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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”:




POSTECH                      2000 ESK/JES
      Body Segments


   Segments
   Usually include

   Above segments may be

   Above segments may be




POSTECH                2000 ESK/JES
     Finding the Center of Mass of the Whole Body




   COM location
   Whole body COM




POSTECH                2000 ESK/JES
    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
 POSTECH                    2000 ESK/JES
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?




POSTECH                2000 ESK/JES
         Q: How much does your thigh weigh?




   Ethical considerations prevent



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




POSTECH                    2000 ESK/JES
      A: About 9.7% of your body weight


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

   Cadaver-based



   Above estimate




POSTECH                  2000 ESK/JES
          Common Assumptions

    All methods
    Segment definitions

    Anthropometric measurements

      

      




    POSTECH                2000 ESK/JES
        Regression Models

   Equations that

    

    

    

    


   Examples:




POSTECH               2000 ESK/JES
      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


    


    




POSTECH                   2000 ESK/JES
    Regression Models (cont)

   Cadaver
    

    

    


   Disadvantage:




POSTECH             2000 ESK/JES
     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)


 POSTECH               2000 ESK/JES
    Geometric Models


   Other shapes may be used:



           example:
   Segment density
   Density assumed




POSTECH                 2000 ESK/JES
        Image-based Techniques


   Use
    

    


   Permits

   Extra




POSTECH               2000 ESK/JES
        Density Depends on Tissue Type


 r skin,fat

   r muscle                          r bone




Data from Visible
Human Project -
www.nlm.nih.gov
  POSTECH             2000 ESK/JES
        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)




    POSTECH                 2000 ESK/JES
     Whole-Body Anthropometry: Example


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


                                        Head-Arms-Trunk
                                          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
    POSTECH                   2000 ESK/JES
     Reconstruction


   Process of

   Actual coordinates are “reconstructed” from

   Uses




POSTECH                   2000 ESK/JES
     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




POSTECH                  2000 ESK/JES
     Automated Motion Analysis (cont)


   Accuracy depends on camera placement:




     GOOD                                   BAD




POSTECH                 2000 ESK/JES
                   swinging arm may
                   obscure marker




                   reflective markers




POSTECH   2000 ESK/JES
     Other Systems


   Electromagnetic systems:
    

    

    

    


   Electrogoniometry
    

       mechanical linkage with




POSTECH                       2000 ESK/JES

				
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