optimization in (sports) biomechanics - aalborg · pdf fileoptimization in (sports)...

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1© Uwe Kersting, 2007

Optimization in

(Sports) Biomechanics

Department of Department of Sport Sport and Exercise Scienceand Exercise Science

SPORTSCI 306 SPORTSCI 306 –– Technique AssessmentTechnique Assessment

Uwe Uwe Kersting Kersting –– LectureLecture 0404 -- 20072007

Center for SensoryCenter for Sensory--Motor InteractionMotor Interaction

Anvendt BiomekanikAnvendt Biomekanik

Uwe Uwe Kersting Kersting –– MiniModuleMiniModule 1010 -- 20082008


Objectives

• Review basic considerations about modeling in science/biomechanics

• Define ’optimisation’ in mathematical terms

• Basic considerations on sprinting biomechanics

• Learn about kinematic descriptors in sprinting

• Learn about kinetic descriptors in sprinting

• Overview over Cricket rules and biomechanics

• Learn about the use of simulation models in cricket bowling

• Research assisted design of Cricket boots


Contents

1. About models (as relevant to biomechanics)

2. Define ’optimisation’ in mathematical terms

3. Apply the concept ’optimisation’ to sportson various levels/examples

- Sprinting - Execution of cricket bowling technique- Design of a cricket shoe

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What is a model?A theoretical construct that represents

something (reality), with a set of variables and a set of logical and quantitative relationships between them

Characteristics of model:

• Reduction / simplification

• Mapping / representation

• Subjectivation / individualisation

• pragmatism


What is a model?

A model is not reality!It is aimed at understanding fundamental

principles, laws, processes.

It can only be validated by applying it to ‘practice’ (experiments)- does it explain past observations?- does it explain future observations?- …


What is a model?

Statistical (black box) – probabilities

Physical models – simple representations

Causal/conceptual models – relationships


Factors high jump

Height

H3H2H1

Body Position

at TO

Vertical velocity

ot TO

Physique

Vertical

impulse

Vertical velocity

at TD

Body position

at HP

Movement

over the bar

Time

of TO

Vertical forces

at TO

3

General idea of prevention circle:

Sequence of Prevention

Quantifying incidence and severity of

sports injuries

Assessing the effects of

preventative measures

Introducing preventative measures

Establishing the cause and

mechanism of injury

3


Models in biomechanics

Fdx

Mz

Fdy

Fpy

Fpx

Fdx

Mz

Fdy

Fpy

Fpx

distal

proximal

Mathematical models – deterministic

- inverse dynamics (‘external’)

- forward dynamics (‘internal’)

- quasi static- mixed

Feffort Fload

axis

d⊥effort

d⊥load

Feffort

Fload


OptimizationMathematical definition:

Given: a function f : A � R from some setA to the real numbers

Sought: an element x0 in A such that f (x0) ≤ f (x) for all x in A

most simple example:

What if: f = f (x, y, t, I, ...) ??


Biomechanics of Sprint Running(Data from: acceleration phase!)

Uwe Kersting &

Joe Hunter PhD, CSCS, SESNZ Accredited

Bruce Pulman Park

Papakura

Department of Department of Sport Sport and Exercise Scienceand Exercise Science

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Overview

Phases in a sprint race

Step length and step rate (kinematics)

External forces acting on a sprinter (kinetics)


15 m

1.7 m~0.9 m

Six LAVEG© Sport Systems

Sprint Competitions WCA 1997


5

7

9

11

5 20 35 50 65 80 95

raw

v [m/s]

Speed Measurement

d [m]

Greene, final run

5


5

7

9

11

5 20 35 50 65 80 95

raw

filtered

v [m/s]

Speed Measurement

d [m]

Greene, final run


DecelerationMaximal Velocity

Phases in a 100 m Race

AccelerationStart


4.0

5.0

6.0

7.0

8.0

9.0

0-10 m 10-20 m 20-30 m 30-40 m 40-50 m 50-60 m

Race section

Velocity (m/s)

6


Step Length and Step Rate(kinematic descriptors)


Definition: Step Length

Step length (m)Step length (m)


Definition: Step Rate

Step Rate (Hz) = Step time

1

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DecelerationMaximal Velocity

Phases in a 100 m Race

AccelerationStart


Importance of Step Length and Step Rate

2.45 m2.45 m 4.5 Hz4.5 Hz11.0 m/s11.0 m/s xx==

2.50 m2.50 m 4.5 Hz4.5 Hz11.3 m/s11.3 m/s xx==

A weakness might be in one or the other factor...

4.0 Hz4.0 Hz2.75 m2.75 m11.0 m/s11.0 m/s xx==

??

Mann et al. (1985): “direct performance descriptors”

Sprint velocity (m/s) = step length (m) x step rate (Hz)


Step Length and Step Rate at Max. Velocity

Elite NZ male

Sprint

Velocity

(m/s)

Step

Length

(m)

Step

Rate

(Hz)

10.5 2.33 4.5

Race

Section

(m)

40 - 60

50 - 70

80 - 90Carl Lewis* 11.8 2.53 4.7

Ben Johnson* 11.8 2.44 4.8

*1987 World Champ. 100 m Final.

Source: Moravec et al. (1988)

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Which factor is more important?

Weyand et al. (2000): downplayed the importance of rapid repositioning the limbs

Mann et al. (1984): “…slightly above average [step] length, while producing an excellent [step] rate.”

Mero et al. (1981): “...[step] rate has a more decisive role than [step] length.”

Above average step length ~ 2.25 m Good step rate ~ 4.8 Hz


1.6

1.7

1.8

1.9

2.0

2.1

2.2

3.5 4.0 4.5

Step Rate (Hz)

Step Length (m)

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1

2

3

4

5

Relationship among Step Length, Step Rate, and Sprint Velocity (Joe’s data)


Results

Name Country Time RT

Greene (USA) 9.86 0.134

Bailey (CAN) 9.91 0.145

Montgomery (USA) 9.94 0.134

Fredericks (NAM) 9.95 0.129

Boldon (TRI) 10.02 0.123

Ezinwa (NGR) 10.10 0.135

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4.0

4.5

5.0

0-30 30-60 60-100 av_sf

GreeneBaileyMontgomeryFredericksBoldonEzinwa

SF [1/s]

Step Frequency

Interval [m]


1.6

2.0

2.4

0-30 30-60 60-100 av_sl

GreeneBaileyMontgomeryFredericksBoldonEzinwa

SL [m] Step Length

Interval [m]


•Two different patterns of step frequency development were identified.

•Step length does not show such clear grouping.

•Both parameters do not show a relationship with the resulting time.

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Other factors: Body mass of sprinters

1967 Olympic

Games

72 kg

56 kg

Males

Females

1996 Aussie

Institute of Sport

76 kg

58 kg

Sprinters are the heaviest of all track athletes

Sprinters are muscular, lean, but not excessively heavy


We may concludeMaybe it is simplistic to think that one factor is

more ‘important’

We also need to consider:

phase of a racestature (leg length, mass, inertia)strength and power abilitiesInfluence of past trainingnegative interaction between step length and step rate

An athlete-specific optimal combination of step length and step rate might be best


External Forces Acting on a Sprinter

(kinetic descriptors)

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BW Wind

Resistance

GRFGround Reaction Force

GravityBody

weight 4 % Body

weight

400 % Body weight

External forces acting on a sprinter


Wind resistance: significance

Altitude (Mexico City 2,250 m)

0.07 s advantage for 100 m

~0.7 m advantage for 100 m

Tailwind of 2 m/s

0.1 s advantage for 100 m

~1 m advantage for 100m


Minimising wind resistanceShaving the head

Wearing tight, smooth

clothes

“Smoothing” the laces

� suits developed based on WCA1997 data

Possible result: 2 % decrease in drag force0.01 s advantage for 100 m

0.1 m advantage for 100 m

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Horizontal GRF

2.80 2.85 2.90 2.95

-0.5

0.0

0.5

1.0

Horizontal

GRF

(kN)

Time (s)


Vertical GRF

2.80 2.85 2.90 2.95

0.0

1.0

2.0

3.0

Time (s)

Vertical

GRF

(kN)


Horizontal GRF

2.80 2.85 2.90 2.95

-0.5

0.0

0.5

1.0

Horizontal

GRF

(kN)

Time (s)

2.80 2.85 2.90 2.95

-0.5

0.0

0.5

1.0

Braking

impulse (N.s)

Propulsive

impulse (N.s)

Relative braking

impulse (m/s)

Relative propulsive

impulse (m/s)

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Vertical GRF

2.80 2.85 2.90 2.95

0.0

1.0

2.0

3.0

Time (s)

Vertical

GRF

(kN)

2.80 2.85 2.90 2.95

0.0

1.0

2.0

3.0Vertical

impulse

(N.s)

BW Impulse

Relative

vertical

impulse

(m/s)


Methods

28 male athletes

sprints, 25 m in length

GRF and kinematic data collected at the 16 m

mark

Calculated variables

Relative impulses (mean of three trials)

Sprint velocity (mean of three trials)


Bivariate regressions

Relative braking impulse

Relative propulsive impulse

Relative vertical impulse

Sprint velocity

Sprint velocity

Sprint velocity

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Relative braking impulse (m/s)

-0.15 -0.10 -0.05

Sprint velocity (m/s)

7.0

7.5

8.0

8.5

9.0

r = 0.19

Results: relative braking impulse

Time (s)

2.80 2.85 2.90 2.95

Horizontal GRF (kN)

-0.5

0.0

0.5

1.0


Results: relative propulsive impulse

Relative propulsive impulse (m/s)

0.25 0.35 0.45


7.0

7.5

8.0

8.5

9.0

r = 0.75***

Time (s)

2.80 2.85 2.90 2.95

Horizontal GRF (kN)

-0.5

0.0

0.5

1.0


Relative vertical impulse (m/s)

0.80 1.00 1.20


7.0

7.5

8.0

8.5

9.0

r = 0.41*

Results: relative vertical impulse

Time (s)

2.80 2.85 2.90 2.95

Vertical GRF (kN)

0.0

1.0

2.0

3.0

Relative vertical impulse (m/s)

0.80 1.00 1.20


7.0

7.5

8.0

8.5

9.0

r = 0.49*

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Conclusions

Faster sprinters produced:

– high magnitudes of relative propulsive

impulse

– moderate magnitudes of relative

vertical impulse


Multiple Regression Approach

Relative braking impulse

Relative propulsive impulse

Relative vertical impulse

Sprint velocity


Results: multiple regression

Relative propulsive impulse,

R2 = 0.56, P < 0.001

Relative braking impulse,

R2 = 0.64, P < 0.05

Relative vertical impulse was not significant

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Conclusions revisitedFaster sprinters produced:

– higher magnitudes of relative propulsive

impulse

– moderate magnitudes of relative vertical

impulse

– lower magnitudes of relative braking

impulse


Simulation models

forward dynamics approach to optimize running strategy for individual athletes ???

Such a model is not available

but we applied one to cricket bowling


Cricket(As Explained to a Foreign Visitor)

You have two sides, one out in the field and one in.

Each man that’s in the side that’s in goes out and when he’s out he comes in and the next man goes in until he’s out.

When they are all out the side that’s out comes in and the side that’s been in goes out and tries to get those coming in out.

Sometimes you get men still in and not out.

When both sides have been in and out including the not outs,

That’s the end of the game.

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Played in middle of Oval

Ball can be hit in any direction

Played on Diamond

Ball must be hit between 1st and 3rd Base

Cricket vs Baseball


Fast BowlersMany Techniques, Different Strengths

Tall, Lean, Flexible

Sites of InjuryKnees

Toes

Heel

Back

Ankle

Shoulder


The back injury toll of cricket

Bowling mechanics and back injuries

Spondylolysis, disk abnormalities and muscle injuries (65%) (Elliot, 2000)

Kinematic predisposing factors:- Separation angle (Burnett et al., 1995)

- Counterrotation (Elliott, 2000)

- Shoulder alignment at BFC (Portus et al., 2000)

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Alignments Definition

+-


Data analysis

0

50

100

150

Shoulder Alignment

0

50

100

Angle [°]

Hip Alignment

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3-40

-20

0

20

time [s]

Separation Angle

BFC FFC BLR FTH

CR


Background

Twisting and bending of the spine under high compressive loads at FFC!

Comprehensive biomechanical testing:

Kinematics

Ground reaction forces

� Three dimensional analysis, full body model ...

Question: Do ‘common’ kinematic measures reflect what is happening at the spine?

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Why models?

Motivation: The back problem in Cricket

Approach:

15 segment three dimensional rigid body model in Mathematica

(Wolfram Research Inc., V. 3.0)


Bowling continuum

Statistical relationships of injury and CR

Study

Shoulder

Counter

Rotation

Correlation Factor

Foster et al. (1989);

Elliott et al. (1992) Less than 10° No reported case of lower

lumbar injury in sample.

Burnett et al. (1996) Greater than 20° Progression of disc

degeneration and pain.

Foster et al. (1989);

Elliott et al. (1992) Greater than 30° Increased risk of sustaining disc

abnormality

Foster et al. (1989) Greater than 40° Increased risk of abnormal

radioiogical features of lower

lumbar vertebrae.


Forward solutions model4 athletes analysed so far:

- ad hoc modifications (actions [=torques] around individual joints)

- no GRF included so far Take-off to BFC (pre-delivery leap)

Results:

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AnimationsFRONT Bowler 1

..\..\Projects_NZ\CounterRotationSimulation\Animations\PaulHitchcock\Hitchcock_Shadows_Front.avi

TOP Bowler 1..\..\Projects_NZ\CounterRotationSimulation\Animations\PaulHitchcock\Hitchcock_Shadows_Top_moving.avi

Results :

Reduction of separation angle at BFC from 30 – 40 deg down to 0 – 3 deg

Main modifications: front arm action + front legtrunk side flexion

‘Out of plane’ movements

Qualitative comparison with ‘odd’ solutions of premiere bowlers (who didn’t get injured) matches up


Head well inside front arm

Front arm abducted and flexed

Front leg adducted

Rear foot straight

Hips elevated

Shoulders could be more elevated

Orthodox type of action for very open shoulder alignment to minimise CR

No straight line alignment

Example: Bob Willis at BFC


Ground Reaction ForcesHave been described but no substantial data

base existent (LCS)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0

1

2

3

4

5

6

time [s]

Force [BW]

Force sideways

Force forward

Force vertical

0 0.05 0.1 0.15 0.2 0.25

0

0.5

1

1.5

2

time [s]

Force [BW]

Force sideways

Force forward

Force vertical

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Ground Reaction Forces

Forces LCS

-6

-4

-2

0

2

4

6

8

Fzmax Fymin

Force component

F [BW]

RF striker

FF striker

Forces SCS

-5

-4

-3

-2

-1

0

1

2

FSymin FSxmax

Force component

F [BW]

RF striker

FF striker


Bowling footwear


Players Modifications

Toe slamming into end of shoeCut holes in toes

Relieve PressurePrevent or at least delay losing toe-nail

Important to reduce anterior shift within shoe

•..\NewZealandCricket_070605\Hamish7-2.avi

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Players’Modifications


Needed: an optimized shoe � Result


Acknowledgements

New Zealand Cricket

Sparc New Zealand

Nike

Bioengineering Institute

New Zealand Academy of Sport – North

The Biomechanics Lab Team

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