centre of gravity and segmental analysis

8/13/2019 Centre of Gravity and Segmental Analysis

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Dr Su Stewart

Semester 2 Lecture 5

Centre of Gravity and Segmental Analysis

Contact details: [email protected]

SP0406 Fundamentals of Anatomy and Biomechanics


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GravityGravitation , or gravity , is the natural

phenomenon by which physical bodies appearto attract each other with a force proportional totheir masses.It gives apparent weight to objects with massand causes them to fall, or accelerate towards,

the ground when dropped.The phenomenon of gravitation is mostaccurately described by the general theory ofrelativity by Einstein, in which the phenomenonitself is a consequence of the curvature of

space-time governing the motion of inertialobjects.The simpler Newtons theory of universalgravitation provides an accurate approximationfor most physical situations including

calculations as critical as spacecraft trajectory
http://www.google.co.uk/url?sa=i&rct=j&q=galileo+gravity&source=images&cd=&docid=7KVviTHaEsihPM&tbnid=9JojKdrvdX55IM:&ved=0CAUQjRw&url=http%3A%2F%2Fisaacnewton272.weebly.com%2Fgravity-and-motion.html&ei=yhsRUdT3LqKM0wWtsYCoBg&bvm=bv.41867550,d.d2k&psig=AFQjCNGR6ynbVy3gfmSu0oGfruBoNLKS8w&ust=1360162091840706


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Equivalence principleThe equivalence principle, exploredby a succession of researchersincluding Galileo, Lorand andEotvos, and Einstein, expresses theidea that all objects fall at the same

rate.If two objects of different masses orcompositions are dropped in avacuum, they will hit the ground at

the same time. All objects fall at the same rate(acceleration) when friction(including air resistance) isnegligible.


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5

Units of measureLength - metres (m)Time - seconds (s)Mass - kilograms (kg)Weight - newtons (N)

Mass is measure of inertiaWeight is measure of gravity acting on object


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Centre of Mass or Gravity?


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Centre of GravityThe C of G and centre of mass are often used interchangeably -difference between mass and weight

Centre of gravity is:the point in a body or system of bodies around which its

mass or weight is evenly distributed (McGinnis, 2005)

Centre of mass is:the point in a body or system of bodies around which theentire mass may be assumed to be concentrated. (McGinnis,2005)


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Centre of Gravity of the Human Body

Body not rigidThe human body is not only irregular butalso changes shape can be calculated byexperimentation: balance board, reactionboard, video, pendulumC of G affected by body composition andsomatotypeC of G normally lies at 57% of height inmales and 55% in femalesC of G depends on position of limbsC of G located at sacral promontory,anterior to S2 (PSIS), at 55% of bodyheight


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Centre of Gravity in Human Movement

C of G can move outside the body:


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Role of C of G in Balance

Balance / Stability is affected byThe position of the C of G relative to the base ofsupport

The height of the centre of gravity above/below thebase of supportThe distribution of the parts of the bodyThe mass of the various parts of the body


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Role of the C of G in Flight

Sport frequently requires the projection of the bodyinto the airChanges in segmental relative position does notaffect the locus of the C of GSome sporting activities exploit the relative location ofthe C of GSegmental position can alter whole body positionrelative to the C of G


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Role of C of G in Rotation

If force is aligned causes linear translation ordisplacementIf force is offset causes rotation (spin)Rotation occurs about the C of GThe greater the spread of weight the slower therotation -

the moment of inertia


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FBDs and the Line of Gravity

The line of gravity is an imaginary line extending fromthe centre of mass vertically down to the ground


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Why calculate the centre of gravity?


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Moments

A moment is a turning force It can also be called torque It is the product of the force applied normal to a lever,and the length of the lever measured in Nm

(Force x radius)

F

radius

Axis ofrotation


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Static EquilibriumFor an object to be balanced, its mass must be evenlydistributed about its support or base:

F1 x d 1 = F 2 x d 2

F 2d 1 d 2

F 1


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Segmental AnalysisBased on the concept that since the body is composed ofindividual segments (each with an individual CofG),location of the total body CofG is a function of the locationsof the respective segmental CofGs

Uses data fornormative locations of body segment CofM as

measured from the distal end of the segment, as a % ofthe length of the segment

normative mass of each segment as a % of the totalmass of the whole body


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The Segmental Method for thecalculation of the C of massThe process of calculating the location of the total bodycentre of mass through considering the body as amechanical segmented model.The process of considering the body in static equilibriumwhere the sum of the moments = 0


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http://www.google.co.uk/url?sa=i&rct=j&q=dempster+segmental+analysis&source=images&cd=&docid=X58DFVSRg9mKwM&tbnid=GbcBbNdFq3Jl7M:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS1350453309001593&ei=Mx4RUeybOcnA0QW10YHYDg&psig=AFQjCNGxYA6W8QLPh1ET_SY-t-xuzMLZEw&ust=1360162671159328


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(adapted from Winter, 1990)

Body Segment

Centre of mass/Segment Length

Segment mass(% body mass)Proximal Distal

Foot 0.5 0.5 1.45

Lower leg (shank) 0.433 0.567 4.65

Thigh 0.433 0.567 10

Trunk + neck + head 0.66 0.34 57.8

Upper arm 0.436 0.564 2.8

Forearm + hand 0.682 0.318 2.2

The normative data for body segments


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Calculating the mass and position ofthe C of M of lower leg

If a = 0.5 m, b = ?normative distance is 0.433%

b = 0.433 x 0.5

b = 0.216m

If whole body is 65kgnormative mass is 4.65%

The mass of the lower leg is therefor(4.65/100)*65 = 3.022kg

a

b


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Segmental Analysis

Need to find X and Y coordinates of CofM:

Xcofg = (xs)(m s) / m s Ycofg = (ys)(m s) / m s


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Assume body mass = 80kg Calculate segment

masses: Foot = (1.45/100) x 80 = 1.16kg Shank = (4.65/100) x 80 = 3.72kg Thigh = (10.0/100) x 80 = 8.0kg

(x3,y3)

(x0,y0)

(x2,y2)

x-axis

y-axis

(x1,y1)

Calculating C of M in a MultipleSegmental System


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Calculating the segmental centres of massCo-ordinates of the landmarks (segment ends)

Foot: x1 = 0.0931 +(0.0753 -0.0931 )*0.5 = 0.084m y1 = 0.2144 +(0.0935 -0.2144 )*0.5 = 0.154mShank: x2 = 0.4100 +(0.0931 -0.4100 )*0.433 = 0.273m y2 = 0.4053 +(0.2144 -0.4053 )*0.433 = 0.323mThigh: x3 = 0.4494 +(0.4100 -0.4494 )*0.433 = 0.432m y3 = 0.7858 +(0.4740-0.7858 )*0.433 = 0.651m

Landmark x-position (m) y-position (m)toe 0.0753 0.0935

Ankle 0.0931 0.2144

Knee 0.4100 0.4053

Hip (greater trochanter) 0.4494 0.7858


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Calculating C of G in multiplesegment system (cont )

Find C of M of total leg: Mass of limb = m1+m2+m3 = 1.16+2.72+8.0 = 11.88kgCentre of mass of limb:

Total system centre of mass coordinates = (0.362, 0.527)

362.088.11432.0*0.8273.0*72.2084.0*16.1

0 x

527.088.11

651.0*0.8323.0*72.2154.0*16.10

y


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Errors in centre ofmass calculations

Data clarity frame rate, definition Spatial model Positioning of anatomical markers

Estimation of joint centres Digitising accuracy Estimating joint centres out of field of view, foreshortening Normative data for distances to segmental C of M Normative data for segmental mass Computational errors


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Segmental definition errors Normative data for distances to segmental C of M Normative data for segmental mass


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Errors in normative data

Limited number of cadaversCadavers all maleCadavers mesomorphic marinesMeasurements of mass untrustworthyDefinition of segments variesDifficulty dissecting out segments

No childrenSegments not evenly denseTrunk difficult to divide into segments


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http://www.google.co.uk/url?sa=i&rct=j&q=dempster+anatomical+segments&source=images&cd=&cad=rja&docid=FK0np-sO4WQ4YM&tbnid=d-gu5Q-ZjMTbUM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0021929006000728&ei=wR4RUc38CoKd0QWEuoHABQ&psig=AFQjCNEdRasq9AZMEiDkcw-EvEIMV-V4tg&ust=1360162859971042


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SummaryThe C of G of a body represents the balance pointIn humans, movement of body segments alters theoverall position of the C of GThe location of the center of mass can be calculated

using the segmental methodStability/mobility is affected by the position of the C of GC of G is an important consideration for flight androtational movements

centre of gravity and segmental analysis

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