and. ~ i. n ea rbeam e q ' l. Ia J l .i : o : n s : 0 1 3 1 be i!J :S le d~be 'COJ1J t ac~


29/45

po.iflt.. po in t A. c han g es o n ~y s~ i.g ntly in ~ h e ran ge o f mo tio n such t f 1 l a t , I ! am i1 ' 2 : ma yb e ,c ~n s:id e :ro di~ no o , c ()nstoo t :; : and t i le : foroe (lfJI, t ihe t1ex : :~b ] !ese gm .en t at.po in t A i s nO l 'l N al to th e t le .x .] ib ,~eegmeut,(a)W o :u~d each o f th e f:onowi~gcn~mgesicre ao c\ decre ase , o r h av e n o c~h3nge

O Il tbe meohatdcal advW l tage 'O f the devke: (1 ) increase .R.~; .00 increaseR2~W ti:) '~ i I lc rea se 1 2 ; ; ( i v )~nc re .w;e th e m om en t o f ~nerti:a.a ss o ci ut ed w i th th e. f I : ~ " - " b , ] ~ . ce ~ c ,---" t(v). jncrease F. ..e!XLe ~g!l1le[L" ". . -.--- - ----- !IlI-(b) Suppose the stress is acceptable but lha~.too ma e h fosee lsrequlredtoae-tuate m e moch f f n~ sm .How ,ce-uldYOll modi fy th e f le x ib le beam to changethe i~pul ,~ore~ wi l tho l ! ! l t , e h a l l l g : i l [ ; l g , th e :s tFe:S~,?

(e ) S uppo se th at. :~nM o t~ .e r case th e stress 'w as lo ob i.,gt\l~n the f l e iX l ,b ! c segmen tand It: Y ie ld s b e fo re .I~doses aU t ~ m W ' : a y ~ e v e n w he n notc-lippiJlgrnai~s.H aw could you moo ify th c f lex ib le beam to i .mpw\ / t : ~bi,s t re~ssc ,h l l l rac ter~isucs:?

(d, ) Ifpo[nt A deflects O.I_ l l~bei fo i l 'e OOl'llitactillgthenaj], how f:at does tbeotllputdefleot?2 .7 A can t i l. e \i ' e red beam h as am em eat lcrl 'ld ,.M I J ~ 'at t h e f re e ; e n d If th e b eam . h as,3 . .max irlm :m s tr es s or :50~OOOps i" , c : a I D c u l : a m the va lues o f t h e momeru! . M , !) "the end angle (6;). and the ! b , ( ) F . i , z : O i l . 1 : t a ~ andvertieal ecordiaates of the end

point (a and, b. respect~.vely) , :Uisa steel. beam witha 1 ! 3 2 i n . x 1.25 ~n.cross~5eclioti. ,and : 0 . i l,eiilgtb of 24 ill.

2 .;8 D e r.~'{ .c th e 'I.arg.e-den :~t'i:o n eqlH:llf:i:ousfQra f lex ib lec~[! tH c;\! \e :r o oam wilh a\~ertical. fOft'e at th e free end, You may ,:v ,an ~to u se .H ll,n dh tw k o /E llip lic .b ue.-gmis. i iJr J!ng.ineers ,and P1rysids, ls~ by P: F. Byrd a m J d .M . D. F r i e d m a n r.97~,

2, . '9 ' UseeIHptli!c ' in te :gr :a ls, to c3kt!lll1!~~t il e d ef te ct io n ta'. b, Of" '}fora s teel . b eamwI th a. U3 , 2 i n . . ,;t 1 . L ) in, cro ss sectio n , a ~ength o f 2 4 jn.~an d th e f oUow~ngload c O J n d i , t l O : I l S ~(a) A straig ht 'b o om whba. vertical fo rce o fO ..2 1 b a nd , I I . hor~zQrn~alo rce (caes-

in gcom p.re ssto n ) o f O.4~b.., ~b} ,Ii. curved beallD,(ra diu s o f c :u r~ va tu :reo f R ; : : : :20 j,~~.):vjtl l a vel1ic:a~force o f0..2 1 1 1 1and ,3 momen t o f 0 0 .2 i n . - l b .

fe ) F in d. th e vC:I1~C'a ]loodfor a . s ' :ra:ight b ean } th al w in caese avertical deflec:~don 0 0112 i D .

.l . l .o A i I .exJb!e SC,gJrnc,,!tl:mlllsl: unde rgQa pMiCUlIru: de t lee t ion ~! O per fo.nn, : i 18 ! f :UI lCrt iO l l lD l l t i t " faills be fo reach iev in g th een tire de :H e c~ io :n ..If th e materi al must:sta;yt ihe:! la:me:,w h at m o d i'f l:c a~ :~ ol1 io ald be m a de to tl'legeometrylo impoo\ \ 'etbepart?

2 ]' 1 '[U).'j,jL of u,.- ~,c",>~'-n,~--~d~t- i-cms,n Fi:tUlre ' P 2 ..Il is more eff icien t ~flarge.,1., U,I I ,C.UI (1" ~ l Je _~OOI , J !L ,g eQ . " _._L __ --- - .1;--- -- . . i5d e: 6 ec tt o n s a re de8~red?Explai .~ why .2.12 List tw o t ype s o r g~mettiJc i I lo.nl~neadti .e .s .2 .,1 .3 ; L is t tw o th in gs fh .a t can b e, ch an ged to ma k e a membe rmor e f ic .~ib le .2 .1 i4 cW b a~[ype-s: ofmaterialscaliil 00 used to make 'co.mlpl:i,antmechaalsms?2.15 Smte th e .B CfAfJuUi .-Eul.cr as. s~mlPt iOI ii l f i jl r b eam s (e ~l~ eT in ~ f1 0f (iJsr eq,uatioll

( 'Orm), I>Cscribelbe smaU dc . f ! !ec t~onass~umpt Io l1 l Q(~en made: with th e B er-noum . -Eu l e r aSS lmptSon .


30/45

F

2 , :1 1 16W b at, i:; the diff tre:nc-e l re t:w oo r na comp~e te and an : i ! lJ L ' O m : p l . e r c c lM p dc i(l!~ c~gm[?2,17 A large~defl.~cti.oiJ1beam has two en d foreesand an . el1l ldmomentas 8hmvn l~u

F. igure P2. ,11~ a(~ d a w. id~b !U1 aid. a .h :e: ight Ii!. Tile beam e c l 1 l d h as c o o . r d i : n ; ) 1 1 e : s ,a ; and. h"(3) W h e~ re ~s[h e m ax im um siress in th ~ :sb eam"(b)W:rite an.eq,ua:t iQU liar the stres:sa~. the tap ()fthe beam l :a!tile wall! .~c) If U 1 : C ; o o a m is made 'O f !P~a:st~cn:(Jthe m a : c J m l i l m :sUfCSS. , e : x , c e e d s ; t h e , yle~d.

strelITigUit, .hou ld (h i! !. b e c ons~de re d faU ure o f tb e pa rt? E x p.la ~n .

. . J

; ,, {

,," ,/, .


31/45

~I.'" e rie s " I .I'sed . . ; 1 ' - -, . ' -ndj ' : .n:-- .~;I.,.. t c : ' ~ I. , ,~f~.d:I ' , - :i'~t.. :t~ c : , ',;A , Co ~ ~- - ~ ~'.,,'rI~:"~, '. , ...., - ' f '~C__~tL :aile U ~pcL __., _ g , om m~,pc CL .~ o a _ ng \_ Y !iI .! lC o r ,td;Ui:;~JUa:.m g) ', m e ~ype 0 1 .m a t . . .~-l1 ( 'd '" c t i1 1 1 1 \ o r . . ...:'t'*11.) an d ~t... ~ -~ '~~d : -a c ~UI~,,"\1 ( ' C I , " " i "M ' s ' e pu ",~' i i 'Ve -et lm C a te ' 0 " ' ; 1 '.. i -~I~~ ,_ ...Q -_,,~-h ...~ '_ . .' U t IJ I. ,I II !\ ;r _. :, !, ;JlWJ,,_ l . t l - . . , ; . ~'_lIIJ~' ' ,-,"" ..~R~'Jr '\._UUi- .. \l.,g!Ii,I,_,' . ' ~ ' I ! ' _ .u , _ ' ,-,'J, ' . . ' f " E 'Ii~~:"- I.' ,I! '. " . r"'~~ (:'.'.'-")'..[, _.;!A' ... ,". w-A .' I" ,&1'1 ~ ' ' ' ' e d . 'I:.," 'avem!~ ~UU1le/.r'iWtlre, 1 1 0 J SLeuuYsm u e , "D~ ]8 f : e l ' i , . e . ,~nex : t , JOtlOW .' . ' ! , J ' y ar e v i e w o f : f I [ u : l 1 ! J a t i ~ g fa1 t t~ tJe loads .

3.2 .11 Ductile Mater ia l 's[ftln~; , i : n : d u c e d stress exceeds tile yie~d .strelgm, of 3, d l J O O l i J e : m a t e r i a l , . I, p e m U 1 0 C l e n td 'eFOI l1 :L IHO~:ocoo t cS~and . t h e ~v. ice m ay No t b e ab~e[ope l fo : rm it s i n t ended f une -ti on ..n.(;tnaxj:muJO sbear Slres_s,(o r Tm s ca) m o o r y ud [b e dlstonlon energy ~Or\fW1,M f_ses-:lf.e.nck,y)lltb.earyare two o f tlte most cnmm nn ly used fail l l1fe theor ies fur' d u e -t i lc~ma te ri a]~ undo r : s t a t i ' c I.oods..ne:: .maximam shea' c$l're:~~theory : rn ai 'll ta in s t ha ~ f ~d lu re ~w iU o c cu r wh e n . the. I l t l v t i i , l I r w W s : h e a r s t t e s s i s e q u a l t o o r p e a ~ - e r than. the s h e a r s t c : e s t i : in a tellsiile~l~s't....l ' iI IPI 'l~. , .. . ' . . . . , . . , a t ' , v; in} ld ' 'I o r - - ,,> J.r-~-""" '" _ .: ! J "" ,t '. .'-

(l.2S)

B y t h i i s t b l : O ~ ; y . f a n u r e ~ ~s;p~nled tJymai!n~ai:ningt:h.e m a x I m u m . s h M F l < i t r - e s s b e l o wh alf th e:y , i : e l : d : strcllgth. T h e safe ty f 'actor~S .~ ] s, tl te n8\1SF = ,......:..:.....- .2t ,- f l 'L l! ! l ! ( 3 . , 2 6 )

~ " " . n :" I - " "r ' I '. : ; " " " , e , 8 : N 1 U . " z : . . . . ~ ~ . ~ .


32/45

StatiC I F a i l l l ' l ! ! I re

Bo th o f t h e -s e tlh e () rL es a rea coeptab le ' fo r failure :prediction o f dU Q ,tile mater i ia~s:witih sta~~cl.oads:.Jso lmp j cma t e i l 'ma~ l p r ope r t i e s ; and ,eqldyal~em ' [ensUe an d comp i l ' es ,~swve s'tremg ,ms . T he t.wo [iI1 e oriie s p ro vwde (:h oesame :re ,suUsfo ,T ' u nia xia l stre -8!l:,~ 1 : l ! t i u

.1Ii . . '1 . '. ' l: ., '. ' h ' . . . . : 1 ; " Lm ost em e r cases U Je ma;xullum sn ear stre ss t. ,eo: ry Ui more loon!i:ervaJt~re tUOIU bu~( !US~OfUone n e r g y t h e o r y . Beeause itis more ,c an s e 'n ! .3 I ti v ea nd e~ie ' l i 'm ca :~e ;uhr te . t i lemax .Lmum sh ear stress t h e o r y ts th e ,mos~ commclI l l l ly used ,wndeslglll" The i l l l lc,reasedacctm tcy o f th e , dis[ (J I1 :~on l e [Je :~y the( )rym~~es i t e s p e c C i a U y use Ju~ in e c s t i m r u ~ t ~ n gsn esse s in ap art [h u, fan ed.

R igu r:e 3.4 show s ~ h e f;aHI!lIf:eHne:s~br tb e m axim u m sb e arsn e ss a nd .th e d is~ :o r~ t i~ on ertc rg yt!h e orh 'l.'S , If th e point : r iC~ re -se lwd by the coomh iJJab :=s(Grn~(Jj)on t ihepJo tI1 I re . in :s~d:e th e safe I!e.gio:n. f : 3 J U I l l T e ,~m n ot o cc llIIr: . If ~ h e ; PO~"'t~:s oUit8~de. failure . i s ,expected to eceur, Duct i . t e mam;er.hds,are , c ommon ly used in ,comp~jantmeclh;aJf i l isms,because t h e y are more fo : rg~.v inf : l ;w:henoverstressed. If ttile stress e . x . ( ; eOOs~hem3~:e - ,daJ. Yl i el d s :t re ll 1gt h, . p~ ast ic d e 'fo r:ma :t i.m i l w m occur; T he componen ts shou l d , b ede"s~g~ledo . ; w . v o ~ d h i s oceurrenee, H o " " v e v e f , inman,) ! c u e s t h I s i s o n ~ Y ' a . : ~ o c a m .e f fec t8!li lIds D T I l c tca~.as'trophi.c. For e,l!!,i l in~ple.eeasider , a C 8 iO m e v e r beam w ithaF o,ooe,a~ thefree. en d!. S uppo se a suess ca:tcu l !a i t~~ndetermines ([flU fh e m:n : .im :um ef fec ll vc: .sure-ss,e.xcee:dl . , ike j,e 'ld )t ~ , .a ';!i:'. 'ilil. .' .,' ",'-, 1- i . ~"i c~c. ... .. " - - . ,"- 'II.c I~' 'II., , . -"~~..,, ..f'_ _ _ _ : I i Y!L '1 . ,. " _ s 'i f e n g Y ! ~ _ ' " ue mg,lmlllm S ,~ , re , 5 So o c u r s a[ l l~ya ~ , ue oU l e . . . . r lIII've[S 0 . _ .the beam at t~efl","ill end "d iu , t '" '1~ ';-'-It'~~; ~'I ,--I c,'I.- .c~; !I~.~ '. I-;c"m-,~ -'W:'II'I ;" ~~IA -,t,. __ _ _ ._ , . _ . _ .~ ~ _ .n :~ en ., .n, ._C~I .e 1I1J : ! :a ,e r . l ,a . :S~C I .W . i l I S , p o w y p r o p y.w e ;n ;e : . . h ., , n ~ w U . ~h ,thatll'll'l'l""( a..dre:dhn'~~;"!nl ' te ~:. .. , . I", ..,A", 'I'" .,...I"...""",;nt'ii'ri"I~"''';;'''] ' 1 1 1 " " . . . . ." " " , , 1 , . ' . . , - ~ . ] ~~'t.''_.1_. . t- '' '' '' ' ~ ~ _ . ,. 1 ,1 : . .. _._i ,- .~ . I I ! . l _ ~ ' _ "I~'" ~""'l'!M~' .:.... 'RYJ_"'Ulu.I'R,,,,,~.I,g,,.. ... 'Ii",.,gl':h~g, p'" i i t~:h, I :Cdefurn1s[]on may be: so smell as not to . be no,tkeab~e. TIle effecQ 'of stress ,C(lncen~tmtions[o:r d~ct i l :e ; I m a l t } r i : a i l l s unde r static ~Q.~d :san u.sn))aH ybeig:n oredbe~,seth eh~g! h is :tre ss le cal iz ed at a s t r e s s c()fID centra~im~W 'meredw8trlbuted as t J i 1 l e m a m : e r i a ~Y ' f e i L d s ~ a r J d . ~ ~e an e oo en tiaU y r o ld \ \ \ ' o r k the . 1 [ I 1 J 3 ! t e l i i a 1 at thSJ1 ~ . o c a l l : i o . n . Thi . s e : x . p ~ a w n : 5wbyK J ::;;;:, I ( i.e ,. , n o S[ft:S5 concentrat . ion le,~ect)isl isted in , ] )b l le 3 .2 fo r diuc t i lemal1.erwa~sl !mndel i 's ta ,tw cl o ad s .. E.l(perie:noedengil1:ee:rs\v~Il ,Q, : f tenusethese ' f! ' .f iects m

IFa i l u ,~eoul) ! j ! ldeSlhad:ed , regl ions I (SF < 1 ,)

~ c. I~~~""~"'I SF .., 1 ~ '. Sy .-SF",t--.

F~g lW 'e 3 . 4 1 . i Fai l, t! fC l rn i! l' lcs ! f o r t he l :1 iUlXi l t l l lUn shci rnI ! :slf;!e-SS [ h eo r y ~ nd j th e d is.\l[IrI :io n e ne rg yth o o ry . . .


33/45


34/45

~:i iUl l ; j 'N!at ! i" , l~p'I 'a!t !D~m

I F ! I I ! i ! l i i 1 i elSeg:menit5 '

11

1 [ le>UeC ' le~ pO i 6 ii li (J ; ii Ir~":Iii;I" _ ,& '~I!!III~:,6 I . ! i l l '\ , ! ! , " :"- ' l~ f I~e . l i ! ' f ! ed1a~e~.)t "5''''~ I . . . : : ! : [ilatform, - . . . . 1 \ I l- '\.. Aeg~e

&e!)me!flt5,ID i !l~E~ t IOI 'l , 041O ne le g

F:~gliliiFC,.S. 'GO.p~liallJii!Cll1.hIJlP~i l lntl i l 'spiril~g" the denec;~ ion ofOlile ~eg . a ii id : a l i l i l iS~f; i' ie tri :c vie\Y'.

IB M iE I -

d i : 5 p h ~ c e : l i n e l 1 ~ of the :p~a l for ,m" , , S " i s , , S , ~ O ,.lll in . ,~o. .762. 1 : 1 1 1 m ) . ,~ , ) Ca~cub!J~e the,1![ i ,uimJUIfi ,d J l ; s p : J , l , c e i f t i , e i l i i ~ : e:~ore y. i,e .~dil l! !, fe} Repea t t l T I l e s ~ : f e t y : r : a c K l w :~mld~J!OCi! i I1~RIJd i 's p h ! l I c e : m e ~ ~ , c a J c l u .~ a : t : i( ) I i l : S ,O l r ~ . l : ru e a s e where tbema:~eiria~~sIlealtre are dm th er d~an;~j}:neal!ed,

SOi'I !I;ttOl ' !: (a) TIlCoung'SMHU]UlS, fur s t a l a l e s s sl:eel~s. HSted~ll 'T h ,M e ; ( : .~ asli= 27.5 Mpsi( 189.6 ( iP .I1) . lilid. th e y ie ld . : s~ re in~ t, hf ~ 1 i type 410an:llealed s,tfl i l l1l]esssw e~ ~s nsn~dinTab~eCJ!i,as S ,~ !4S ; kps~{310 lvIPa)l. The n rliio o f .b [:o I J ls ,3 ", a n dTab! le 3...~ , g h r e s . a v a J I u J Q : o f C T .~. 3.. . '4 fOF l o t r s i, o : n : a m s ~ : m s s , i m 1 l . a . ~ tM l l g ; u ,b t r e M !S S o o c -don. 'T h~ pdlc ' ipa~stlJ ie;Sses~of ~his o O l l 1 1 g u f , l d o n . o f ' drue mtho,p la l l !a f spii~lg\:veref o u n d symlbo lh : : ;~Uy i :1 In~ l i r u l ' ! : e x , : l I ! I 1 l I p , l ! e ,in SOC~.~QflI3 . L . I i . T l l e . bend. i ,~g : s ~ : r e : s s i !S [oundi i li o m J le q u i1 J ~ , ii o n ( 3 . , 1 8 ) 1 a s

(3..34)

I(O,()3 , t i l l i . } ,(O J)7 h 'D J.)(2 :7 .S M ~) (O ,1Q i! in,)(1J~)2(0.646 ,in.)l

NOl I e tmlm [h e b en dilm ll stre ss ~ s U V lG l ' s .e ve m nmes , g ream.e r lham l~be I t omhJ la i st ir le .S 'tre


35/45

Fatig_ :FaUum(I;,',', I"" ,~'~~,..tI.'C'"- 11a~- ,''''_; 'I- T ,.,;~'~o - :~ ~ ", ," Ai - -, - :1 " ~ , - I!--V'~' 1i::-,~"~,~-,-r1r'-dc'~,~'.:-'., ,~- ,~~~,"- __Q,mp . 130" 0" U1II,JP, _nar ,SP, [ i ] Il! uIS CU !:O S !,;1 U e ar.l le ,1 j" n a ~e uX!i;.U gU b,~1 i ,; l~,spnlgrS I n l senes ,lIle eq:uatf .oD relaU ng stress 1 :0 de:floc,tioll!l,st~e: same fo ,r b o , t 1 1 . ''[b emi:m'~ because 't he re : is : 1lC;g;l~g ;i Jb leo rs i( )n , t he : m a x i i m l u m , nominall, stre ss t h e : stre5s ealcu1:attd,beJure taking into acoou:n;tthe sl!e sse o lim e lllra tio lil)1 C ,3 '1 '1 1e found from equalJioll( 3 ' , 1 8 ) as

F or a briule ,m ate ,dal the flid I,steess , c o n c - e ; n l r , a t i o l l l factor is t ak en i: n'o ac t1 o u :n :t ;~ ~I tb emax imum ~ tre .sis

or" .. ,- 'II ' 2 ~~ ~ " \ -2 ; ' : M ~ I ) , , , , ) , , , , , , 1 ,11. :1 " , I i' - p vm!l!;~ .,.. ' ~ " -' li .. .~ " - '. ",r~. = ~."u l'VJ,_ y,

'T he sh ea r st~c~ses:aPCI~cg .Hg ib~c ; .so ~ h e p rin d pj}1 s t re .ssc- -.~areo~ : : 1 4 6 ,M P , a .'''~ ~. 0'.ud o J ~ o .B e c a u s e Gl '~:0 a n d ! G'J .~-;S" ' t ' eijll:I.UiOfl:~ [3 .4 4 ) a_n ;d(3 .4 6 ). a re l u s e d t o predit1t' the safety fac to r (ur" b rilfJ e t laHu re Il!Is~ u gtitle COUl~o rnnb=Mo l i J r\boory andl l \e mo di ..: f i e d . M o h r t l loory.re..' i jpecti l l i 'e:ly. These two e q u 3 ! l i . O ' n s prov i de n le same : res,ul t~

S ;f)':I~1 - M - p . . .SF ; ~IU ... ' ,~_;J!!)~~ :; li401 1 4 6 M Fa . - ~ (3.5.5

3,,3FAnGUE F A 0 I L U F I . E,fo r so me , cO imp~l i ,ants tructure s th e de sire d I l lQI, io[ ' l :m .ay o c e u r onJyo l lC le an d U le~!na~fcf:wlu1!e;thoorie-sa 'bo rvemay be C11 i ( ) ! ! lgh f o r a n a : I , y s ic s , . H o w c ; y , " b, ' ihe , d e . f i n i , t i : o l t l ,o f o om p l. iia n l. m ~C I 1 !a i! il i. sf ll ils it~ ' !! il k f1 lown (ha t, de~nec t ion ofne - iU: i l e memb e r s Isr e q 1 l t i r e d tot l t iQ t 'l 1 i . U l l , UsruaUy:,. 'm :~ d~f ! ii rod thatlhe m'hani:sm. be capab.le o l l l ; t o d e . r > '; g Q , i: D , g : t h c motlonmalY times...f lnd dcs:i lgf I l .reql l ! l i remc.n~:s;rnay be m a n . y m i . l i I J r C J , E l s o f~el:ecs o : r " :i :n f il ni l l e r 1 i L f ' C . . ' l i h i s re 'p~m i@d . [ o a d i i: Q , g . IC~U '~ O u c t l l J a t h i l , g s . t f eSC-S : inl( l le,i l l l .e:moorn and can :resu~!t~nfal~glieftlit,'Jlre.. , F a l i g l l l . e


36/45

d eae e in p rOO u fts : '~ ib :a ta lii pmm a tu r e ly . :F o r th ese an d otb~r r e a s on s ~thi eritieal thmf h e f a t l s t l c I I ! feoF' a C U lm p ,l l i m l l t m c c h : a . f t d S D l I be~,allalyzed a n d . de: lennined ' x p e r i l J l 1 e n . - I t a l l ' l y ~T h is se ctto n eonta i insQ . s l ! i lmm~ o f f i 4~ ig~ l t~failure t i c Q r y used in d e s ~ gn .]t ispl!JCSenlediasa I~[CW and j. t is as su :m e d.1 h at t he iw a de .r has: h ad wme ,e;xpoSUIie lofatigue! ; a n : a I J S i : s ~ suc'h l as i n . a.roachine de.slgn course, ' T h e : review' ' W : i1 1 I e : m p : I l : l s , i i z C ii C iW : . i c e p t s that a t e p ;u t i c U t la iJ !y . jm . p c !t 1 a n t . f u r o O i i l . p l i a n t : mec. hmds.ms ..

3 .1 ." Pa il:g ;u :e IB aslc s: P a t ' i l g , u c : f a U ' l l 1 J ' e ' e e e a r s iH~hrree p l n t ~ ; c n \ C , 1 i ; i n U i a ! H o i l i . era.ck!l : :row(b, a n d fracture,'Ue: ~6_rstp 'bBselnv61\f -es.. crock. th at may' e-v ,en be to o :~maUl io dct :oct al t ir,st . Crocks.may result fll'o .l1 I1M ate rial imperfccti~ns. n'l ' :muf:actU!ringp~-~~. ' 1 ) 1 ' m!lny Qt!b~t: st ll i. u ce s .'f besba rp c rack c a u s e s , a 8 t ' r e S S oonc~ l i l tm f io :n [ !h :a t '~nc , rea .~he h X : : l 1 : I . s , t . : : e s s ,: a t : i l J l e : I c r a c k ~[p'.A emctata. :S!I1ieiS ,eonc(uu_ratlon u f t h e pad (slllc:h3~a :nmt: .h orab o Je ) a:n 1 pIU ie s,' r n e stressiunller. Whe n ,3 s< tre S8 no rmal to tb e crack cau:ses th ee m.ct .to o ,p en (a t 'ens:il~e s ; t re~) tb~ higli l l S~5s , a t . 'dle 'CQc iktt .P cause sth e m ateriall ~uytJ:I.dat (b at ] lx ,J 'O (a n.d lt lte s~ i~ .e0 1 " d l e ~ ' ( '' 1 : ' a c k ~bllcrrea~s . .Wid ] a f lucluadng l o a d : 1 0 0 :stress, w'nl~lb e released (.or:B~lea~t dec reased l ) ] and a-,n] ' .ed apL'l~n.n sam s~ -,e. C.'-.~- .~ -- __I!L~_ . __,~ --------.-- ..P.r-- _~_ , , _ ~ e _ _ ,~e_eqlue:nccwl i~noc-our the. nex t: time the Inad.!5 a :~pHed andthe .10:1cb s. ize;wil lincrease funher .Jf~u,eR.uctuati:n:g &~~cS1S J s . a~w :a:y$ i n eompr, e! is io . n , : 8 , t u : : h {hat it c.ausc,s t~le eraek H );. .. .~ , . .. ., .. . M , 1 ;. "r ' ~ I f" " n . .. ~'O:> ~iL" eraek wi:l'~~.,." 'Po : :


37/45

L I~ I_ _ _ _ - - - - - J - - - - ~ - - - -I ~I II ~I II' ~

1.._-1I~

1.-1')--'-" - 1-2--1 .-3--1----;1 0: : 1 e .,' r '. ~~O 10' ~ 1 I 0 1 Hil '101 10-W 1'010IN!u :mher o f c yc le s AI:F igu rc 3 . 8 : . . T y p i t' ;l ) J IJ SoN d i ! li l, g rnmfQ : ! " s~oo t

Palj_~,lle ~esthill!:rc~ltlI~,:sn a ],;,trge ,a_mount o f ~il!ne[ in th e te -S1:re~lld~s,b G c a l l i s c , t 1 i m ~ yd i : f fe ren~ t:ac~:ornlnfluelilce fatilguc[adUiIlC;. SOllilC; o t~ ~hese;factt lr ,s .3R i: n the ,engi.n"'c"'' ' '~, c'''''''' ro o I ' ", "' d o " - h 'c r ' " '. .. .. .. 'n'''~ ~E-''' ' 'a'"' ' ' 'p~'''s~n " '~u ,~ c,,~''''''';~ eon"' ' ' ' 'n-,t-r' '~';') 'n-'' 'SI"i,J.u"'lo.~I_.I~I N .'!i;;nJiI.~1L .. \ I ;UU. ' "t ... ,.,l! 1 " . ' " I '!i.. ! ! ! I : . '--AI -11~,IL.-'~"r.1' iii i'i.I. Ju ' :iil,II"Irf~ii~' '.. . '!i2, rllii'WI,,, _"dllliti'I'!u r L ! ! l i j i ~_:. , . \I:IJQ~!\j ;;: f iip i.sb" m 3! [~r :i3 i ll i rn lpenect lon_s. inmillial1si~e '(If c rac k s, t empe :r J,mre~ CtJIws :lve ele-Imclll!ts inH.e len\ ' lru:fuftel l l !~~ and S(1 I(]in , E i~ f~ n lp i . l~ i~he,df at li .gu : e spec ;~me on ,: f im l l l , ~hesame batCh of rrnneruaJ and o f ~h e same size e 'x h ib h c oN ste iiem b le sc aU ~ r: A P'lI1, ' i : l i 1~rvioe h _ U k ~an le etl~ ",i;d e r m ;wg e o f ' f n i J l l 1 _ ~ r e ( f u , U I ! . Becall l~ (If If:tis,,j t ts'~lJ dimou~t ~o[p.R.>dklfal:ig]IlC faUure with mU!i lchat."clJrac)~, an d tccsling: is e . ' i , " ; i e o l t J l a lAhh ou gb fad S Ju c f~ iJ ure ~ s c l!i:ff ic uh 'Q ,p .re ~ U cil:m . ; " C l r a l e l y . a n t i l J 1 I . d : e B ta r u U l Il I : g o f. flu: .igue;fuj lure poo{UcdonaJ1d p r e v - e , ,- n d O I il is eryhe'~p,ful l i l l i l t h e design o f c { l I o o p H a n : tIm~ha:ni:smiS. Th.el:Hi.Jry can be used to lk$~gn devic :est l l1at . wiUw,t~~t3ind Ulilefl[lul~t !um:i.n,gSIIl!8Ses. l'e~linSdilen reveals th e SUCt'l':S of' t he~d'es~gn~ l innthc; l l n l l I i ! a : l i 3 ' _ l l a ' ~ y ' ~sis an d. dc.slgra are . c n t i c : a l .fur dbtuJ_nJ l9ga de~sli lg,Dlbat . isaeip table; , . , . r i thmuunde'f!!,cril i l,g n ~ a n f b u i l d 4 1 1 n d ; " , [ c s ' t l e . [ _ m t ~ o n - ~.S~\!Ie ,[a:1mootd . saru 3.vai lb. :b le: fo r .~all:gu:~ral.hIre _predie:liion. Tille .ftTttS5-Ji/'e " . , " , > d c "Is th e (1l()~'[: stra' i .ghtfUrYI,aroalild m()s ' t comm~:ml ,y lsed..In :th e d~j .gn , o f ' medha l l i Q - a ~C : Q - Q i l i p o : n e . I U S , .1 1 . 1 ' 5 : t ~ o o ry i s lM ' o s t : a p p .M p m . a t e f o r pans '[h at: U lU I I ' J e ~ r g ocons~s t em : a r m l lIn.,...."jl~,~".'~~.., 'n I " , . iU-i~il'~"" .,.,.'.,....,., ~. ' ~ M ' ~ n\t 'mo' , , : I r ! ' 'C""'mN""Il"'*i"~' ~,. 1 1 , n t ' o t 1 h 'i , - , . . t-,,",-j!\ "1"nI,!."'~'''''I,f~1;~~.U"'~..n ,_,_,...c,..a~._.ng , : ;; ,~~..~" ~. '_"'_a_I . . . . ' . ' _ '. ~.c,!,~,_., > t;......t"~.,." . ~ , I , , ~ ,u. ,., '. ' .. . s ... ....~ \ . , . I ' "b ec au se th e~ r 1111l:ni( ) ln and loa(jh' laro de f i n ed . by Ineki .nemall iCE of t ih t ! m6C1na I i l I J j lrliLFolf ' th e . ~ 3 t i : 1 J etca:s(lil. t i hestK '~~ . i j ; , i l J : i moo t , c ow [ p'llia .lu me ehanism s a re : a t ~ o c~ l i l I ~d~~e l 1 : taid. prodic labJ,e. , Far e:Kampl le~ tbe~c ) !m p llia nt rn e(;h a:n ism ~ Ih ow n i inPigu1fC 3;. '9 'wiUunde: rg , , ( )p , f( \dk t il~ l ,e deA~ c t jons ; andthere;s~ld~~g stt"ah~~a:nd $. t re ' "se,s ' ca ;~be 'cidcUi~ia te d. O t h er m o d e l l s - " s uc h a s ~ h e f ra em re -me ch aai es a p p . r o a . c , b . can be u s e d F o r . o t h e . r
mailto:Ineki.nemalliCEmailto:Ineki.nemalliCE


38/45

'FaUurePrev"ition

Fi,pn 3.9.,CQm!p~~an~rnehani:sn:! . with cOnSi!!l~n[ ru ldpred , i , c t~b le 8rres;~s OlilUx : I fl: c xib l, em e rn b e : f ; . . .

t ypes ,o F c o m p o n t m t S J , such . as 3lrplan,e w in is~ th ar unde,cso t an .domi l ) r varyi:n,g: s t J r r e s s e s .T h e :stre ,so sU few ,o de l is used to p :re iH c t th e: fad !S ue s tre ng,t t l fo r a nlumber o fcyctes. , Thestresses are ' th en kept wen foo~ow tbe fa ' t tgt le streng~:l l to e lllrS u re dm tfat igul !if ai lu re wU l n o~:o c.cl! .'l r. F or some materi:ab; It~s poss~bte ; to kcc~p th e :stre sse sbe low ,i,l i l , eve l .where c M . n : ; k ~ ,w in n O l , tp:mpagat :eat . a I U , .PaliDU""S'WH.Q~'" ' 'j i :1 i - , . Int~'9U'" d:r;oI.o#l . '~'IL!( '~'1...., m a ' i " ' : I m ~ - I u - ' m - I I t' o "l -a ' l ~ y " '. .. . , , 1 " ' . .. , . . -,1 ~~'''''''''''."__----.,etL--,.;.1 -~,-.II-""a.-'!!I !I~'~J,p-'''n'--'~ ,IiJLl!j!r~~_.al!j!I!i1! ,~IJ'~ ~_. ! ! I 1 J I I I i I o ' ' . . A,_,_!, ., ,. ,,'__ ._ , 1 1 : , : IIJ'Ij"j;-.".~I,;'H,.:.U o:_!UlJI....~i;;l!: ( f J a l : , 3 r a t l . p .- . . u e s ~ c i m e l l canendu r t f O : ! i Ncvdes. R~anthat . F . ~ u . " l l r e 3 , 8 Hllu8U'a: tesa,I F ' ' ! ' ! ' " [II'!" , C ' , ityp ica l !,"-N dJ ,agrrun .fa .r s le d . T h i s typ e 6 1 diagram ~seon s t r a c t ed by tesdng mayd i . f f e r e n l ' , spec imens a t d i : f f ' e ' r e n l values o f s t r e s s and. Icot l !nt ing thClliUUl!be:r ofcydi!!ito ' fa~llure. . ',lottjlng th ese po in :ts o n. a .l og , t og , : sca te resu~~, in . [b e S~Nd Iag ram .. T h e n !'t S a knee i:nthe S-N diagram for m1llly 'm~ateriaJs at tbe t m l ! i : i :~ : IO . o be tween low- andbig,b-qd,c.fa1figue.a:round 1 x H ~ J C j 'C J : C M S , : S o m e m ; , m ; : r l a l , s ! such a s "manyllo,w~~trengt!bcarbon andaUoy steels, S J O i l 1 : l e sUl: inless steels, irons~ ruoIybdeanrnaUQyS,tltanjum ,alloys an d. B omepo :lymers U08] have a secondknoo. caned th eenduml~'Ct!t:lmil~S~.Ut i le s tW - 'o~5 f ,s main ta lnedbe . l !ow th e ; e ad u ran ee ~ im i t . fSltiaue~ ~ ~: fa ihJ:re w iU A.ot ooc.urta :nd tb e part h as infin,ite liflt. . .Th.~s ls"o l ' e ry l l i l l !pona l . l 1~ { 'O i ld ev ic es th at m u s{u nd .e lg ormm y m j~ U on s o f c yc le s W it llO liit fu _Hu re .

O n a,log:-. log sca le~ , the ,$-N diagmm can . b e ap pro x .im at :e das a s :c ri !c < so f stm ig jh tUn es ..Th.e i ' f f i t l i i n e : goe4 ; : fm l ln lb :e stre ng th . at 11cycle ( t h e un~ma t e strength, S ~ _ t ] 1 ItOt h e ! strength : i n ~e:O~t k n e e (S/J" This .Hrst t .n . te isassunied to' OCCUir at , I X~ I O ~cyc le s . .The ; . h i } ' \ \H ; y - c l e f t I J ti .g l l I D o o g i m e I ; S . t b e D : a p p r o l , iJ m a l to o . by a s . t r a i g : 1 u H R . e ~ o : n tbelOl l i - lop S-N diatl 'rambelw~;n t h e ; c( " -1 ' rd in " it"'N ((0 ,'" , ' ) 1 ~ - . . , ( ] X ~ 'O , 3 . (. . ) ,. - T I l " - - : v ' I - '- .,o-c- '..,~'-..... - -'- .-- --'--.- -'"...lI',. ...,~...,~ .-t .J~i'r anV l \.. . t __ ,0),'.'. " l ie. , i : t . .u:eof Sf, can , b e app ro x iuH l ted as [J 09 1

0.,56)


39/45

,fatigue Fai lure

bend~ngax i3 1 l oad ing (3 , ,57)

T h e n a t u r e o f I h e h : i , g h .- c y c l e : f a t igue p o . r t i o l ofd lC S -N 'dlagmm de pe ndS O Mwhe t h e r 0 1 1 ' n o l t h e ma ic r.i ~l lhas an e nd ~f an ce H m i t . F i r s 1 " c 1 o n s ; i . d . e r mater ia ls with qe~duraUl'C U :m l i I . The endurance ]i lmU i : ! ; o t l en taken to o o e u r a'aJbo~t 1 x ~0 :6 cyc le ,sfor steeh and o t h e r I T IW l 't t lr i a l !> . 1beHuj,w t . life pordon o f r f f i l e h lg ;h .~cyde f a 1 ! i ; g u e r e g i o His th en 3 , ' p p r o J L i m 3 ! t e d on tb e I lo g .Kea ].e,n f~ b e S & . N d i ag r n_m , ; ; 1 5 , a. s t r a i : g _ h : l ' .~ j :nefromt h e p rev l i oYs ; knoo at ( I . x I T c S t ) to ih c; s e e c n d knee a ~ : .he ~nd~u:mlil':~n l U of{ I. , x I(Jr\,~ S I , ' },,~ftb e !Um :SB ~ s m a r u n t ;i li le d [below' d I e , , e n d J l l ! J r a l l l o e~irunil~th e [part w ~ U rialfail regm:dl~ of the n b J m O O r of cydes~t undergoes ( li n fi J ll it e U f e ) . nlc~re'~ore,h eI n e < X l ~i inefur male:riaJl;swith an end:U:mJnc,eMIiIl~I. is :ah(lrizontal . l ine at: SI! ~h:a,te' lJ tl :nd!5f r o m , N = 1x H)6 , ' C J c , l e ; ! i h l i .n f i l i il i ty . .

Fo r marerriols,w i th (m~ .a rn eud l lr a_nee ~im~t. 'he U!l1er( l rhl~I i I . ' -C) ' ic , te~ 'f:l 't~g !U os-~ an s.J ~ ,_ _ - _ 1 ! _ . . . . - -th e sam e P Q i h n a : t ( 1 1x l 0 " ' " ,S d "bu t . ,ex lend' ! i to a I X l ' l m o f km:r ' :YI l : f i t l ' l g , u e s 't r e ,n g f j l [ 'Ora .k IHow nnw m b er ,o f 'eye.les (N ~ S J),.F o r e x:a:IEI;p ~e .o t aJ~miO !un l ~ ~ a;:~ !:ue stmDgt t l l

- 1 ' I o ~ 0 1 : ' 0 0 ' " ' 1 1 0 6 1 . . . . . ] . " . . . . . : 1 ' -.! I. . . . . . 1 " . f l i . . . . , 'a il, h .~ . ,~ . _.. .I . > ; ; ,1'-' CY~! I :es ;Sc ummon : y !I!i~J ru l ! I t ~ _ J e secoll"pon'hiO~" b.: !~d!ilC;,' Theh igh~yC ' ; I I c f i : u~g , i I lC~nc s e g . r n e n t . c an be de. 'l{~nbed b~: t i t l e e q l ! l a t i o A I

( : ts :S)'w:J.--- ,'. >~I~ A! t. .~,~":- c . _ _ t ic., - c-n'- ~r--c '~hat must 00 ftmn-il 1 ) - . r a .,-'l"l'lcular male.u ,e re tlJ 3LW UI are c u rv e , ." J i il_ a rn e _ e rn ~ . -_ _ __ __ ._U . u _ p;1 L_ --'----Ir ial art c -o m po ne ntB ce :3 iU lse U m re -are (WO ~nknm :V .l1 Is "(Jt and hi)' h~ O ,cqu m :lo ns are'n-~.J~)I ,~,,,,,,,,, t"IfIi"''''lt,;",,'I1'''' ''"t''rflripf ' o : \ I ; 1 J 1 ' l r ' "".~~~l~-U-I~~n"!:!' . .. " ', ~ " . . I,U...c., , , , , f ' I ; O 'al-.I ,:"~'''I '' i I i ' ~ " " ~u",~I, ~~ U,~ ~ IJ ,u .... : J < . . . . . ' _ - . . ~IIt4!",IY'iII~ ! ' 4 . o - , l . . J ! l d l ' , I ! \ i i l 1--,,~'!Il..'~'~'I!' ~!Ij.lII~!lk~ _:_l!J'-'-e ._111. . . . . .'I! ~ lI _ , ~~ y ~ I..il'\l, ,~",' ~I~ I"r ,~.~ ' ! I l .n~know n. po bu s on lfu c c urv e. The :s;l l)bsti:tuli ion and . so~un() lnaresiml'pJ. if iGd. by 'wr i t i :n ;e q . u : a l i . o t i l (3. : 5 8 ) , ~ .

fo r m ate ria 'is w i th : a r 1 ! endurance l im ~~ . S flli ~ c~.d .N !1 ~ l x H r\ Sfl ~ Sr'and ' :N~ = = I x : m ( ) . Sub~t. i t1Utin,g ' inln,~ql!a; 'Q:n CtS9) resuljt~jn

a n d .

(3..62)


40/45

,comi" l : i ,am~ meehan i sms can. be [lli'Io ldedof one nieee ofnbl.sUc, wJl i l iC:h.c l ln re.~UI~t~ a"" . f , ' " ' I i i " ".s.ig n :i:f ic a nt c e srre d u en en oomp 'a re d . to fUbr.i!catJingand as.sembl:~ng Il l lany "a TItS,AdvOO JiJco Sin matedals h a:v ,o ma.de I : tpos.s~ble to d esign roU~bb!oom:}X) f l ;c l l lS : ,~dt1gengineer~lng polymers.lbe , a i b I U t y ~opredie:t the beh~vi(lr (}t polymers has:~aggedooh~'nd thead.VIDl :Cie8ln~' l1ema~eria ls . One re aso n rQ l r~ .h~ s~s that pol , lymers are signi l1icant ly mare diffi lGU~t

~Qan,a lyze" T i ll is d i f f f u c : u l t y s tems 1 0 0 . ~o:n~i! leal i iU>e-s ~nlleren~ ~n th.elr'beha'lrlo:r:. timedep en den ce o f preperties.nnd man y o th er factors that are usua]]y Dot ml issue wilthmetals suchas steel..andaluminnm, A few O 'f lh : c f utQ ,FS tllilat in lHucncc;th.e : (a t i g~ue lo fp o lyme r~ a re :

V isco c]a:sdcity C reep S tre slii Ire]lax.a:l~i() l j l T e : m p e r n t l ! l l r e depeadenee D ependen ce o n tfrequ.crn cy o [,lo adin g. ' D am p iln g N o :nUn :ear elast ic materl al p rope rti es Q rie n .la ti.oA u f po lymers.' D ifferen t. ptope;rtl:e;,') f ( J I r diJre ,re ;nt load~:n:g c ( ) ! n d ~ t h J ~ s ,C~P " st~e ssre lax :a[io n .,. an d! vi !leoe]a!l~:~c~tyre related and C"3USC tbe meehoo" :

c a l belm:.v: ior o f llh eA la .f ,e lr h _; d [0 a ry w h h ~ i i m e ,. The ' F n a t e r ! i i ! i l , j o ' i l l ~ f l l owwihe l i l a.po~y"me:ri.s under ~oad! because of vi.scoelas~k material. p ro pe n :ie .s .. Th i s lsa :OOI : lH :nea l r~time-dependem phenomenon.. The "! i i scoe!asf icproper t ies wiUIvary depend~ng onth e r m a l 1 ; e r i i a l : ~ h ( J w mu.c t1 ig ]as:s:re i ,n force l le ID~: ~s: i iAch.u. led.n d th e t e l1 1 l p c : r a m r e . Creep 'o ee u rsw h en a m a tc da lt ilo w Y l due to a load, ' C a J U i S , l l 1 ig the defIJection to ;tn c:re ase w i tht ime . S t res .s re l axadof J ooc l l i f sw ihen a d~spbLCe:ment isrtp pU e d an d [!h e rcaeU ofl fo rce .decreases over lime."V en do rs sh ould be asked to supply ' m a . t c : r i a ~ P l r o p e r t , y d ! a l t . a . f 'Orth em ate rials used l,. a n d t e .s !i i n g .shou !d be pen oflIled fo r !n e p ru 1 :ic u 1aJ app l ~cation~ n; m l n c t

'Them.edilallkal pro1pertics of po~ymc['S atte very sensitive 1 .0 temjperntu~. As ag..."'.. . . , , 1 ru ' II . . , " ' . " " , > 1 " , , t h " , " ' d Y ; . . . I n ( I , ~ < " ' ~-IO'II'ln.. ~I"'-rea~" ' "' a ' " ' ~m ' "Iilf'!'-U~;'0' "ra"e ...c . n . ' : ' ,ii!.. ,.,..;;~ln;;-;I'''IL .'1, J t . . ; ; . . ~ ~II'lI;;rUb !, j IMi~I !I ,' , , iV" . 'Ie,. , i ' : ! i I' 'jIi.J\.lIW. J~~1 ! i i f I . ! I ! ' - ' . . . . . J . -; - S.; . . .!i~J II:wI J~ ,~,I'l'~I"!WI'" -_!I!~' I, j ~J ~ !Ir .- Ii !I ~" "" \ . ... 'e ',I i J~'Iis im pn rtR llt 1 0 cons i de r

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Compliant Mechanisms by Larry L. Howell