Centre Of Gravity

Segmental Method

Lesson Objectives

Demonstrate ability to calculate Centre of mass using the Segmental method

Identify the strengths and weaknesses.

Segmental method

The segmental method is the estimation of the location of the body’s total centre of gravity

It is based on the concept that each individual segment has its own centre of gravity

A standard set of values for mass ratio, and centre of gravity for each body segment is used.

Cartesian coordinates are obtained for each segment

Segmental method A study on cadavers by Dempster (1955)

helps us quantify body segment parameters

Dempster collected data from 8 complete cadavers to determine centre of rotation at each joint, segment lengths masses and volumes.

Segment Centre of Gravity Location Relative Mass(% of length) (%)

Head 59.8% from Vertex 6.94Trunk 44.9% from supersternale 43.46

Upper Arms 57.7% from shoulder 5.42Forearms 45.7% from elbow 3.24

Hands 79.0% from wrist 1.22Thighs 41.0% from hip 28.32Shanks 44.6% from knee 8.66

Feet 44.2% from heel 2.74

Step 2Carefully Mark the following segment endpoints on your drawing:1. Vertex2. Chin-neck Intersect3. Suprasternal Notch4. Shoulder axis5. Elbow axis6. Wrist axis7. Knuckle8. Hip axis9. Knee axis10.Ankle axis11.Heel12.toe

Step 1Make an educated guess as to the location of the centre of gravity

Step 3Construct a stick figure, by drawing straight lines between appropriate end points

Step 4Measure the length of each segment and record in table 1

Step 5Using the lengths, and the data expressing each body CG as a percentage of segment length, calculate the CG of each body segment.

Segment Length (mm) Centre of Gravity Location Centre of Gravity Location(% of length) (mm)

e.g. Head length x 0.598

Head 59.8% from Vertex

Trunk 44.9% from supersternale

Upper Arm 57.7% from shoulder

Forearm 45.7% from elbow

Hand 79.0% from wrist

Thigh 41.0% from hip

Shank 44.6% from knee

Foot 44.2% from heel

Step 7Plot horizontal and vertical axis. Then for each segment, measure the horizontal (x) and vertical (y) distance from each CG location to each axis

x

y Step 6Mark the segment CG locations on your diagram

Segment Relative Mass Horizontal CG Distance (X) Horizontal Moment Vertical CG Distance (Y) Vertical Moment

(%) (mm) (mass % x X) (mm) (mass % x Y)

E.g. 6.94 x X E.g. 6.94 x Y

Head 6.94

Trunk 43.46

Upper Arm 5.42

Forearm 3.24

Hand 1.22

Thigh 28.32

Shank 8.66

Foot 2.74

∑= ∑=

Centre of Mass Location X = E.G ∑ horizontal moment 100 Y =

E.G ∑ Vertical moment 100

X = Y =

Step 8To find each segment moments about each axis. Multiply the relative mass of each segment by its distance from the axis

Step 9Calculate the X and Y co-ordinate for the TOTAL BODY CENTRE OF GRAVITY by dividing the sum of segment moments about each axis by the total relative body weight (100, which represents 100% of body weight)

Step 10Plot the Centre of gravity location (x,y) on your diagram

Check against your estimated guess.

x

y

Weaknesses / Strengths.....

Data based on 8 cadavers, old ones at that. Is this data relevant to athletes? (muscle structure)

Human error in plotting points Time Consuming

Can be applied to actual sporting movements and techniques

Computer software could be used to improve accuracy/ speed.

Can be fully automated using computer system to get quantitative analysis.

Conclusion

Demonstrate ability to calculate Centre of mass using the Segmental method

Identify the strengths and weaknesses.

Segment Length (mm) Centre of Gravity Location Centre of Gravity Location(% of length) (mm)

e.g. Head length x 0.598

Head 59.8% from Vertex

Trunk 44.9% from supersternale

Upper Arm 57.7% from shoulder

Forearm 45.7% from elbow

Hand 79.0% from wrist

Thigh 41.0% from hip

Shank 44.6% from knee

Foot 44.2% from heel

Segment Relative Mass Horizontal CG Distance (X) Horizontal Moment Vertical CG Distance (Y) Vertical Moment(%) (mm) (mass % x X) (mm) (mass % x Y)

E.g. 6.94 x X E.g. 6.94 x YHead 6.94Trunk 43.46Upper Arm 5.42Forearm 3.24Hand 1.22Thigh 28.32Shank 8.66Foot 2.74

∑= ∑=

Centre of Mass Location X = E.G ∑ horizontal moment 100 Y =

E.G ∑ Vertical moment 100

X = Y =

Table 1

Table 2