# lecture anthropometry No Title by sanmelody

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```									   WHOLE-BODY ANTHROPOMETRY

Overview
 Anthropometry; definitions

 Body segmentation

 Whole body center of mass

 Whole body moment of inertia

POSTECH                2000 ESK/JES
Anthropometry

   Measurement of
   Includes measurement of








   Useful for




POSTECH                  2000 ESK/JES
Review of Terms

   mass:

   center of mass:

   moment of inertia:

   “inertial properties”:

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Body Segments

   Segments
   Usually include

   Above segments may be

   Above segments may be

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Finding the Center of Mass of the Whole Body

   COM location
   Whole body COM

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Weighted Average

Straight average: x =

x1 + x2             1·x1 + 1·x2
=
2                  1+1

m1·x1 + m2·x2
Weighted average: x =
m1 + m2

Larger m means

POSTECH                    2000 ESK/JES
Center of Mass Formulae

m1·x1 + m2·x2 + ...           S mi·xi
xCOM =                                  =
m1 + m2 + ...                 mB

where xCOM = x-coordinate of center of mass
m1 = mass of first segment
m2 = mass of second segment, etc.
mB = mass of whole body
x1 = x-coordinate of first segment center of mass
x2 = x-coordinate of second segment center of mass, etc.

POSTECH                       2000 ESK/JES
Center of Mass Formulae

m1·y1 + m2·y2 + ...           S mi·yi
yCOM =                                  =
m1 + m2 + ...                 mB

where yCOM = y-coordinate of center of mass
m1 = mass of first segment
m2 = mass of second segment, etc.
mB = mass of whole body
y1 = y-coordinate of first segment center of mass
y2 = y-coordinate of second segment center of mass, etc.

POSTECH                       2000 ESK/JES
COM Example
y

m1 = 12 kg
m2 = 4 kg

x

POSTECH          2000 ESK/JES
COM Example

m1·x1 + m2·x2
xCOM =
m1 + m2

+
xCOM =                   = 1.5 m
+

POSTECH            2000 ESK/JES
COM Example

m1·y1 + m2·y2
yCOM =
m1 + m2

+
yCOM =                   = 3.25 m
+

POSTECH            2000 ESK/JES
COM Example
y

whole-body
COM

m1 = 12 kg
m2 = 4 kg

x

POSTECH            2000 ESK/JES
Finding the Moment of Inertia of the Whole Body

   First,
   Given moment of inertia of each segment about its
COM,

   Parallel axis theorem:

POSTECH                   2000 ESK/JES
Moment of Inertia Example
y

whole-body
COM
(1.5, 3.25)

m1 = 12 kg                               m2 = 4 kg
I1 = 5 kg m2                            I2 = 2 kg m2
x

POSTECH             2000 ESK/JES
Moment of Inertia Example

y
find distances (use a2 + b2 = c2)
d1 = 0.901 m
d1                           d2 = 2.704 m

d2

x

POSTECH                 2000 ESK/JES
Moment of Inertia Example

IHAT’ = IHAT + mHAT dHAT2
IHAT’ = 10 + 46 · (0.62)2
I1’ = 27.7 kg m2
ILEGS’ = ILEGS + mLEGS dLEGS2
ILEGS’ = 5 + 20 · (1.44)2
ILEGS’ = 46.5 kg m2
IWB’ = IHAT’ + ILEGS’ = 74.2 kg m2

POSTECH                    2000 ESK/JES
SEGMENT ANTHROPOMETRY

Overview
 Review: whole-body anthropometry

 Determination of segment inertial properties

   mass
   moment of inertia
   location of center of mass

POSTECH                        2000 ESK/JES
Whole-Body Center of Mass

m1·x1 + m2·x2 + ...           S mi·xi
xCOM =                                  =
m1 + m2 + ...                 mB

where xCOM = x-coordinate of center of mass
m1 = mass of first segment
m2 = mass of second segment, etc.
mB = mass of whole body
x1 = x-coordinate of first segment center of mass
x2 = x-coordinate of second segment center of mass, etc.

POSTECH                       2000 ESK/JES
Whole-Body Moment of Inertia

I’leg          Ileg
d

segment center of mass
whole-body center of mass

I’leg = Ileg + mleg d2
I’total = I’leg1 + I’leg2 + I’arm1 + I’arm2 + I’head + I’trunk
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We can find the whole-body center of mass and
moment of inertia if we know the segment masses,
centers of mass, and moments of inertia …
… but how do we find the segment masses, centers
of mass, and moments of inertia in the first place?

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Q: How much does your thigh weigh?

   Ethical considerations prevent

   Three commonly-used alternatives:
1)
2)
3)

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   Dempster WT: Space requirements of the seated
operator. Wright-Patterson AFB, 1955

   Above estimate

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Common Assumptions

    All methods
    Segment definitions

    Anthropometric measurements





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Regression Models

   Equations that









   Examples:

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Regression Models (cont)

   Statistical regression relates

mass = a*circ + b
segment                                          a = slope
mass                                          b = intercept
a,b determined using
simple linear regression

circumference

POSTECH                    2000 ESK/JES
Regression Models (cont)

   In general,

   e.g.,
   Multiple independent variables requires





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Regression Models (cont)







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Geometric Models: Example

y
r and h determined by
measuring circumference
and length
h
modeling the forearm as
a cylinder gives:
mass = r p r2 h
r      x
Iy = ½ m r 2
forearm     cylinder
COM (x,y,z) = (0,0,h/2)

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Geometric Models

   Other shapes may be used:

example:
   Segment density
   Density assumed

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Image-based Techniques

   Use




   Permits

   Extra

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Density Depends on Tissue Type

r skin,fat

r muscle                          r bone

Data from Visible
Human Project -
www.nlm.nih.gov
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MOTION MEASUREMENT I

Overview
 Anthropometry review and example

 Why measure motion?

 Image-based motion analysis systems

   Calibration and reconstruction
   Types of systems
   Other systems: electromagnetic, electrogoniometers

POSTECH                         2000 ESK/JES
Anthropometry Review

   Inertial properties of segments determined by:
1)
2)
3)
   Whole-body inertial properties determined by:
1)
2)
3)

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Whole-Body Anthropometry: Example

   Two-segment body model; find whole-body mass,
COM location, moment of inertia:

mass = 46 kg
y                               COM = (3,3)
Iz = 10 kg m2
Legs
mass = 20 kg
COM = (4.4,1.5)
Iz = 5 kg m2
x

POSTECH                 2000 ESK/JES
Example (cont)

mWB = mHAT + mLEGS
mWB =         =

mHAT·xHAT + mLEGS·xLEGS
xCOM =
mHAT + mLEGS

xCOM =                          =

POSTECH                    2000 ESK/JES
Example (cont)

mHAT·yHAT + mLEGS·yLEGS
yCOM =
mHAT + mLEGS

+ 20 ·1.5
yCOM =                       = 2.55 m

POSTECH                2000 ESK/JES
Example (cont)

Whole-body COM:
located closer to HAT
y

dHAT
dLEGS

x

POSTECH                2000 ESK/JES
Example (cont)

IHAT’ = IHAT + mHAT dHAT2
IHAT’ =            .
I1’ = 34.5 kg m2
ILEGS’ = ILEGS + mLEGS dLEGS2
ILEGS’ =            .
ILEGS’ = 45.3 kg m2
IWB’ = IHAT’ + ILEGS’ =       .

POSTECH                2000 ESK/JES
Why Measure Motion?

   Motion sometimes

   Accelerations may be used to

   Uses for








POSTECH                  2000 ESK/JES
Image-based Motion Analysis

   Uses cameras to
   Not

   May be
   May be
   May or may not

POSTECH               2000 ESK/JES
Calibration

   Relationships established that

   Uses
   2D calibration involves correction for

A        Closer objects appear
larger;
B
Box A appears
smaller than Box B

POSTECH                    2000 ESK/JES
Calibration (cont)
    3D analysis and calibration uses at least two
cameras

IMAGE 1     IMAGE 2

1

calibration object
2
calibration object        Computer
size and position

transformation between
images and actual coordinates
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Reconstruction

   Process of

   Actual coordinates are “reconstructed” from

   Uses

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Reconstruction (cont)

IMAGE 1                  IMAGE 2
y                   y

x                        z

Reconstruction

actual (x,y,z) coordinates
of points

POSTECH                   2000 ESK/JES
Manual Motion Analysis

   Uses video or
   Markers
   Markers or body segments must

   Time consuming
   Marker identification

POSTECH                     2000 ESK/JES
Manual Segment Identification

POSTECH            2000 ESK/JES
Automated Motion Analysis

   Markers
   Markers may be passive (reflective) or

   Computer performs

   Use of multiple cameras

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Automated Motion Analysis (cont)

   Accuracy depends on camera placement:

POSTECH                 2000 ESK/JES
swinging arm may
obscure marker

reflective markers

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Other Systems

   Electromagnetic systems:








   Electrogoniometry
