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Modeling and Kinetics: Forces and Moments of Force*

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Title: Modeling and Kinetics: Forces and Moments of Force*


1
Modeling and KineticsForces and Moments of
Force
  • Some of the materials used in this lecture are
    derived from
  • Winter, D. A. (1990). Biomechanics and motor
    control of human movement (2nd ed.). New York
    John Wiley Sons.
  • Brown, E. W. , Abani, K. (1985). Kinematics
    and kinetics of the dead lift in adolescent power
    lifters. Medicine and Science in Sports and
    Exercise, 17 (5)554-566.

2
Lecture Topics
  1. Bone-on-bone vs joint reaction forces
  2. Kinetic link-segment model and calculations
  3. Force platform
  4. Interpretation of moment of force curves

3
1. Bone-On-Bone vs. Joint Reaction Force
  • Bone-on-bone forces
  • Actual forces experienced at the articulating
    surfaces
  • Include the effect of muscle contraction (e.g.,
    compressive, possibly shear and torsional forces)
  • Joint reaction forces
  • Forces experienced between segments in a free
    body diagram

4
Bone-On-Bone vs. Joint Reaction Force
  • Case 1
  • Weight of suspended shank and foot 100 N
  • 50 N of force transmitted to each of 2 muscles
  • Bone-on-bone force 0 N
  • Joint reaction force 100 N

5
Bone-On-Bone vs. Joint Reaction Force
  • Case 2
  • Weight of suspended shank and foot 100 N
  • Each of 2 muscles contraction at 85 N
  • Bone-on-bone force 70 N
  • Joint reaction force 100 N

6
2. Kinetic Link-Segment Model and Calculations
7
Because we cannot typically measure internal
forces and torques in a biological system
directly, we depend on indirect measurement of
these parameters using kinematic and
anthropometric data.
  • Force Mass X Acceleration
  • F MA
  • Torque or Moment Moment of Inertia X Angular
    Acceleration
  • T or M I ?

8
If we have a full kinematic description, accurate
anthropometric measures, and external forces we
can calculate the joint reaction forces and the
net muscle moments.?Inverse Solution? insight
into the net summation of all muscle activity at
each joint
9
The validity of any assessment is only as good as
the model itself!!!Requirements accurate
measures of1. segment masses2. centers of
mass3. joint centers4. moments of inertia
10
Relationship among Kinematic, Kinetic, and
Anthropometric Data and the Calculated Forces,
Moments, Energies, and Power Using an Inverse
Solution and a Link-segment Model
11
Assumptions in Using a Link-segment Model
  • each segment has a fixed mass located as a point
    mass at its center of mass
  • joint centers are considered to be hinged or ball
    and socket joints
  • mass moment of inertia of each segment about its
    mass center (or either proximal or distal joints)
    is constant during the movement
  • length of each segment remains constant during
    the movement

12
Equivalence between Anatomical and Link-segment
Model of the Lower Extremity
M1, M2, and M3, considered to be concentrated at
points (center of mass of each segment) length
of each segment and length from proximal and
distal joints to segment center of mass
considered to be fixed moments of inertia I1,
I2, and I3 about each center of mass considered
to be fixed
13
Forces Acting on aLink-segment Model
  • Gravitational Forces
  • Ground Reaction and/or External Forces
  • Muscle and Ligament Forces

Where do we obtain the data for the various
parameters?
14
Steps in Solving Kinetic Link-Segment Problems
  1. Draw free body diagram including forces (joint
    reaction, weight, ground reaction, other
    external), net muscle moments, important
    coordinates (e.g., center of mass of segments,
    ends of segments, center of pressure), segment
    orientation, and linear and angular acceleration

Can you draw a free body diagram?
15
Steps in Solving Kinetic Link-Segment Problems
  1. Draw free body diagram including forces (joint
    reaction, weight, ground reaction, other
    external), net muscle moments, important
    coordinates (e.g., center of mass of segments,
    ends of segments, center of pressure), segment
    orientation, and linear and angular acceleration

16
  • 2. Write all knowns
  • Subject mass
  • Subject height
  • Segment proportion of subject height
  • Segment proportion of mass
  • Segment orientation
  • Segment radius of gyration/segment length
  • Linear and angular accelerations
  • Joint reaction forces
  • Ground reaction and other external forces
  • Net muscle moments
  • Center of pressure
  • Etc.

17
  • Write all unknowns that must be solved
  • Joint reaction forces
  • Net muscle moments
  • Others
  • Decide an order to the solution process
  • Usually distal segments first (distal to
    proximal)
  • Usually reaction forces solved first
  • Usually net muscle moments solved after reaction
    forces
  • Solve problems
  • Determine if results make sense

18
Example Problems from Class Text
19
Example Problem from Class Text (continued)
20
Example Problem from Class Text (continued)
21
Continued
22
Example of Research Models
Brown, E. W. , Abani, K. (1985). Kinematics
and kinetics of the dead lift in adolescent power
lifters. Medicine and Science in Sports and
Exercise, 17 (5)554-566.
23
What is a kinematic model?
24
Kinematic Model
  • describes the linear and angular position and
    motion of segments

25
Example of a 2 Dimensional Single Segment
Kinematic Model and Equations
26
Two Dimensional Human Model
What is the purpose of defining events?
27
What is a kinetic model?
28
Kinetic Model
  • takes into consideration forces and torques
    associated with linear and angular acceleration

29
Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model
30
What is nomenclature?
31
(No Transcript)
32
Purpose of the Kinematic and Kinetic Model
  • to facilitate the documentation of kinematic and
    kinetic characteristics of the dead lift as
    performed by teenage power lifters
  • to determine relationships among these
    characteristics on the basis of information from
    film data and data from body segment parameters

33
Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
34
Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
35
Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
36
Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
37
Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
38
Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
39
Equations for calculating accelerations
40
Equations for calculating forces
41
Equations for calculating moments
42
What are the assumptions used in this research
model?
43
Assumptions Associated with Multiple Segment
Kinematic and Kinetic Model
  • Lifter and bar system are bilaterally symmetrical
    in the sagittal plane (2 dimensional).
  • Body segments could be treated as rigid bars.
  • Dempsters data could be used to represent the
    segment mass proportions and centers of gravity
    locations in the population.
  • Joints, which link the segments together, could
    be treated as a frictionless and pinned.

44
Assumptions Associated with Multiple Segment
Kinematic and Kinetic Model
  • The segment connecting the center of the shoulder
    joint and the center of the neck at the level of
    the seventh cervical vertebrae could be treated
    as a massless segment with defined length which
    transmits force and torque.
  • The location of the center of gravity of the hand
    could be treated as coincident with the center of
    the bar, and no torque was applied to the bar by
    the hands.
  • Acceleration of the ankle joint was equal to zero
    throughout the entire lift.

45
What happens if we change from a dynamic to a
static model?
46
Static Versus Dynamic Model
  • Static Model
  • Considers positions of segments
  • Does not consider linear and angular
    accelerations to move from one position to
    another
  • Assumes that linear an angular acceleration are
    equal to zero
  • Assumes forces and torques associated with
    acceleration are equal to zero
  • Dynamic Model
  • Considers positions of segments
  • Takes linear and angular accelerations into
    account
  • Assumes that linear and angular accelerations may
    not be equal to zero
  • Forces and torques associated with acceleration
    may not equal to zero

47
Static Model
48
How do the equations change when changing from a
dynamic to a static model?
49
(No Transcript)
50
3. Force Platform
  • What is a force platform and how is it used in
    biomechanics?

51
Force Platform (continued)
  • Metal platform in which force transducers (e.g.,
    strain gauge, capacitive, piezoelectric,
    piezoresistive) are embedded
  • Force transducers change electrical resistance in
    proportion to load applied
  • Used to measure common three dimensional force
    (ground reaction force) and moments acting on the
    body

52
Force Platform (continued)
  • Types
  • Metal plate supported by 4 triaxial transducers
    (see figure)
  • Metal plate mounted on central pillar (see figure)

53
Force Platform (continued)
  • What is the center of pressure and how is it used?

54
Force Platform (continued)
  • Center of Pressure (COP)
  • Displacement measure indicating the path of the
    resultant ground reaction force vector on the
    force platform
  • A heel to toe footfall pattern runner
  • B mid-foot foot strike pattern runner

55
Force Platform (continued)
  • Center of Pressure (COP)
  • Equal to the weighted average of the points of
    application of all downward acting forces on the
    force platform

56
Force Platform (continued)
  • Center of Pressure (COP)
  • Used in conjunction with kinematic information
    about the body part (e.g., foot) in contact with
    the force platform

57
Force Platform (continued)
  • Center of Pressure Calculation

58
Force Platform (continued)
  • Problem
  • Fy 200N
  • F00 50N
  • Fx0 50N
  • Fxz 50N
  • F0z 50N
  • X 100cm
  • Z 100cm
  • Guess cop location?

59
(No Transcript)
60
Force Platform (continued)
  • Problem
  • Fy 200N
  • F00 100N
  • Fx0 50N
  • Fxz 25N
  • F0z 25N
  • X 100cm
  • Z 100cm
  • Guess cop location?

61
(No Transcript)
62
Force Platform (continued)
  • Fy interpretation?

63
Force Platform (continued)
  • Fy
  • First peak mass accelerated upward
  • Second peak push off
  • Valley unloading during knee flexion

64
Force Platform (continued)
  • Mz interpretation?

65
Force Platform (continued)
  • Mz
  • value indicitave of cop behind pillar
    (counterclockwise torque)
  • - value cop forward of pillar (clockwise torque)

66
Force Platform (continued)
  • Fx interpretation?

67
Force Platform (continued)
  • Fx
  • First peak - force, push back against foot
  • Second peak push off of foot

68
4. Interpretation of Moment of Force Curves
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