Title: Modeling and Kinetics: Forces and Moments of Force*
1Modeling 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.
2Lecture Topics
- Bone-on-bone vs joint reaction forces
- Kinetic link-segment model and calculations
- Force platform
- Interpretation of moment of force curves
31. 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
4Bone-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
5Bone-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
62. Kinetic Link-Segment Model and Calculations
7Because 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 ?
8If 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
9The 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
10Relationship among Kinematic, Kinetic, and
Anthropometric Data and the Calculated Forces,
Moments, Energies, and Power Using an Inverse
Solution and a Link-segment Model
11Assumptions 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
12Equivalence 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
13Forces 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?
14Steps in Solving Kinetic Link-Segment Problems
- 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?
15Steps in Solving Kinetic Link-Segment Problems
- 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
18Example Problems from Class Text
19Example Problem from Class Text (continued)
20Example Problem from Class Text (continued)
21Continued
22Example 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.
23What is a kinematic model?
24Kinematic Model
- describes the linear and angular position and
motion of segments
25Example of a 2 Dimensional Single Segment
Kinematic Model and Equations
26Two Dimensional Human Model
What is the purpose of defining events?
27What is a kinetic model?
28Kinetic Model
- takes into consideration forces and torques
associated with linear and angular acceleration
29Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model
30What is nomenclature?
31(No Transcript)
32Purpose 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
33Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
34Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
35Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
36Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
37Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
38Example of a2 Dimensional Multiple Segment
Kinematic and Kinetic Model -Close Up View of
Segments
39Equations for calculating accelerations
40Equations for calculating forces
41Equations for calculating moments
42What are the assumptions used in this research
model?
43Assumptions 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.
44Assumptions 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.
45What happens if we change from a dynamic to a
static model?
46Static 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
47Static Model
48How do the equations change when changing from a
dynamic to a static model?
49(No Transcript)
503. Force Platform
- What is a force platform and how is it used in
biomechanics?
51Force 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
52Force Platform (continued)
- Types
- Metal plate supported by 4 triaxial transducers
(see figure) - Metal plate mounted on central pillar (see figure)
53Force Platform (continued)
- What is the center of pressure and how is it used?
54Force 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
55Force 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
56Force 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
57Force Platform (continued)
- Center of Pressure Calculation
58Force Platform (continued)
- Problem
- Fy 200N
- F00 50N
- Fx0 50N
- Fxz 50N
- F0z 50N
- X 100cm
- Z 100cm
- Guess cop location?
59(No Transcript)
60Force Platform (continued)
- Problem
- Fy 200N
- F00 100N
- Fx0 50N
- Fxz 25N
- F0z 25N
- X 100cm
- Z 100cm
- Guess cop location?
61(No Transcript)
62Force Platform (continued)
63Force Platform (continued)
- Fy
- First peak mass accelerated upward
- Second peak push off
- Valley unloading during knee flexion
64Force Platform (continued)
65Force Platform (continued)
- Mz
- value indicitave of cop behind pillar
(counterclockwise torque) - - value cop forward of pillar (clockwise torque)
66Force Platform (continued)
67Force Platform (continued)
- Fx
- First peak - force, push back against foot
- Second peak push off of foot
684. Interpretation of Moment of Force Curves