KNR 352:
Quantitative Analysis
in Biomechanics
Dr. Steve McCaw
227B
438-3804
www.castonline.ilstu.edu/mccaw
Topics
• Basic Operations required
• Dealing with vectors
• Review from 282 (Basic Biomechanics)
• Kinematics
• Calculations of basic quantities
• Displacement, velocity, acceleration
• Kinetics
• Calculations
• GRF, CofP, JMF
• Energetics
• Calculations
• Power, Work
Performance
Injury
Performance
Injury
TASK
Task Factors
• Basic Skill
• Walking
• Jumping
• Take off & Landing
• Running
• Take off & Landing
• What joint actions are occurring?
• What muscles are active?
• What are the risks?
Task Factors
• Basic Skill
• Complex Task
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Throw
Assembly Task
Curl up
Hitting a baseball
What joint actions are occurring?
What muscles are active?
What are the risks?
Performance
Injury
TASK
Environment
Environmental Factors
• Weather/field/floor conditions
• Friction====>stability, tissue loads
Environmental Factors
• Weather/field/floor conditions
• Gravity
• space travel & platforms
Environmental Factors
• Weather/field/floor conditions
• Gravity
• Open/closed task
• dynamic vs. static environment
Environmental Factors
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•
•
•
Weather/field/floor conditions
Gravity
Open/closed task
Rules on the game/of the job
• # of players
• field dimensions
• workplace layout
• temporal constraints
Performance
Injury
TASK
Individual
Environment
Individual Factors
• Cognitive ability
Individual Factors
• Cognitive ability
• Anthropometrics
Individual Factors
• Cognitive ability
• Anthropometrics
• Psychological state
Individual Factors
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•
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Cognitive ability
Anthropometrics
Psychological state
Fitness & Health
Skill level
Performance
Injury
TASK
Individual
Environment
Performance
Injury
TASK
Individual
Environment
Performance
Injury
TASK
Individual
Environment
Modulated by force: described by mechanics
Every structure that participates in the
movement of the body does so according to
physical and physiological principles.
Hamilton & Luttgens, Kinesiology:
Scientific basis of Human Motion,
10th edition.
Mechanics
influence of force on bodies
• Biomechanics: force on biological
organisms
• biomechanics of fluids
• circulation (lung, blood, artery)
Mechanics
influence of force on bodies
• Biomechanics: force on biological
organisms
• biomechanics of fluids
• biomechanics of deformable solids
• bones, ligaments, tendons
Mechanics
influence of force on bodies
• Biomechanics: force on biological
organisms
• biomechanics of fluids
• biomechanics of deformable solids
• biomechanics of rigid bodies
• body as “rigid links” at “frictionless hinges”
Rigid
Bodies
Statics
No accleration Present
Dynamics
Acceleration Present
Kinematics
motion patterns / motion descriptions
Kinetics
study of forces causing motion
Mechanics
• Kinematics
• description of
pattern of motion
• how far
• how fast
• how consistent
• Kinetics
Mechanics
• Kinematics
• description of
pattern of motion
• how far
• how fast
• how consistent
• temporal aspects
• durations
• sequencing
• Kinetics
Mechanics
• Kinematics
• description of
pattern of motion
• how far
• how fast
• how consistent
• temporal aspects
• durations
• sequencing
• Kinetics
• study of forces that
cause motion
Mechanics
• Kinematics
• description of
pattern of motion
• how far
• how fast
• how consistent
• temporal aspects
• durations
• sequencing
• Kinetics
• study of forces that
cause motion
•
•
•
•
magnitude
direction
line of action
point of application
F=ma
F=ma
Force CAUSES acceleration
F=ma
Force CAUSES acceleration
Force CAUSES injury
Fundamental Concepts for
Biomechanical Analysis
• Units of Measure: ISU (International system
of Units, ie the Metric System)
Fundamental Concepts for
Biomechanical Analysis
• Units of Measure: ISU (International system
of Units, ie the Metric System)
• Base Units
• length: meter (m)
• mass: gram (g)
• time: second (s)
Motion
• Change in position of a body with
respect to time
Motion
• Change in position of a body with
respect to time
• quantify POSITION
• location in 3D space: P
• three reference axes: X, Y, Z
o
• Cartesian system: axes at 90 (orthogonal)
ISB Convention: 2D
Y
Progression
0,0
X
ISB Convention: 3D
Vertical
Y
Medio-Lateral
Z
Anterior-Posterior
0,0,0
X
Scalars and Vectors
• Scalar quantity
• described by
magnitude alone
•
•
•
•
mass
volume
distance
speed
• Vector quantity
• requires description of
magnitude and
direction
•
•
•
•
•
•
force
momentum
impulse
displacement
velocity
acceleration
Parallelogram Law for
Addition of Vectors
• Sum of two vectors (resultant, R) equals the
diagonal of the parallelogram with sides
equal to the two vectors.
• Draw on board, tail to tail
• Triangle Rule: tip to tail
• commutative: R = A + B = B + A
• Polygon Rule: extends to 3 or more vectors
Review: Basic Trigonometry
• Right angle Triangle
• naming conventions
• Pythagorean Theorem
• Trig functions
• Sine, Cosine, Tangent (slope)
• Inverse Tangent
Coordinate Systems
• Rectangular or Cartesian Coordinate System
• P = Px + Py
• Polar coordinate system
• P = r and Ө
• Polar to rectangular
• (use SOH and CAH)
• Rectangular to Polar
• use Pythagorean Thereom and arctan
Examples: P to R: 270 N @ 23 degrees
R to P: Fv= 1300 N & FA/P = 100 N
Adding Force (vectors) by
Summing Components
• Force: magnitude & direction need to be
calculated
Adding Force (vectors) by
Summing Components
• Force 1 = 50 N at -45 degrees
• Force 2 = 30 N at 90 degrees
Solve for Resultant
Adding Force (vectors) by
Summing Components
•
•
•
•
Force 1 = 50 N at -45 degrees
Force 2 = 30 N at 90 degrees
Force 3 = 75 N at 28 degrees
Force 4 = 15 N horizontal & 13 N vertical
Solve for Resultant
New & Useful Information
Radian
– the angle created by the arc on a circle with the
•
length of the radius of the circle (~ 57.3 degrees)
Arc length = 1 radius
Calculate the resultant force from
Coracobrachialis and Pectoralis Major
Coracobrachialis = 1200 N, PM = 1700 N
Effect of tension
development on angle of
muscle insertion and
muscle activation level.
Given:
Muscle force = 90 N /cm2 x-sectional area
X-sectional area = 4 cm2
Muscle Ө relaxed = 50°
Muscle Ө active = 85°
Required: 150 N force along tendon
Calculate: Percentage of max muscle force
developed to produce the 150 N of force.
Additional Problems
Available
from web
Motion
• Change in position of a body with
respect to time
• quantify POSITION
• quantify TIME
Motion-capture
systems
Motion Capture
• Pre 1985: Film
• RedLake Locam: 500 fps
• ~ $125 roll (film + developing)
• Working in the “dark”
• Record
• Send for processing
• Hope it all turns out ok.
• All black, badly focused, missed critical event
• Manual Digitizing
Motion Capture
• Pre 1985: Film
• Post 1985: High speed video
•
•
•
•
Immediate feedback
Easy to adjust
Reduced cost (once system paid for)
Auto Digitizing Available
Example Video
Example Video
Reflective Markers
Motion Capture
• Pre 1985: Film
• Post 1985: High speed video
• Post 1990: Active Marker Systems
•
•
•
•
No visible recording of performer
Tracks x,y coordinates of markers only
FAST.
$$$$
Principles of Recording
1. Maximize image size within field of view.
Field of view: rectangular area recorded
Field Height
Field Width
Field Depth
Photographic Dimensions
Principles of Recording
1. Maximize image size within field of view.
Optimize calibrated volume.
Volume: Height x Width x Depth.
Principles of Recording
1. Optimize calibrated volume
2. Ensure always within field of view
Principles of Recording
1. Optimize calibrated volume
2. Ensure always within field of view Stay
within calibrated volume
1. Landing
2. Run
3. Jump
Principles of Recording
1. Optimize calibrated volume
2. Stay within calibrated volume
3. Ensure adequate pre and post recording
Torry’s 16 mm thesis recording
1. Landing: air time, post max knee (max extension)
2. Lifting (bench & squat): before descent, post
ascent
Video Tapes are Cheap
Principles of Recording
1. Optimize calibrated volume
2. Stay within calibrated volume
3. Ensure adequate pre and post recording
Torry’s 16 mm thesis recording Capture
adequate pre-initial and post-final activity
1. Landing: air time, post max knee (max extension)
2. Lifting (bench & squat): before descent, post
ascent
Server space is Cheap
Principles of Recording
1. Optimize calibrated volume
2. Stay within calibrated volume
3. Ensure adequate pre and post recording
Capture adequate pre-initial and post-final
activity
Important for video processing
1. Smoothing process
Principles of Recording
1. Optimize calibrated volume
2. Stay within calibrated volume
3. Capture adequate pre-initial and post-final
activity
4. Use as slow a video speed as feasible
• Standard video: 30 frames per second
• High speed: 60, 120 2000 fps
Lo speed = Improved quality of recording
Hi speed = capture more frames of activity
Principles of Recording
1. Optimize calibrated volume
2. Stay within calibrated volume
3. Capture adequate pre-initial and post-final
activity
4. Use as slow a video speed as feasible Set
at 200 fps.
Ensure an even multiple of EMG or GRF (??)
Principles of Recording
1. Optimize calibrated volume
2. Stay within calibrated volume
3. Capture adequate pre-initial and post-final
activity
4. Set at 200 fps.
5. Make shutter speed as short as possible
Too short: not enough light
Too long: “comets” rather than round markers
Principles of Recording
1. Optimize calibrated volume
2. Stay within calibrated volume
3. Capture adequate pre-initial and post-final
activity
4. Set at 200 fps.
5. Make shutter speed as short as possible
Too short: not enough light
Too long: “comets” rather than round markers
Principles of Recording
1. Optimize calibrated volume
2. Stay within calibrated volume
3. Capture adequate pre-initial and post-final
activity
4. Set at 200 fps.
5. Make shutter speed as short as possible
6. Depth of field
1. Is 2D an appropriate assumption?
2. ISU Lab: record 3D even if 2D is of interest
Principles of Recording
1. Optimize calibrated volume
2. Stay within calibrated volume
3. Capture adequate pre-initial and post-final
activity
4. Set at 200 fps.
5. Make shutter speed as short as possible
6. Depth of field
1. Is 2D an appropriate assumption?
2. ISU Lab: record 3D even if 2D is of interest
Principles of Recording
1. Optimize calibrated volume
2. Stay within calibrated volume
3. Capture adequate pre-initial and post-final
activity
4. Set at 200 fps.
Pilot Test
Calibration
• Real Life recorded on Video
• Scale video dimensions to real life
• 2D: set up camera, record known length in
plane of action
• Perpendicular alignment is critical
• Scaling factor
• Digitize recording of ruler
• Sf = actual length (m) / digitized length (arbitrary units)
Calibration
• Real Life recorded on Video
• Scale video dimensions to real life
• 2D: set up camera, record known length in
plane of action
• 3D: set up cameras, record calibration Wand
and calibration triangle on Force Platform.
Marker Selection
• Where to put the
reflective markers?
• What are you
measuring?
• Segments & joints
of interest
• Lower Body?
• Upper Body?
• Trunk?
Stick figure of landing in sagittal plane
Marker Selection
• Where to put the
reflective markers?
• What are you
measuring?
• Segments & joints
of interest
• Lower Body?
• Upper Body?
• Trunk?
Stick figure of landing in sagittal plane
Marker Selection
• Where to put the
reflective markers?
• What are you
looking at?
• Landmarks defining
segment endpoints
Marker Selection
• Where to put the
reflective markers?
• What are you
looking at?
• Landmarks defining
segment endpoints
ISU Lab
•All landings on force platform
•Spatially synchronized within
calibration grid
•No need for markers on floor
Motion
• Change in position of a body with
respect to time
• quantify POSITION
• quantify TIME
Linear Motion: translation
rectilinear
curvilnear
Motion
• Change in position of a body with
respect to time
• quantify POSITION
• quantify TIME
Linear Motion: translation
rectilinear: straight line
curvilnear: curved line (parabolic)
Motion
• Change in position of a body with
respect to time
• quantify POSITION
• quantify TIME
Linear Motion
Angular Motion: rotation
Motion
• Change in position of a body with
respect to time
• quantify POSITION
• quantify TIME
Linear Motion
Angular Motion
General motion
Motion
• Change in position of a body with
respect to time
• quantify POSITION: from motion tracker
• quantify TIME  ?
Linear Motion
Angular Motion
General motion
Time in Video Analysis
• 200 images per second
• 1 second / 200 frames = 0.005 seconds
between frames
Motion
• Position: location in space
• Displacement (distance)
• change of position
Motion
• Position: location in space
• Displacement (distance)
• change of position
• Velocity (speed)
• change of position with respect to time
• This is motion
Motion
• Position: location in space
• Displacement (distance)
• change of position
• Velocity (speed)
• change of position with respect to time
• This is motion
• Acceleration
• change of velocity = change of motion
Force
• Push or pull exerted by one body on another
body that causes or tends to cause a change
in motion of each body
Force
• Push or pull exerted by one body on another
body that causes or tends to cause a change
in motion of each body
• a derived unit in mechanics
• body: mass
• change in motion: acceleration
• new location in space and time
1 newton = 1 N = 1 kg • m / s / s
Mass
• Quantifies linear inertia
• resistance of a body to a change in linear
motion
• Anthropometry
• measure of body dimensions
• ht, wt, girth, segment length, density
• Body Segment Parameters
• mass, center of mass (gravity), radius of gyration