Download Lecture XII

Modeling and Kinetics:
Forces and Moments of Force*
*Some of the materials used in this lecture are derived from:
1.
Winter, D. A. (1990). Biomechanics and motor control of human movement (2nd
ed.). New York: John Wiley & Sons.
2.
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)554566.
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
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
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 =
0N
– Joint reaction force =
100 N
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
2. Kinetic Link-Segment Model
and Calculations
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 
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
The validity of any assessment is
only as good as the model itself!!!
Requirements: accurate measures of
1. segment masses
2. centers of mass
3. joint centers
4. moments of inertia
Relationship among Kinematic, Kinetic, and Anthropometric
Data and the Calculated Forces, Moments, Energies, and
Power Using an Inverse Solution and a Link-segment Model
Assumptions in Using a Linksegment 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
Equivalence between Anatomical and Linksegment 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
Forces Acting on a
Link-segment Model
• Gravitational Forces
• Ground Reaction and/or
External Forces
• Muscle and Ligament Forces
Where do we obtain the
data for the various
parameters?
Steps in Solving Kinetic LinkSegment 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?
Steps in Solving Kinetic LinkSegment 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
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.
3. Write all unknowns that must be solved:
a. Joint reaction forces
b. Net muscle moments
c. Others
4. Decide an order to the solution process:
a. Usually distal segments first (distal to
proximal)
b. Usually reaction forces solved first
c. Usually net muscle moments solved after
reaction forces
5. Solve problems
6. Determine if results make sense
Example
Problems
from Class
Text
Example Problem from Class Text
(continued)
Example Problem from Class Text
(continued)
Continued
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.
What is a kinematic model?
Kinematic Model
describes the linear and angular
position and motion of segments
Example of a 2 Dimensional Single Segment
Kinematic Model and Equations:
Two Dimensional Human Model
What is the purpose of defining events?
What is a kinetic model?
Kinetic Model
takes into consideration forces and
torques associated with linear and
angular acceleration
Example of a
2 Dimensional
Multiple
Segment
Kinematic and
Kinetic Model
What is nomenclature?
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
Example of a
2 Dimensional
Multiple Segment
Kinematic and
Kinetic Model Close Up View of
Segments:
Example of a
2 Dimensional
Multiple
Segment
Kinematic and
Kinetic Model Close Up View
of Segments:
Example of a
2 Dimensional
Multiple
Segment
Kinematic and
Kinetic Model
Close Up View
of Segments:
Example of a
2 Dimensional
Multiple
Segment
Kinematic and
Kinetic Model Close Up View
of Segments:
Example of a
2 Dimensional
Multiple
Segment
Kinematic and
Kinetic Model Close Up View
of Segments:
Example of a
2 Dimensional
Multiple
Segment
Kinematic and
Kinetic Model Close Up View
of Segments:
Equations for
calculating
accelerations:
Equations for
calculating
forces:
Equations for
calculating
moments:
What are the assumptions used in
this research model?
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.
• Dempster’s 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.
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.
What happens if we change from
a dynamic to a static model?
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
Static
Model
How do the equations change
when changing from a dynamic to
a static model?
3. Force Platform
What is a force platform and how is it
used in biomechanics?
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
Force Platform (continued)
• Types
– Metal plate supported by 4 triaxial transducers (see figure)
– Metal plate mounted on central pillar (see figure)
Force Platform (continued)
What is the center of pressure and how is it
used?
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
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
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
Force Platform (continued)
• Center of
Pressure
Calculation
X
x
2
 F  F   F  F 
x0
xz
00
0z
1 



Fy
Z
z
2
 F  F   F  F 
0z
xz
00
x0
1 



Fy
Force Platform (continued)
• Problem
Fy =200N
F00 = 50N
Fx0 = 50N
Fxz = 50N
F0z = 50N
X= 100cm
Z= 100cm
Guess cop
location?
X
x
2
 F  F   F  F 
x0
xz
00
0z
1 



Fy
Z
z
2
 F  F   F  F 
0z
xz
00
x0
1 



Fy
X
x
2
 F  F   F  F 
x0
xz
00
0z
1 



Fy
100  50 N  50 N   50 N  50 N 
1


2 
200 N
x  50cm
x
Z
z
2
 F  F   F  F 
0z
xz
00
x0
1 



Fy
100  50 N  50 N   50 N  50 N 
1


2 
200 N
z  50cm
z
Force Platform (continued)
• Problem
Fy =200N
F00 = 100N
Fx0 = 50N
Fxz = 25N
F0z = 25N
X= 100cm
Z= 100cm
Guess cop
location?
X
x
2
 F  F   F  F 
x0
xz
00
0z
1 



Fy
Z
z
2
 F  F   F  F 
0z
xz
00
x0
1 



Fy
X
x
2
 F  F   F  F 
x0
xz
00
0z
1 



Fy
100  50 N  25N   100 N  25N 
1


2 
200 N
x  37.5cm
x
Z
z
2
 F  F   F  F 
0z
xz
00
x0
1 



Fy
100  25N  25N   100 N  50 N 
1


2 
200 N
z  25cm
z
Force Platform (continued)
• Fy interpretation?
Force Platform (continued)
• Fy
– First peak – mass
accelerated upward
– Second peak – push
off
– Valley – unloading
during knee flexion
Force Platform (continued)
• Mz
interpretation?
Force Platform (continued)
• Mz
– + value indicitave
of cop behind pillar
(counterclockwise
torque)
– - value cop forward
of pillar (clockwise
torque)
Force Platform (continued)
• Fx interpretation?
Force Platform (continued)
• Fx
– First peak; force, push back
against foot
– Second peak;
push off of foot
4. Interpretation of Moment of Force Curves