Todays Plan

1
Todays Plan

• Kinematics Article Discussion
• Questions on Kinematics Assignment
• Begin Kinetics Today (Lecture 8)
• Kinetics Assignment Posted

2
Kinetics

• ESS 5306
• Lecture 8
• Readings from Winter, Chapter 4

3
Part 1 Models, Equations Measurement

• Reading Winter Chapter 4 (4.0 - 4.2.4)

4
Basic Outline

• Force Transducers and Force Plates
• COP versus COM
• Pressure Measurement Systems
• Link-Segment Models
• Forces acting on the segments
• Joint Reaction Forces and Bone on Bone Forces
• Basic Equations and the Free Body Diagram

5
Force Measuring Instruments

• Force platform
• Accelerometer
• F ma
• Pressure sensitive devices
• Switch mats
• Insoles
• Isokinetic Dynamometer
• Other general force transducers

6
Force Platform System

• 3 Major Components
• Transducer
• Signal Modifiers
• Amplifier
• Filter
• Signal Output

Force Plate Signal
Amplifier
A/D Converter
Computer
Storage (disk)
Output
7
Types of Platforms

• Based on type of transducer
• Spring
• F -k ?x
• Strain Gauge
• Current (I) Voltage (V) / Resistance (R)
• ? deformation determined relative to ? R
• ?I is calibrated to the load
• Ex. AMTI (multiple strain gauges), Wheatstone
  Bridge
• Piezoelectric (quartz) Crystal
• Crystal generates a voltage when deformed
• Voltage is proportional to the load
• Ex. Kistler (multiple pillar stacks of 3
  orthogonally cut crystals)

8
Transducer Performance

• AMTI ORG-5-2000 and ORG-7-2000
• Output Range 10V
• Loading Range
• Fx and Fy 4000 N (900 lbs)
• Fz 10,000 N (2,250 lbs)

9
Common Force RangesMaximum Expected Values

• Running
• Fz 35 N/kg
• 75kg 35 N/kg 2625 N
• 3.5 BW
• Fy 5 N/kg
• 75kg 5 N/kg 375 N
• 0.5 BW
• Fx 2 N/kg
• 75kg 2 N/kg 150 N
• 0.2 BW

• Landing
• Fz 150 N/kg (vertical)
• 75kg 150 N/kg 11,250 N
• 15 BW
• Fy 35 N/kg
• 75kg 35 N/kg 2625 N
• 3.5 BW
• Fx 25 N/kg
• 75kg 25 N/kg 1875 N
• 2.5 BW

10
Transducer Performance

• Reliability and Validity
• Precision
• Deviation of measured value from mean value
• Random Error
• Accuracy
• Deviation of the mean value from the true value
• Systematic Error

11
Calibration

• Calibration Cycle
• Known weights are sequentially applied and
  removed
• Sensitivity
• How closely does output represent input?
• Linearity
• How closely does calibration curve approximate a
  straight line?
• Hysteresis
• Difference in output when input is applied in
  ascending and then descending order.

12
Other Performance Considerations

• Crosstalk
• Force applied to one channel appears as a signal
  on another channel
• Natural Frequency
• Frequency at which a self-sustaining internal
  vibration occurs
• Ringing
• NF for AMTI is 400 Hz
• Temperature Range
• Overheating can damage the transducers
• Caution when used in direct sunlight and warm
  environments
• Measuring Range
• Number of mechanical units per volt of output
  (e.g. 500 N/V)
• Set this value to maximize the 10V range
• Improve signal to noise ratio
• Reduce influence of FSO error

13
Cautions and Concerns

• Noisy Data
• Plate contacting an external object
• Loose mounting bolts
• Floor vibration
• Assure proper mounting
• Test in clear area
• Care for Cables
• Turn off power when inserting cables
• Dont step on, stand on, or pinch cables
• Care for pins dont bend
• Ground pins by touching with screwdriver

14
Software Settings

• Zero the Channels
• Prevent voltage offset bias

15
Sampling Frequency

• 100 Hz?
• 500 Hz?
• 2000 Hz?
• Consider
• What variables do I want?
• What is the greatest frequency in the movement I
  want to capture? (Get this from the lit.)
• Do I want to capture impact?

16
Information Output - Data

• Direct
• Orthogonal ground reaction forces (GRF) X, Y Z
• Time
• Derived
• Resultant GRF and Force Plate Moments about X, Y
  Z
• Resultant Joint Moments
• Computed (or otherwise determined) Variables
• Force Magnitude (peak, mean, _at_ event or time)
• Temporal Information (e.g. time of peak force)
• Integrals (e.g. Impulse area under curve)
• Derivatives (e.g. Loading rate slope of loading
  curve)
• Center of Pressure (coordinate data off plate)

17
Direct versus Derived Information

• () indicates direction of applied force
• (-) indicates direction of GRF
• Use right hand rule to determine direction of
  Moment

18
Resultant GRF (derived)

• Magnitude R v Fx2 Fy2 Fz2
• Resultant of the 3 reaction force vectors
• Angles
• ?yz tan-1(y/z)
• ?xz tan-1(x/z)
• ?xy tan-1(x/y)

19
Force Magnitudes and Time
20
Derivatives and Integrals
21
Normalizing Force Values

• Comparison among subjects
• GRFNorm GRF / kg of Body Mass N/kg
• GRFNorm GRF / kg of Body Weight N/N BW
• Other (e.g. N / momentum)

22
Normalizing Temporal Variables

• Converting Time to of cycle
• Ti (Ti / Ttotal) 100
• Where Ttotal (Tn T1)

23
Center of Pressure

• In force platform coordinate system
• COPx (My Fx dz) / Fz
• COPy (Mx Fy dz) / Fz
• Weighted average of the forces
• dz 3.9 cm (Ex. for our AMTI platforms)

24
COP

• In kinematic coordinate system (markers)
• COPy COPy dy

25
Pressure Measuring Systems

• Insole and Plate Systems
• Pedar
• RScan
• Tekscan (F-Scan)
• Others
• Instrumented sheets or matrix of many cells
  each of which deforms and sends a signal
  proportional to the pressure applied.
• Allows for the tracking of the center of pressure
  within the base of support during static (quiet
  stance) or dynamic (walking, running) tasks.

26
Example F-Scan
27
Pressure Systems

• Advantages
• COP tracking within BOS
• Useful research and clinical tool (e.g. elderly,
  diabetic, amputees)
• Allows simultaneous collection of ground reaction
  force and foot pressure data (i.e., using force
  plate and insoles)
• Disadvantages
• Sample rate
• Resolution
• Accuracy

28
Recall the Rigid Body Model
29
Rigid Body Model

• Assumptions
• Segment has fixed mass located at a point mass at
  its com location.
• Location of com is fixed for any given segment
• Joints are hinge or ball and socket
• Mass moment of inertia about com (or ends) is
  constant
• Length of each segment remains constant during
  movement
• Marker movement represents movement of skeleton
• Sowhat are we ignoring with each assumption?

30
Free Body Diagrams

• Segments of interest (sticks)
• Axis of rotation
• Forces with directions (arrows)
• Moment arms (- distances from axis to force)

31
A Free Body Diagram

• More parts
• More complicated.

32
Valid FBD

• A valid diagram requires
• Segment masses
• Segment COM position
• Joint center location
• Segment moments of inertia
• Relevant angles of segments (orientations)
• Why?
• To determine forces acting on each segment, as
  well as joint reaction forces and bone on bone
  forces

33
Forces Acting on Links

• Gravity
• Acts on segment masses through com position
• External Forces
• Ground Reaction Forces (GRF)
• Internal Forces
• Muscle and Ligament Forces
• Recall contact and non-contact forces
• Reaction Force, Inertia, Friction,

34
Joint Reaction Force

• Encompasses forces acting on joint due to gravity
  and other external forces (e.g. weight of limbs,
  body weight)
• Does not include muscle forces (e.g. tensile
  forces, compressive forces from muscle action)
• Resultant of the compressive and shear forces
  acting at the joint

35
Bone on Bone Forces

• Actual cumulative forces seen across
  articulating surfaces including muscle activity
• Active compressive forces due to muscle and
  Joint Reaction Forces (which dont include
  muscle action)

36
Free Body Diagram
37
Link Segment Information

• Known Information
• ax, ay - Acceleration of segment com
• ? Angle of segment in plane of movement
• a Angular acceleration of segment in plane of
  movement
• Fxd, Fyd Reaction forces acting at distal end
  of segment
• Determined from a priori knowledge of proximal
  forces on distal segment
• Md Net muscle moment acting at distal end
• Determined from analysis of the proximal muscle
  acting on distal segment
• Also need to know moment arms (d-)
• Distance from joint center to line of force
  application
• Unknown Information
• Fxp, Fyp Reaction forces acting at proximal
  joint
• Mp Net muscle moment acting on segment at
  proximal end/joint

38
Link Segment Equations

• S Fx S max
• Fxp Fxd max
• S Fy S may
• Fyp Fyd mg may
• Recall that g is -9.81 m/s2
• S M I0a
• Moment about center of mass

39
Statics versus Dynamics

• Static Analysis (2D example)
• Acceleration is zero
• Dynamic Analysis
• Acceleration is not zero and is significant
• Force and thus accelerations are changing over
  time

SFx 0 SFy 0
Horizontal Component Vertical Component
SF 0
SF Smiai
40
Example 1

• Person standing on 1 foot on a force plate
• GRF is acting 4 cm anterior from ankle joint
• Subject mass is 60 kg
• Foot mass is 0.9 kg
• Center of mass location of foot is 6 cm anterior
  from ankle
• Calculate the joint reaction forces and net
  muscle moment at the ankle

41
Example 2

• Swing phase of gait (foot)
• Subject mass is 80 kg
• Ankle-metatarsal length is 20 cm
• Calculate the muscle moment and reaction forces
  at the ankle

42
Part 1 Summary

• Force Measurement
• Center of Pressure
• Free Body Diagram
• Reaction Forces
• Resultant Joint Moments

43
Part 2Force Interpretation and Applications

• Reading Winter, Chapter 4

44
Force Interpretation

• Force Plates
• Pressure Insoles
• Strain Gauges
• Others
• Force data open for interpretation

45
Force Interpretation

• Force measured in three orthogonal planes
• Anterior-Posterior
• Medio-Lateral
• Vertical
• What information can we infer from each of these
  measures individually?
• What information can be inferred from the
  combined measures?

46
Kinetic Parameters

• Force Plate Data (raw or filtered)
• Time
• GRF (force data) - ML, AP, VGRF
• Parameters (measured, processed, calculated)
• Peak forces (3 planes, mean peaks)
• Ground reaction force vector (used in RJM
  calculation)
• Loading Rate, Propulsion Rate (peak or mean)
• Impulse
• Landing velocity, landing height, jump height
• COP (e.g. sway, velocity, jerk)
• Phase durations (e.g. braking, propulsion,
  decent, recovery)
• Energy (potential and kinetic)
• Others

47
Effects of a Force Over Time

• Mechanical Impulse (Ns)
• Product of force and time change
• Recall finding area under force (grf) curve?
  Each box has area F?t.
• Impulse-Momentum Relationship

F?t
F?t mvfinal mvinitial
48
Momentum

• Momentum (?)
• The product of the mass of the object and the
  change in velocity
• ?? m(vf vi)
• ? m?v
• Since F ma
• then F m(?v/ ?t)
• soF (m?v)/?t
• and soF ??/?t

49
Momentum

• Quantity of Motion (momentum)
• Linear ? m v
• Angular H I ?
• In human movement, most changes in momentum occur
  by changing velocity.
• Four Basic Goals For Altering Momentum
• Increase momentum
• Decrease momentum
• Transfer momentum to another object or body part.
• Manipulate momentum for performance outcome
  (e.g., change speed of rotation)

50
Impulse

• So, to change momentum, apply an impulse.
• Linear Impulse F ?t
• Angular Impulse M ?t
• Examples
• Running GRF curves (vertical, A-P)
• Jumping
• Catching a ball
• Landing
• Impulse Strategies

51
Impulse-Momentum

• Concept
• To create a change in momentum an impulse must be
  applied.
• Momentum is the quantity of motion
• Impulse is a force applied over a period of time.
  
• Formula F?t m ?v
• Relevance to Movement
• Humans exert impulse to either increase or
  decrease momentum. Different force-time
  strategies can be used depending on the desired
  outcome.

52
Impulse - Momentum

• Recall
• Impulse F?t
• F m a
• a ?v / ?t
• Impulse
• F ?t
• m a ?t
• m (?v/?t) ?t
• m ?v
• m ?v
• m (vf vi)
• ?Momentum

53
Locomotion
54
Running GRF Curves
Vertical GRF
Antero-Posterior GRF
55
Breaking and Propulsion
56
Jumping GRF Curve
F ?t m ?v So, ?v (F ?t) / m
57
Impulse Strategies

• To absorb shock
• m v force time

• To improve performance
• m v force time
• m v force time
• m v force time

58
Applications to Joint Load and Injury

• Influence of loading rate and impulse
• Loading Rate (What influences loading rate?)
• Impulse (What influences impulse?)
• Significance of Time
• So which is more critical with regard to injury?
• Large peak force realized in a very short period
  of time has greatest potential for joint injury.

59
Loading Rate and Impulse
60
Pressure

• Ratio of the force applied to the area over which
  it is applied
• Ex. Shoulder pads and other protective equipment
  are designed to distribute the force of impact
  over a large surface area, and thus reduce the
  pressure applied to the tissues.

61
Walking versus Running
62
Soft and Stiff Landings
63
Calculating Jump Height from VGRF
64
Example Calculation

• Given
• Computed impulse of landing is 500 Ns
• Subject bodyweight is 600 N
• Determine the height from which the subject
  dropped
• Steps
• Set up equation
• Determine landing velocity (vf)
• Determine height (ht)

65
Additional Concepts of Momentum

• Conservation of Linear Momentum
• Collisions
• Formula m1v1 m2v2 msysvsys
• Example Colliding hockey players
• Conservation of Angular Momentum
• Spinning activities
• Manipulating I to change ?
• Example Figure skater
• Transfer of Momentum
• Throwing, kicking, striking activities
• Kinematic chain
• Example Bull Whip, Force dissipation

66
Part 2 Summary

• Force Interpretation
• Impulse and Momentum
• Impact and Injury
• Applications to running, jumping and landing
• Application of impulse-momentum relation and
  loading rate
• Kinematic and Kinetic Analyses

67
For next time

• Kinetics and Kinematics Applications
• Work, Power and Energy (part 3)
• Gait Analysis Video
• Discuss final project topics, article critiques
  and presentations.

68
Part 3Analyzing Kinematic and Kinetic
DataWork, Power Energy

• Reading Winter, Chapter 4

69
Types of Mechanical Analyses

• Effects of forces at an instant in time.
• Static and dynamic applications of instantaneous
  forces.
• Effect of forces applied over a period of time.
• Impulse, momentum, and their relations.
• Effect of forces applied over a distance.
• Analysis without Newton
• Work, power, and energy applications.

70
Mechanical Work Power

• Concepts
• Work The ability to change the amount of energy
  in a system. When work is performed, the state of
  the system or the environment is changed.
• Power The rate at which work is performed.
• Formulas
• Work (joules) W F d
• Power (Watts) P W t F v
• Relevance to Movement
• Moving the body or lifting an object requires
  work. The ability to do work is related to
  strength. The ability to exert power is related
  to both strength and speed.

71
Mechanical Work

• Application Provides a method for quantifying
  mechanical effort.
• Example Which is more difficult?
• Lifting a 100 N weight 1 m vertically, or
• Sliding a 100 N weight 1 m horizontally?
• Example Standardizing workload for two weight
  lifters.

72
Mechanical Power

• Application Provides a method for quantifying
  performance abilities.
• Example Power Continuum
• Example Quantifying jumping power using
  regression equations.
• Example Quantifying jumping power using GRF.
• Max power is generated by an individual at about
  1/3 max load or 1/3 the max velocity.

73
Power Continuum
74
Calculating Power Regression Equations

• Lewis (1974) -- modified
• P (4.9)½ mass g (jump height)½
• Units are Watts. Mass in kg, jump height in m, g
  9.81 m/s2.
• Underestimates peak power by as much as 73.
• Harman et al. (1991)
• P 61.9 jump height 36.0 mass 1822
• Units are Watts. Mass in kg, jump height in cm.
• Underestimates peak power by as much as 9.9.
• Sayers et al. (1999)
• P 60.7 SJ height 45.3 mass 2055
• Units are Watts. Mass in kg, squat jump height in
  cm.
• Error approximately 3 depending upon jump type
  and gender.

75
Power from Jumping VGRF
F t v m v F t m Power (Fpk
FBW) v
76
Mechanical Energy

• Concept
• Energy is the ability to do work. W ?E
• Two types of mechanical energy are kinetic and
  potential. Two types of potential are
  gravitational and strain.
• Formulas
• KE ½ m v2
• GPE m g h
• SPE ½ k x2
• Where, k stiffness constant x deformation
• Relevance to Movement
• KE and PE are inversely related and are
  determined by velocity and position of the body.
• Relevant for projectiles and stretching of
  tissues or materials.

77
Conservation of Energy
ET (top) ET (bottom) mgh ½mv2 Uses h v2
2g v (2gh)½
Recall v2 u2 2as where u 0 m/s and a g
-9.81 m/s2
78
Impact

• Concept
• Extremely large force acting over an extremely
  small time interval (lt 50 ms).
• Formula e is the coefficient of restitution.
• e vseparation vimpact
• eest (hbounce hdrop)½ when one object is the
  ground.
• Relevance to Movement
• The outcome of the impact depends upon
  impulse-momentum factors and strain energy
  return.
• Factors that affect e material properties,
  temperature, air pressure (e.g., ball).

79
A Theory of Injury

• Injury Mechanism?
• Large forces (grf)
• Trabecular Micro-fracture
• Bone Remodeling
• Resultant Stiffening of the bone
• Increased stress on Articular Cartilage
• Cartilage Breakdown
• Joint Degeneration
• Radin et al., (1972) J Bone Jt Surg, 54B723-728

80
Theory of Injury

• Osteoarthritis
• Affects 50 of population
• Present in 85 of 70 to 79 year olds
• Theory to be tested
• Magnitude of force impact peak is directly
  related to overuse injuries in running and
  degeneration in joints
• Question
• How can such a theory be tested?
• One way Examine the Function of the Shoe
• Especially shock absorption

81
Examination of GRF - Running

• Center of Pressure
• Point on the force plate that the resultant force
  originates
• Foot Strike Index
• Rear Foot Striker (rear 1/3 of foot)
• Mid-foot Striker (middle 1/3 of foot)
• Fore Foot Striker (front 1/3 of foot)
• Rarer

82
Examination of GRF - Running

• VGRF is the most common variable studied
• The largest component is often the first peak
• 1st peak is much larger in rear foot strikers
  than mid-foot strikers.

83
Examination of GRF Running

• Loading Rate
• Gradient (slope) of force trace to first peak
• Some Previous Research Findings
• Dickinson et al., (1985) J Biomech, 18415-422
• 2 main findings
• Barefoot impact peak and loading rate are higher
  than shod
• Harder shoe sole resulted in higher loading rate
• Nigg and Bahlsen (1988) Int J Biomech, 4205-219
• 1 main finding
• Harder shoe sole was not associated with higher
  loading rates

84
Examination of GRF - Jumping

• Vertical force trace of a vertical jump
• Stationary phase
• Counter-movement phase
• Time of take off
• Flight phase
• Landing

85
Counter-movement Vertical Jump
86
Further Calculation

• Impulse
• Product of force and time
• Given data ground reaction force, impulse is the
  area under the force-time curve
• Easily measured using a computer
• Impulse Force x Time
• Impulse Change in Momentum
• Momentum Mass x Velocity
• Thus,
• Impulse Mass x (Final Velocity - Initial
  Velocity)
• Or
• Impulse is proportional to the Change in Velocity

87
Impulse - Momentum

• Recall
• Impulse F dt
• F m a
• a ?v / ?t
• Impulse
• F ?t
• m a ?t
• m (?v/?t) ?t
• m ?v
• m ?v
• m (vf vi)
• ?Momentum

88
Impulse - Momentum

• Positive Impulse
• Increasing Velocity
• Negative Impulse
• Decreasing Velocity
• If max speed is the goal
• Apply a large force for as long as possible
• Unfortunately the human body is not capable of
  applying this maxim directly so we compromise.

89
Inverse Dynamics

• Method of determining forces from measured motion
• Kinematic Data Kinetic Data

• Video
• Free Body Diagrams (Stick Figures)
• Anthropometry (segment masses, com)
• Acceleration (2nd derivative of displacement
  from marker data)

• Joint Reaction Forces
• Linear Forces (on COM and Segments)
• Resultant Joint Moments

90
Combining Kinetics and Kinematics

• Rarely use only kinetic (force) analysis
• Exceptions
• Postural sway (COP trajectory)
• Strength assessment (hand grip, force production)
• Pressure assessment (COP, prosthesis testing)
• Materials testing (Coefficient of restitution,
  HIC)
• Usually collect kinematic and kinetic data
  simultaneously

91
Kinematic and Kinetic Analysis

• Gait Analysis
• Force plates and motion analysis
• And usually EMG
• Landing and Jumping (general locomotion)
• Materials Testing and Impact Testing
• Stiffness
• Surface testing (damping, energy dissipation and
  return, deformation)
• Object trajectory and impact force estimation
  (soccer heading)
• Helmet testing
• Crash testing

92
Time

• Analog versus Digital
• Streaming
• Clocked or Counted
• Sampled kinematic and kinetic data are by default
  digital data
• Sampling Frequency data points collected per
  second
• Hz (cycles per second)
• So there is a time component to nearly all data
  sets.

93
Temporal Parameters

• Timing of Events during task performance
• e.g. heel strike, time of peak force or max knee
  flexion
• Phase Durations
• Durations of phases of the motion
• e.g. countermovement, propulsion, landing,
  descent, recovery, swing phase of gait
• Sequence or Patterns of Events or Movement
• e.g. patterns of hip, knee and ankle motion,
  sequence of ankle, knee and hip flexion during
  toe off, patterns of peak resultant joint moments
  during landing
• Loading, Unloading, or Transition Rates
• e.g. Angular velocities and accelerations,
  Loading or unloading rates (d/dt Fz), Weight
  Transfer (sit to stand, or 2 plate landings).

94
Inverse Dynamics

• Possible to compute the position (kinematics) of
  the center of mass from the ground reaction force
  data.
• Acceleration
• F m a F m (a g)
• a F / m a (F m g) / m
• Velocity
• Impulse m (vf vi)
• If the initial or final velocity is known then
  the given mass and impulse velocity can be
  computed
• Displacement
• Integration of the velocity will give
  displacement
• Where integration is the reverse of the
  differentiation process

95
Part 3 Summary

• Work, Power and Energy
• Impact and Injury
• Application of impulse-momentum relation and
  loading rate
• Kinematic and Kinetic Analyses
• Temporal Aspects
• Inverse Dynamics

96
For next time

• Research Applications
• Gait Analysis Video
• Discuss final project (lit review) topics