INTRODUCTION TO BIOMECHANICS

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INTRODUCTION TO BIOMECHANICS

• SECTION 4.2
• CENTRE OF MASS

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CENTER OF MASS (CENTER OF GRAVITY)

• We model the body as a system of linked segments,
  where each segment is a mass.
• We don't generally attempt to define mass, and
  instead appreciate it intuitively as one of the
  fundamental properties (along with time, length,
  and electric charge) of our physical world.

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CENTRE OF MASS

• Definition (geometric) point around which every
  particle of a body's mass is equally distributed.
  A body behaves as if its entire mass acts or is
  acted upon at its center of gravity.

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WHOLE BODY

• COG located at sacral promontory, anterior to S2
  (PSIS), at 55 of body height

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• The COG of the entire lower extremity, the body
  segment that lies distal to the hip
  (pelvi-femoral) joint, is located just proximal
  to the knee (Smith, Weiss, Lehmkuhl, 1996,
  p.55).
• This information comes from an anthropometric
  table that specifies typical segmental masses and
  centers of gravity.

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Human Anthropometric Data

• Remember that "proximal" means closest to the
  centre of the trunk or closest to the heart in
  some cases
• Data are from Winter DA (1979) Biomechanics of
  human movement, p. 151 - Now published as
  Biomechanics and Motor Control of Human Movement

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Segment Definition Segment Wt/ Total Body Wt Centre of Mass / Segment length Centre of Mass / Segment length Radius of Gyration / Segment length Radius of Gyration / Segment length Radius of Gyration / Segment length
      Proximal Distal C of G Proximal Distal
Hand see also wrist/knuckle II digit 3 .006 .506 .494 .297 .587 .577
Forearm elbow/ulnar styloid .016 .430 .570 .303 .526 .647
Upper arm G.H jt/elbow .028 .436 .564 .322 .542 .645
F'armhand elbow/ulnar styloid .022 .682 .318 .468 .827 .565
Upper limb G.H jt/ ulnar styloid .050 .530 .470 .368 .645 .596
      .        
Foot Lat. mall/hd. MT2 .0145 .50 .50 .475 .690 .690
Shank Fem.cond./med. mall .0465 .433 .567 .302 .528 .643
Thigh Gr.troch/fem. cond. .100 .433 .567 .323 .540 .653
Footshank fem. cond./med. mall. .061 .606 .394 .416 .735 .572
Lower Limb Gr.troch/med. mall. .161 .447 .553 .326 .560 .650
               
Head, neck, trunk Gr troch/G.H joint .578 .66 .34 .503 .830 .607
Head, neck, arms, trunk Gr troch/G.H joint .678 .626 .374 .496 .798 .621
Head and neck C7-T1 and 1st rib/ear canal .081 1.000 .000 0.495 1.116 -
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• WHETHER A MASS IS STABLE OR MOBILE ...
• depends on its size, the location of its COG, the
  size of the mass' base of support (BOS), and the
  location of the COG's vertical projection into
  that base of support

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CENTRE OF MASSSTABILITY VS MOBILITY
STABILITY MOBILITY
mass large small
position of COG low high
size of BOS large small
vertical projection of COG to point near center of BOS to point near boundary of BOS
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CENTRE OF MASSREVISITED

• The c/m is the point in the body where all of the
  torques causing rotation in one direction are
  balanced by all the torques causing rotation in
  the other direction.
• -Analogy to weights on a balance

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CENTRE OF MASS

• IMPORTANT TO UNDERSTAND AND LOCATE THE CENTRE OF
  MASS- greatly contributes to our understanding of
  motion

X
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1. GAIT ANALYSISIn walking the path of the c/m
forms a sinusoidal curve

• The gt the displacement of C/M the gt the amount of
  energy expended. The smoother the curve the less
  energy expended

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• The normal amount of rise and fall in an adult
  male approx 5 cm
• If 1000 steps/day raise and lower the body
  5000cm
• Work (force)(distance) The gt the work done the
  gt the energy expended
• By translating the c/m through a smooth
  undulating pathway of low amplitude the body
  conserves energy

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C/M AND POSTURE

• The bones of the skeletal system make up a series
  of links connected by joints and held upright by
  muscle and ligaments
• If these are stacked so that the line of gravity
  goes directly through the supporting links the
  lever arms (FORCE ARMS) 0 (or close to it)
• If 0 moment arms then 0 torques established
• -gt only a resulting downward force

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No torque
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• As soon as the c/m shifts a moment is
  established. To remain in equilibrium forces must
  be exerted to create an equal and opposite moment
• Muscular effort increases -gt strain
• When one segment moves forward another must move
  back to compensate

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x
http//www.phy.ntnu.edu.tw/java/block/block.html
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SEGMENTAL METHOD

• Process for calculating the location of the total
  body centre of mass from projected images of the
  body.
• The location of the total body c/m is a function
  of the location of the respective segmental C/Ms
  
• The calculation finds the location in 2 or 3 D
  where the sum of the torques 0

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Find the position of the c/m

• Sum of the individual torques resultant torque
• T1T2T3resultant torque

Resultant Torque (FR) (Fa)
.45m
.35m
.2m
7N
5N
15N
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.45m
.35m

Force arm
.2m
X
7N
5N
15N
FR
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Force arm
X
FR
(15)(.2)(7)(.35)(5)(.45)27(Fa) Fa .29m The
Force arm gives the location of the centre of
mass relative to the axis
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EXAMPLE

• Find the position of the centre of mass of the
  following system

F3
F1
2.8
5
F2
2.3
10
1.9
8
x
1.7
4.6
6.3
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y
F3
F1
2.8
5
F2
2.3
10
1.9
8

• F Fax Tx Fay Ty
• 2.8 28 1.7 17

x
1.7
4.6
6.3
23Fax 54.7 Fax 2.38 23Fay 85.3 Fay3.71
8 1.9 15.2 4.6 36.8
5 2.3 11.5 6.3 31.5
SUM Tx 54.7 SUM Ty 85.3
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(3.71, 2.38)
3.71
y
C/m
2.38
x
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Finding C/M in 2D when absolute masses unknown

• - therefore weight unknown
• - since actual segmental weights are unknown must
  use proportional weights
• The proportional weights are expressed as a
  percentage of the total body weight

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• The segmental method employs each segmental
  weight as a separate force acting at some
  distance from an arbitrary axis

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• MASS F Fax Tx Fay Ty
• Prop prop
• .45 .45 7 3.15 3 1.35
• .43 .43 4 1.72 5 2.15
• .12 .12 5 .6 7 .84
• Sum F 1 Sum Tx 5.47
  Sum Ty 4.34
• About the x axis
• sum Tx (Fresultant) ( Fax)
• 5.47 (1)(Fax)
• Fax 5.47
• About the y axis
• sum Ty (Fresultant) ( Fay)
• 4.34 (1)(Fay)
• Fay 4.34

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4.34,5.47)
X

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Center of massThe segmental method

• We need to know
• - Location of segment c/m expressed
• as distance from prox end
• Segment mass expressed as a
• of total body mass
• - Position of segments -gtclear image

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http//flash.lakeheadu.ca/health/menu.html
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Fay
Fax
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Total body Centre of mass
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TEXT BOOK

• PAGE 436-441