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Solution Manual for Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, 1st Edition

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    2. : » - . J Find pot of // CONC rant yr fy // . deter pine How ; i Usa on veobor oy divection of - [] de estimmede Phe” — [= / Theme A Fn hs / / waamibode ob FA / oa / co” i Te / Tp. / Ww cast) / bp=dW fo 2 Pa ; / ARS / I FA Ps VAR BPR / LF / FEI AW, / ye / is 1 [a] / Sa AP SS £7 VA EE L/ ~ ‘ / SW i eee re amet me Sn pm roe — Dew fg * | A ~ Fo) I=) PAN — N Nan i Study © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel, Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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    Downloaded from StudyXY.com ® + StudyXY Sd Ye. o> \ | iF ’ pr E \ 3 S Stu dy Anything This ContentHas been Posted On StudyXY.com as supplementary learning material. StudyXY does not endrose any university, college or publisher. Allmaterials posted are under the liability of the contributors. wv 8) www.studyxy.com

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    2.2 My =1,0 (eo Yi & = 7, - dy yr 8 Ty =( 1, AT Diy + dy Mar 8 rai dy = Kiar Yigg Mis (kyr gy = -621%.52x1.8=0.581 mm, my, =.678x70 = 47.46 kg dy =. 374%.52x1.8= 350m Tap dy = 581° x 47.46 =16.02 kg -m’ 7, =16.02x3+.350x47.46x9.81 = 48.1+162.9=211.0 N -m | — Study © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel, Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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    2-3 About the hip SM, =lu Ty, =mpgdy =m, gd, +1,y=U,+1,),a Uy =U) + rd, my, T=), +), + +d, Ym, Jot mgd, +m, gd, +1) 7, = (4+.05+5(40+.20) (2) + (8)(9.8)(.18) + (5)(9.81)(.20 + .40) T,=48N-m For the lower leg SF, =m, (a), Foo=my a, =m, (I, +d, ya Fo. =m, (I, +d, )a+m,a, Fy, =5(4+.2)(2)+5(9.81) F,, =55N About the mass center of the lower leg SM = a=T,~d, I To =lg,0+d, Fy, 1, =5(2)+.2(55) T,=11N-m ©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel, Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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    2-4 About the hip SM, =1a Ty + mpd (ay — ag) +m, (+d; Nay, —ag)=U, +1), a, = ad, a, =a, =al, Up) =U), my, (+d) Ty = Up +1), +m, (dy) Ja ~ mpd, (ody = ag) =m, (1, +d, od, ~ ag) T, =[4+.05+5(4+.2)° J) = ®)(I8)[(D(18) = 9.81]=5(4 + .2)[(3)(4) ~ 9.81] T,=46 N-m For the lower leg > Fo=m,(a,), a =d, Fp =m od, +m, a, =m (cl; +a) F, =5[3(4)+9.81} Fe, =55N About the mass center of the lower leg SM =lga=T,—d,F, Te =dgutd, Fy 1, =.05(3)+.2(55) T, =11N m ©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel, Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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    ments about the shoulder My =m, gd, (m+ m)g(L, +d,) = 1+ [dxm}] RHS of the equation (+1) +d,ma,+ma JI +d? +m, +m)a IE +(L, +d,) a,=da a = aL +d; a, = aL, +(L, +d,) (4, +1)a+dma+(L +d)ma+(L +L, +d) (my + m,)a solving for the moment Mg = mgd, +m, +m)g(Ly +d) +a 1+ 1, + dim, + (1 +d] ym, + (+ (1, +d,) om, + my) | substituting values yields My =1202N-m moments about the elbow My =m, gd, =m, + m)g(Ly +d,) = YL a+ [dm] M,—mygd, —(m,+m,)g(L, +d,)= dima +(L, +d, y (my, +my)o M,=m,gd, +(m,+m,)g(L, +d,)+ dima +(L, +d, y (my, +my)a substituting values yields M, =10.66N-m

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    2-6 T=), + Uy) Jo (Ly = Uy )p + mpd,” = 4.2+.045(8) = 7.081b- sec’ -in (y=) +m, (+d) =1.4+.025(18 +8)" =18.31b- sec” -in 1, =(7.08+18.3)x20=507.6in-1b > Fo= my, x, =F > Fo=m, Vy = Fy, m8 . ) in . Y= +d, ou =(18+8)x20= S20 ¥,=0 Feo =m, %, (1)=.025x520 = 13 Ibf >My =U )a Oy =T —ay Fy, Te =U) 8, +d, Fy =1.4x20+8x13=132in-1b Study © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel, Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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    2.7 Ty =U gro +d ympag, + +d, mya, T, =) go +d) mae + (L +d, Wp myo To =U Yar + (dy my +p +d Wm, Ja 7, =[4.24(8)° (045) + (18 + 8)(18)(.025)[20 = 376 in-1b For the lower leg > =my(a,), a =a, Fy, = my, dlly + mya, =m, (dl, +ay) Fi, =.025[20(18) +9.81] Fo =9.25 Ibf About the mass center of the lower leg My =lgo=T,-d,F, Te=1lga+d, Fy T, =1.4(20)+8(9.25) Te =1021b-in ©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel, Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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    J 2 8 = ozs oF oY ooo = = == 3 z J © Aw |= » i I th = > T BL. >=5 |. 2 slelalzlzl®l Ee PN 3 ES] EERIE: oes Ti+ PLINER) IS ER ESE a ad TRIS FE [ES 3 TS a. [Ee N 3 SEER ER gio jonor ov == TIS: o> [vod ~8 +) $ iS ! | | l= x 3 | we IN HB] JN UR FR Zils] 5 Ei ragga Th < = IN © ®IO IN | = = | N = ood wo F | =| * g T | = =) h WINN N I ~~ Nowy wh oN © | I=] £ | IEE 3H ° | | olo|oie 3 | | OR | | |@ | li RNARRS | I © a | eel C13 BERERL | Lob IR 2a no (N | Ix N|=lele ololo old | I gS |e I T TT BRAARS NEIL =O 00) | olo|o|o 3 | @ | | I i ] hom foln | € oleltiw g ggg! td ° 8 EEN |= I! | IN] | do (om | ®@i=]s eae © ®lQ se Sa | SSS SNS SS SE — — Study ©2007 Pearson Education, Inc., Upper Saddle River, NJ. Al rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel, Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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    CeO Or90000rY 0000 rE 5 5 = < w 852358838usRg3585a588 ¢ ¢ = §2 3% ¢ o 2 oz 85 = ° Il 2 Zz 3 = = [i [[——— . g H —_—— a = IZ = SF = == 7 ER Leg Too 00x wooo x === 2 =< 2 WT og OU Nw 30 | 2 $F 2 UNO gd N=, ©wooy == < > & ag 3 3 allo I pIEE & 8 == s 3°57 % fod = iN ME I NEN © m ® ww = = = 8 coon FAFTFS TF BR 8 OLe®g I] < 5 5 5 3 =~ 3 3 [= 3 5|f = aooux oO SIISARS = BE2IE ABBR TT H Noo ooow oy Hel 3 = 3 3 = 1x1 S 5 RS EE RT RT CE S208 9a NR py i DwWo my B® I= F 3 3 = A Ie iY = NN og [SESS <4 oN NX DAR OX == coco® ooo Sl= El El = & @ ® oss ono sg coo coos E ° 3 5 5 NN = DONDE ® BSR % 3% x ocoo® coob E} 3 @ @ oo bog LE coos co 3 E BE) o o 3 3 wo [a ~oog cog aN ooo @ @ Study ©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel, Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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    “¥ ~ Coelcolore thio {eco Flows ob Hie ams EP g BEE =P SAD SVR SN so covrdieda systems Hodined on Semen A 7 Tecmnent A 200, - | | i | i | ES Tl — T 0 = ET — IN J a Ey | Tot, ike | N | BE Ee EE Sil \ \ \ Lh ; : H \ [wn i S | \ \ | ; ) \ : li li 3 . i ied N \ ' \ \ ! i N i } ov / { AEN | NEN H Co R — ES Ee A : wo NN we wo io 200 240 a i re Ie Stud gs 4 ~~ \ Eg © 2007 Pearson Education, Inc.; Upper Saddle River, NJ. All rights reserved. = - For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel, Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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    TO. Cake caves A Ooo 0! x © Tox 7 = 4 ol [at 1G.= EP 2 -na 24.2 120.7 - 10%, 3 > (aed ert aro oor 2 151.1 5 1 257.2 ae) 170.0 £27 Tr a) i Loo 7 vo etme be Vv cmenegee® A Sven Nelege) x ~ bd = he i SHA] 1579 7 0 A Sia 24.4 PAN Pp SE B Cu aad coord EY : 220 ] 4 q [fe 222.7 7 Co Kobo vr 7 Kee [RIZE i : [00 [ew 2ng” Leon oi | ET oT TTT hd Taehe [deacaes] Tle ort Domai A Zoodiaade bea a - ) “ he 7 on pe Laz - 94.8 25h in Son CRE bir precefs 2 Foes meget ©oh RL TI SC SG : TC write Senwment A Cooedivade Sade. melita en Tn bs RE ata % v ~EE.3 zed. Study 3.34 [Ta 28.O £19 ©2007 Pearson Ediication, Inc., UppérSadlle River, NJ. All rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Doriald L- Barfel, Dwight T. Davy, and Tony M. Keaveny. #5 ISBN 0-13.008909-5

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    2-11 Minimize S,5, = Su, +S, = Fu /3.0+ Fy [4.5 Nem” Subject to the moment equation: Ti KW, +1 XW, + Typ X Fy +75 X Fy = 0 Fy XW, = (320)%(=5.5%9.81]) = —1726k N-cm Fry xW,., =(13()%(~1.6%9.81]) = ~2.04k N-cm Foo X Fy = (ST +17) % Fy [cos(135)] +5in(135) J] = 4.24 F,,k N-cm Ty X Ey = (30 +1))* F,[cos(120)i +sin(120) j]1=3.10F.k N-cm Plugging in the numerical values (similar to the homework problem) yields: 4.24F,, +3.10F,, =1930 N-cm, or in terms of stresses 12.728, +13.955,, =1930 N-cm 200 ———— 180 XK - N ~ | 160 «a ' | RY ERE 140 SN | NN | a NON | B20 nw NON = AN SOON 100 «SoC TN Sos . g DUE ES Moment Constraint | | IT NN NR - @ Coon, nel ENE NAN 60 STRETER NN AN - i Soon TN, NN AN AN AS ~ ~ 40 | CONONN T NON ANU Soon Ns NN | 20 N ~ ~ ~ ~ SONNY, SON NN 0+ = Sei 0 50 100 150 200 | i Brachialis Stress | Plotting values of the objective function yo; = Spp +Sp= constant, along with the moment equation demonstrates that the minimum stress will occur at the point where the Brachialis stress is zero and the Biceps stress is 138.5 N/em™, corresponding to a force of 622.6 N. Study © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel, Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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    Sel 5d Hees] 4. ES ; “ N ig f : } BT on i 7 br - — a. . “, Was — Rg de 4 on ~ . i ; wo R576 = be ar « = cE oz A 5 TPE ELL] a we A nn ais TE 5 ry “A FARES i ww [LY a fo v3 li Study © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel, Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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    Loi Desi = ated ~ gy {iy IK { | uc ER w= EYL oe - ) ! | ES PY - PE RY Va, | X “ z ~ : H 5 Pos Pi ‘ i IS ‘ we L% fe SY Mo oe GOR CO ga TOO Rg EL Yl | EN, Fook {a abadiviecy tn wad fey ak [ay a ery x a he He J, HE a — ) Pp & “. be = | ? . 4 by, A i CEL FECAL Cdn oe HOON IG 0 Ye 13% . 2a fdr x Limi A 2 CE aa 3 AY Tg 5 PY oe a forded Ba he i oe 7M fg 5 : af SV EN cen Te (0 0 eM Stud ty, CL : y =o SZEN TD : . iy ©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. For the exclusive use of adopters of the book Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems, by Donald L. Bartel; Dwight T. Davy, and Tony M. Keaveny. ISBN 0-13-008909-5

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