This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Please review and complete the required information on this cover page
before answering the questions. Biomechanics BMED4540 Department of Biomedical Engineering
RenSSelaer Polytechnic Institute Inclass 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:: : [WWre“ 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 (crossproduct) to determine the moment of the force at
C about the shoulder (Point A). Result should be expressed in Cartesian components. (25 points)
MmeM 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’ Jae36‘ MJﬂwma._u_._._w_____.——a————_._____:\h
fgdgeaé + M7; _. N7 1: m
_,,.. Lf_#n_,___.g_,r_/ mewm__b________"M_,_,.Hr h; F: A} V451}? QéWL.) ,4 Q WWWD?‘ Maid; .5? x4?er WWT/ 07f WK AWV?/—" :4 15 (/1 u— » A
rm: 252+ 3a ,2 (ism) 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 crosssection 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‘ Jag27 (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 SlnﬂZr } 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 ﬂawWM 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 iris3M fig! «’12 Mi ﬂag. 7 Mia .. . may wart m: we we W77 6W” C I device“! P 50% “f v w W ' gag61.5%? ‘ ...
View Full
Document
 Fall '07
 Vashishth

Click to edit the document details