ch 13,on biomechanics in bio medical engineering
TRANSCRIPT
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-
13 , EQUILIBRIUM AND
HUMAN MOVEMENT : ][TEXT BOOK: BASIC-BIO-MECHANICS BY SUSAN-J HALL ,
3rd EDITION ];
6/20/2013
BIO-MEDICAL ENGINEERING GUIDE.INC
MUHAMMAD-SIKANDAR-KHAN-LODHI
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
Page 2-OF-45
Table of ContentsEQUILIBRIUM AND HUMAN MOVEMENT: .................................................................................................... 3
1. TORQUE :- ......................................................................................................................................... 3
DIAGRAM: [ fig # 13.1 ( a )] [ Moment-Arm ] ........................................................................................ 4
Fig # 13.2 [ b and c ] .............................................................................................................................. 5
DIAGRAM [ fig # 13.3 ] :- ....................................................................................................................... 6
DIAGRAM [ fig # 13.4 ] [ stage-a ] : ....................................................................................................... 7
DIAGRAM [ fig # 13.5 ] [ stage-b and c ] : .............................................................................................. 8
COUPLING-FORCE-NUMERICAL [ SAMPLE-PROBLEM # 1 ]:- ................................................................... 9
DIAGRAM [ fig # 13.6 ] :- .................................................................................................................... 10
LEVERS :- ..................................................................................................................................................... 12
HUMAN-SYSTEM ACT AS A LEVERS SYSTEM:- ........................................................................................ 12
DIAGRAM [ fig # 13.7 ] First Class of Lever :........................................................................................ 14
Example : [ fig # 13.8 ] ......................................................................................................................... 15
DIAGRAM [ Fig # 13.9 ] ........................................................................................................................ 16
Fig # 13.10 [ a ]: ................................................................................................................................... 17
Fig # 13.10 [ b ] .................................................................................................................................... 18
3rd CLASS OF LEVER:- .......................................................................................................................... 18
Fig # 13.11 : ......................................................................................................................................... 19
Fig # 13.13 : ......................................................................................................................................... 21
MECHANICAL ADVANTAGE:- ................................................................................................................... 21
[ Fig # 13.15 ] ..................................................................................................................................... 24
EQUATION OF STATIC EQUILIBRIUM :- ....................................................................................................... 25
Diagram: [ Fig # 13.16 ] [ Bicep work out ] .......................................................................................... 26
[ Fig # 13.17 (a ) ]. ................................................................................................................................ 27
FIG # 13.17 (b) ..................................................................................................................................... 28
SYSTAMATIC DIAGRAM: [ Fig # 13.19 ( a) ] ........................................................................................ 31
Fig # 13.20 (b) ...................................................................................................................................... 32
Diagram : [ Fig # 13.21 ] ...................................................................................................................... 34
Fig # 13.22 ........................................................................................................................................... 35
Fig # 13.2 ............................................................................................................................................. 36
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
Page 3-OF-45
[ Fig # 13.26 ] ....................................................................................................................................... 40
DYNAMIC-EQULIBRIUM :- ........................................................................................................................... 43
Fig # 13.29 ........................................................................................................................................... 44
Fig # 13.28 ........................................................................................................................................... 45
EQUILIBRIUM AND HUMAN MOVEMENT:
EQUILIBRIUM:
1.TORQUE :-a.TORQUE [ DEFINITION # a ]:-
The torque [ ] is the product of force [ F ] which acton the body and the moment-arm .
MOMENT-ARM [d ] : Its the perpendicular distance from the force [or
forces ] line of action to the axis of Rotation is called Moment-Arm .
FORMULA:
[ ];
Where :
F = Applied Force .
d = Moment-Arm.
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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DIAGRAM: [ fig # 13.1 ( a )] [ Moment-Arm ]
TORQUE : The Rotary effect created by the applied force is known as
torque .
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Fig # 13.2 [ b and c ]
[ ];[ ];
b.TORQUE [ DEFINITION # b ] :-The length of moment-arm and the magnitude of applied force cause
to effect the amount of torque , if we increasing or decreasing thevalue of moment-arm and magnitude of applied force so it cause to
change the value of torque .
c. TORQUE [ DEFINITION # c ]:-
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
Page 6-OF-45
In this case we applied force on the point of axis of rotation , so then
the moment-arm become zero [ d = 0 ] so, then there is no torque (
Turning effect ) will be produced on that rotator object .
That is :
DIAGRAM [ fig # 13.3 ] :-
Mathematically :
[ ]; {:. [ moment arm = d = 0 ] }[ ];---------finished-here------
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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EXAMPLE :
Q) There is a task we have if a person take bicep exercise so, its torque
will be change in each condition , so what we do to maintain some
torque in each complete cycle event of bicep curl?
SOLUTION:
DIAGRAM [ fig # 13.4 ] [ stage-a ] :
[ ];
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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DIAGRAM [ fig # 13.5 ] [ stage-b and c ] :
In the complete bicep curl the torque will be change because themoment-arm [ moment arm : the perpendicular distance from
line of action of force to the axis of rotation [ d ]], .
In each position , if moment-arm will be change so, then thetorque will also be changed so if we want to produce the same
torque in each above three stage [a,b,c ] so, we want to prevent
more force F on the stage [ b,c ] where , [ ] AScompared to force [ F1 ] in stage-a because , we do this because in
stage b and c the moment-arm [ d ] will be decreased.
[ ];
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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---------------------FINISHED-HERE---------------
COUPLE-FORCE:-
coupling force are those forces in which the two forces which areplaced on both side of the center-of-rotation, and one of these
forces act in the clock-wise direction while the other force act
on the anti [or counter ]-clock wise direction, and it produced the
same effect is known as Coupling-Forces.
---------------------
COUPLING-FORCE-NUMERICAL [ SAMPLE-PROBLEM # 1 ]:-
Q ) The two children sit on a opposite side of a play-ground see-saw. If
joey weight = 200N, is 1.5m from the see-saws axis-of-rotation, and if
Susie weight = 190N, is 1.6m away from the axis-of-rotation so,
which end of the see-saw will drop down towards ground surface?
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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DIAGRAM [ fig # 13.6 ] :-
SOLUTION:
{:. Clock wise direction = negative direction }
{:. Counter [ anti ]-clock wise direction = Positive direction }
DATA :
FOR Joey :-
[ ];[ ];
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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FOR Susie :-
[
];
[ ];
DISCRIPTION:
As we see in the above diagram that there are coupling forces that is [
Fj = Wj = 200N ] and [ Fs = Ws= 190 N ] act on the Axis of rotation but
in opposite in direction, so, the [ Fs = Ws= 190 N ] act in the counter
[anti ] clock wise [Positive ] direction , also the [ Fj = Wj = 200N ] act in
the clock-wise negative direction , we just sum-up the both torques
produced by the both bodies to find the resulting torque .
1.TORQUE GIVE BY JOEY :-Its a clock-wise direction so, torque is negative
[ ];2.TORQUE GIVE BY THE SUSIE :-
Its a counter-clock wise direction so the torque is positive .
[ ];Now we compare both torque with , so if the magnitude of anytorque is greater than the other one so then as the result of it the seesaw move on that directions , now by adding the eq-i with eq [ ii ] , we
get , the resulting torque we sum-up both torque then we get,
[ ];
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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[ ];CONCLUSION:
The torque give by the Susie is greater than the torque give bythe joey , so, as the result of it the torque which give by Susie causeto rotate the see-saw on the counter-clock wise [ positive ] direction .
--------------finished-here-----
LEVERS :-
The liver is a Rigid-bar , which can rotated around its axis under the
action of some external forces.
HUMAN-SYSTEM ACT AS A LEVERS SYSTEM:-
In the human body there are the some biological liver are presentspecially occurs in the limbs.
In the Biological system the both limbs act as a Livers .so as we consider the upper-limbs, in the Upper-Limbs the
Humerious [bone of arm ] and the radius + ulna [ both bones
of fore-arm ] act as a rigid bar and the joint is act as the axis-of-
rotation and the bi-cep and tri-cep act as a applied force on
the rigid-bars of the Levers.
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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there are three types of Levers which are given below.
That is :
1.1st Class of Levers:2.2ndClass of levers.3. 3rd Class of Levers.
1.1st CLASS OF LEVERS :-
In the 1
st
class of levers , the applied force [ F ] and the resistanceforce [ R ] are located on opposite site of levers .
This applied force [ F ] and Resistance force [ R ] are both in theopposite in direction one force is in the clockwise [ negative ]
direction and the other 2nd
force is in the counter-clock wise in the
positive direction.
There is an another possibility is that the both forces Appliedforce [ F ] and the resistance force [ R ] in equal in distance withrespect to the Axis of rotation, with each other .
Or , its also be a possibility that the one force is approximatelynear [ or far away ] with respect to the axis as compared to the 2
nd
force.
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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DIAGRAM [ fig # 13.7 ] First Class of Lever :
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EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Example : [ fig # 13.8 ]
2.2nd CLASS OF LEVERS :-The applied force [ F ] and resistance force [ R ] on same side of liver in
which the resistance [ R ] is lie near to the Axis-of-rotation .
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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DIAGRAM [ Fig # 13.9 ]
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Fig # 13.10 [ a ]:
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Fig # 13.10 [ b ]
3rd CLASS OF LEVER:-
In the 3rd
class of lever the applied force [ F ] and resistance [ R ] are lie
on same side of lever where force [F ] lie too near to the Axis-of-
Rotation.
Example:
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Fig # 13.11 :
Diagram: [ fig # 13.12 ]
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EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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-------------finished here ----------
Example :
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EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Fig # 13.13 :
When ever the moment arm of applied force is greater then the
moment arm of resistance [ R ] so, the magnitude of applied force [ F ]
is smallest then the magnitude of resistance [ R ].
--------------finished here ------------
MECHANICAL ADVANTAGE:-
The mechanical advantage is the ratio of moment arm of applied force
[F ] over the moment arm of resistance [ R ].
FORMULA :
[ -> Mechanical-Advantage = moment arm [ F ] / moment arm [ R ] ];
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EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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[ ];[
];
{:. its mean much less then, or vice verca };Fig # 13.14 [ MECHANICAL ADVANTAGE ]:
Example : [ Mechanical-Advantage
1 ]:
When the moment-Arm of force [ F ] is greater then themoment-Arm of the resistance [ R ] , then the mechanical-
advantage is equal to greater then one.
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EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Because , this value of mechanical advantage shows us that whichis a greater then one [ Mechanical advantage 1 ] .
We cause to applied less magnitude of force [ F ] then ascompared to the force of the resistance , because this greater
moment arm of the force [ F ] give the greater amount of torque
which cause to pull the heavy resistance force [ R ] so, its the
mechanical advantage for the Applied force [ F ] .
----------------finished ---
EXAMPLE-2 : [ MECHANICAL ADVANTAGE ] :
[ ];[ ];
Condition => [ Mechanical Advantage 1 ];
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I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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[ Fig # 13.15 ]
In the above condition when the moment arm [ ] is smallerthen the moment arm [ ] , then , if we want to move the leverso, we should be provided to more forces [ greater force ] , Then
the resistance so the Mechanical advantage is much less than [
] 1 .This value of mechanical advantage much less than one indicate
that this arrangement is less effective in the sense we provided
greater external applied force to move the lever , [ as we compare
to the previous example].
---------------------finished here -------------
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EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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EQUATION OF STATIC EQUILIBRIUM :-
When ever the body is in the state of motion less or in rest state [ or
its in the state of static ] , so then this body in the state of Static-Equilibrium , also , there are three condition to set the body in the
state of Static-Equilibrium , that is .
1.The sum of all Vertical-forces act on that body is equal to zero .2.The sum of all horizontal forces act on that body is equal to
zero .
3.The sum of all torque acting on the body is equal to zero.[ ];
[ ];[ ];Key point => if any one of above these three condition is not equal to
zero , so then this body is in the state of Motion .
------------finished here------------
SAMPLE PROBLEM-2 [ STATIC-EQULIBRIUM ] :-
Q ) how much force must be produced by the bicep brachii , attaching
at 90 degree to the radius at 3cm from the center of rotation at the
elbow joint to support a weight of 70N held in the hand at a distance of
30cm from the elbow joint ?
Note : we neglect the weight of the fore arm and hand , and neglected
any action of other muscle ( Triceps).
Solution:
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EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Diagram: [ Fig # 13.16 ] [ Bicep work out ]
DATA :
Its the 2nd class of lever, in which the bicep muscle act as aresistance against the external applied force [ F ] .
Where , this condition is the static condition , so all the sum oftorque forces acting on that body is equal to zero .
[ ];[ ];
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EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
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R = ?
F = external applied force = 70 N ;
[ ];SYSTAMATIC-DIAGRAM:-
[ Fig # 13.17 (a ) ].
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EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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FIG # 13.17 (b)
Req :
R=?
SOLUTION:
As we know that given in the question that the body segment in the
state of Static-Equilibrium, so all the sum of torque forces whichacting on that body segment is equal to zero.
[ ];Formula:
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[ ];FOR R :-
[ ];[ ];[ ];[ ];..
R = 700 N . Answer .
--------------finished-here--------
SampleProblem 3 [ Static-Equilibrium ]
Q ) Two individuals apply force to opposite side of a frictionless
swinging door .if A applied a 30N force at a 40 degree 45 cm from
the doors hinge and B applied force at a 90 degree angle 38cm fromthe doors hinge, what amount of force is applied by B if the door
remains in a static position?
Diagram : [ Fig # 13.18 ]
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EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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SOLUTION:
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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SYSTAMATIC DIAGRAM: [ Fig # 13.19 ( a) ]
[ ];Required :
[ ];
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Fig # 13.20 (b)
[ ];So,
Key point: As we know that the body segment is in the static-position
, so the sum of all the Equivalent torque [ ] forces is equal to zero,[ ];Formula:
[ ];Where :
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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[ ];[
];
--------------
Plus sign shows that the counter-Clock wise [ Positive ] direction .
And
Minus sign shows that the clock wise direction.
------------
Now placing the above value in eq-A, then we get.
[ ];[ ];[ ];[ ];[ ];..
[ ]; Answer . [ its the Force applied by the B bywhich the body segment stay in the static-position.
CONCLUSION:
We want to provide the FB = 35.52 N to the perpendicular to the door
so, then the door will stay in the static position.
---------------finished-here------------
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Sample-problem [ STATIC-EQULIBRIUM]:
Q) The quadriceps tendon attaches to tibia at a 30 degree angle 4cm
from the joint center at the knee , when an 80N weight is attached to
the ankle 28cm from the knee joint , how much force is required of the
quadriceps to maintain the leg in a horizontal position ( or in static-
position) ?
a. what is the magnitude and direction of the reaction force , exerted
by the femur on tibia?
Note: Neglected the weight of the leg and the action of other muscles.
Diagram : [ Fig # 13.21 ]
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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SOLUTION:
Fig # 13.22
FORMULA:
[ ];
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
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I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Fig # 13.2
[ ];[ ];
[ ];So,
SOLUTION:
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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SCHEMATIC-DIAGRAM: [ Fig # 13.24 ]
REQUIRED :-
PART (a) :
[ ];PART (b) :
Magnitude and direction of force by the femer on the tibia => R = ? , QR
=? .
Part (a) :-
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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For FQ:
FREE-BODY DIAGRAM OF FQ :- [ Fig # 13.25 ]
So, this body segment is in the state of static-equilibrium, so, sum of all
forces torque are equal to zero.
[ ];Part-a :
For FQ:-
[ ];
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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[ ];{:.
}
[ ];[ ];.
[ = 1120 ] ; its the required torque force for the static-condition.
PART b :
FOR MAGNITUDE AND DIRECTION OF FORCE [ R ] BY THE femer ON
tibia QR :-
FOR R :-
FREE BODY DIAGRAM OF FEMER EXERTING FORCE ON THE TIBIA:
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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[ Fig # 13.26 ]
FOR Rx :-
ACCORDING TO THE STATIC-EQUILIBRIUM :
[ ]; sum of all forces in the x-component is zero.[ ];[ ];[ ];[ ];
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
Page 41-OF-45
FOR Ry :-
According to static equilibrium
[ ]; sum of all forces in the y-component is zero.[ ];
[ ];[ ];Pythagoreous theorem:
[ ];
[ ];
[
];
[ ];[ ]; Answer-1 , its the magnitude of the resultantforce.
FOR-DIRECTION-OF-R :-
Fig # 13.26
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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[ ];[ ];
[ ];So,
[ ];[ ]; its the direction of R , Answer-2.---------finished-here---
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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DYNAMIC-EQULIBRIUM :-
when any body in the state of motion is known as Dynamic-
equilibrium
so, in the dynamic equilibrium there are all types of the forces act in the
body that is ,
[ sum of all forces acting in a body in x-axis ];[ sum of all forces acting in a body in y-axis ];
[ ];----finished-here--------
CENTER-OF-GRAVITY:-
[ OR CENTER-OF-MASS = CENTER-OF-GRAVITY ]:
CENTER-OF-MASS :-
There is a point in every body where the body mass are equally
distributed in all direction, this point is known as center-of-mass or
Mass-centroid.
CENTER-OF-GRAVITY:-
If we analysis this body in the gravitation forces , so, the center-of-
mass of the body is also known as center of gravity,
Key-point=> the center-of-gravity is that point on the body where sum
of all the torque produced by weight of the body segment is equal to
zero.
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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Fig # 13.29
[ ];[ ];[ ];[ ]; net torque is zero.
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
Page 45-OF-45
Fig # 13.28
-------------finished here---------
----------CH-13 ON BIO-MECHANICE IN BIO-MEDICAL ENGINEERING
FINISHED-HERE----------------
XMUHAMMAD-SIKANDER-KHAN-LODHI
OWNER-OF-MY-PERSONAL NOTES Thursday, June 20, 2013
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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-13 ,
EQUILIBRIUM AND HUMAN MOVEMENT : ]
I [ W W W . M E D I C A L - I M A G E - P R O C E S S N G . B L O G S P O T . C A B Y
M O H A M M A D - S I K A N D A R - K H A N - L O D H I ]
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