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Unformatted text preview: Please review and complete the required information on this cover page before answering the questions. Biomechanics BMED-4540 Department of Biomedical Engineering RenSSelaer Polytechnic Institute In-class closed book exam (Include Crib Sheet) Date: September 28, 2006 Duration: One hour and 50 minutes (2 PM to 3:50 PM) Total points: 100 Name: This examination accounts for 15% of your final grade. Please read the instructions carefully and answer each question to the best ofyonr abilities. Not all questions carry equal weight. The points are indicated in parenthesis by each question. Total number of pages including cover: 9 flung/w I. Consider the leg curl exercise shown below, and assume that the patellar tendon is the only active muscle in the lower leg. The patellar tendon attaches to the lower leg at a b distance E r» 0.08 , the center of weight of the lower leg is a distance z 0.14, and the lower limb is of length»; = 0.28 , where h is the total body height, and distances are all measured from the knee joint along the lengthwise axis of the lower leg. The patellar tendon makes an angle of 9 = 15° with the lengthwise axis of the lower leg. The lower leg segment weight is WL = 0.08W , and the external weight is WE : 0.15W , where W is the total body weight. Determine the force in the patellar tendon, FM, and the joint reaction force at the knee, FJ, during the leg curl, as a function of the body weight, W, when the lower leg is horizontal, and when it is flexed 60D down from a horizontal position. Solution should include free body diagram(s). (25 points) _— r ‘ go'é do, flfiflfi/ W F Maw-‘2’) 6% £422" wflér {Ta/"1M? fl 25W; “fl 7‘ “’35:: : [WW-re“ fl gm” M” 2. The figure below illustrates a person using an exercise machine for their left arm. Points A, B, and C correspond to the shoulder joint, elbow joint, and hand, respectively, Relative to the person, the upper arm (AB) is extended towards the left (x—direction) and the lower arm (BC) is extended forward (z—direction). At this instant the person is holding a handle that is connected by a cable to a suspended ZOON weight. The lengths of the upper arm and the lower arm are a=25 cm and 13:30 cm, respectively. The pulley system lies in the X—y plane, and the pulley 0n the left, in this View, has coordinates (15, 40, 0) cm. Use the vector method (cross-product) to determine the moment of the force at C about the shoulder (Point A). Result should be expressed in Cartesian components. (25 points) Mme-M Wgérflfet . . . . .. M : I; I .4 , If? 4;, ‘79,,“ ,3 .5ka??) M 6 7g “4%?- W _ r as.ch 31 a A LL .4. g” ' I -/02’+ 4'0;- fffiwww e M w: = am) ~..,fl_—.-«-,:-—n~.~ , er? /CD/ 7’(—/§) 4 46’ Jae-36‘ MJ-flwma-._u_._._w_____.——a————_._____:\h fgdgeaé + M7; _. N7 1: m _,,.. Lf_#n_,___.g_,r_/ mew-m----__b________"M_,_,.Hr h; F: A} V451}? Qé-WL.) ,4 Q WWWD?‘ Maid; .5? x4?er WWT/ 07f WK AWV?/-—-" :4 15 (/1 u— » A rm: 252+ 3a ,2 (is-m) A ‘ 24 J ____b __5 6 j M16”? A AC .473 M77 —»//7 IL 3; 0 U m A (3 w j z; 30/W «wfl/ 514 //f7 ’H’] #39,: 4/7 ,5 .4. ,. _;_._._rfl fl,_w_i--/-IMW—~—MH\ .... v- r"' "'_ "’ "" T“ "i 5' A/~m H 347: 20 3+ / 7, Mf + 3932’» A ,4 Mfg/"Mi mfl’r/fl—m """"—“*---—.r...__-W.-._.__,_,___g_n-_mVF—m“pw __.-’// 3. Consider the arm shown in Figure at below. The elbow is flexed to a right angle and an object is held in the hand. The forces acting on the forearm are shown in Figure b below. Point O designates the axis of rotation of the elbow joint, which is assumed to be fixed for practical purposes. Point B is the center of gravity for the forearm, and C is a point on the forearm that lies along a vertical line passing through the center of gravity of the weight in hand. The distances between 0 and B, and O and C are measured as b and c, respectively. W0 is the weight of the object held in hand and W is the weight of the forearm. The model assumes that there are three muscles that flex the arm: the biceps, the brachialis, and the brachioradialis (Figure b). Let FMl, FM; and FM3 be the magnitudes of the forces exerted on the forearm by the biceps, the brachialis, and the brachioradialis muscles with attachments at A1, A2, and A3, respectively (Figure b). Furthermore, let 01, 92, and 83 be the angle that the biceps, the brachialis, and the brachioradialis make with the long axis of the forearm and a1, a; and a3 be the locations of A1, A2, and A3 along the long axis of the forearm, measured from the elbow. The angles, distances and weights should be treated as known quantities. Assume that each muscle exerts a force proportional to its cross-section area and that Al, A2 and A3 are the known cross—sectional areas for the biceps, the brachialis, and the brachioradialis. Thus, FM; : kzl FMl k21 : and FM3 3 k3] FM] k31 : (A3/A1). Determine the magnitude of the three muscle tensions, and the joint reaction force at the elbow. (25 points) ' 1: 3/9 as Asswma ,9 ,9 31),, an: (ma/Hal, J‘o‘zzytzi‘ £5.3/Zf/Z4TW; VEJIT'I 4X' Problem 3 (continued) W511i MW€ flfig‘gzgfma {3% WM é) WL"f/:L"Z’{szfi‘fi"w W 72:! ) 5/ W% Ma W zit/1’ “’6‘ if; /fl,5/fléi 4%; 21—42542 fizéggfié = “4%,,{5 MJNM_._.W*,M_H_Q___“_” Mfme w W a}? WWW” (FL/"x r“ W6 J Md; Hun—"W F 3 W7?" ,4 3 . bzflfi, 5/M5{, 7‘ Jag-27 (j/néz '/ 443 :47 Swat] “\ngmwk H // 62: I Qf M; ’M __. // ,5 , fl 5% A __/ % ’4/ I / // W \k_x‘-k‘ /./ “uii—‘l— / 42. 61+” 4 _... wé‘ + j; WI;] 7 <2 = ‘7’er Lia. __ -, My, 4; ] /f # [W54%C][w§/ v42: w% ,(«A/ 5 H ————-.——. ’4 Z' ' A? ' 51 ‘7} 5/175: Iffiz Z7 Slnfl-Zr } r I # Hm" _w_m—W— ~mfl mm'm—f/w % 2347? :0 AZ“ £8355? #1] M x’” I“; : WM? - 5w, [5mg] * gaff? ,4, ,, """"""""""" jfiiflm g d; if my 5;] / [W5+%C]/5rm-§/ W Z WWW—M f :1.‘ "'- fi __ ~WA Z ~m__v__m___m ~ (9 ’1 ‘ ‘ _...-— 5 m 2. f7 Lani/V16} @ngwflzaééffll / /] ’ W flaw-WM Problem 4. The figure below shows a gait cycle, following the (darkened) right leg. a. Identify and briefly define the major phases of gait. (3 points) b. Identify each of the key events of a gait cycle, beginning with the first figure on the left. (11 points) C. For each event, identify one mechanics—relevant change that would make a free body diagram of this event different from the previous event (begin with the second event from the left). (ll points) ; 5M} ’5, “*% M 55' —'—~—-—-——wuu—-::P- iris-3M fig! «’12 Mi flag. 7 Mia .. . may wart m: we we W77 6W” C I device“! P 50% “f v w W ' gag-61.5%? ‘ ...
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Exam 1 Solutions - Please review and complete the required...

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