Kinetics (continued)
Dr. Moran
EXS 587
April 12, 2006
Course Outline
• From Static to Dynamic
• What changes?
• Measurement of Force
• What devices to use?
• Operating Principles of the Force Plate
• Combined Force Plate and Kinematic Data
• Lab Experience
• Collecting Force Plate Data
Inverse Dynamics
External Forces
Distal Forces + Moments
Motion
Newton-Euler
Equations
Proximal
Forces + Moments
Standing Still
What forces are active?
• When standing still your
weight vector is seeking
to accelerate you
downward at 9.81 m/s2.
• The person does NOT
accelerate downward
because the ground
exerts an equal and
opposite force upward
W
Fg
W + Fg = 0
Fg  ground reaction force
What if it is not a static situation?
• ∑Fx = max
• ∑Fy = may
• ∑M = Ioα
• Example #3 (con’t from last lecture)
From the data collected during the swing of the foot,
calculate the muscle moment and reaction forces at the
ankle. The subject’s mass was 80 kg and the anklemetatarsal length was 20.0 cm. Use Table 3.1 to calculate
the inertial characteristics of the foot.
•
•
•
•
Table 3.1 Calculations
m = 0.0145 * 80 = 1.16 kg
po = 0.475 * 0.20 = 0.095 m
Io = 1.16(0.095) = 0.0105 kg ∙ m2
Example #3 (continued)
• Measured Kinematics
Ry
M
– Accelerations of Center of Mass
Rx
• Ax = 9.07 m/s
• Ay = -6.62 m/s2
• α = 21.69 rad/s
– Distances From Ankle Joint to Center of Mass
– What are we solving for?
FW
Solution: see handout
• Ankle Joint Reaction Force
• Muscle Moment about Ankle Joint
Example #4
• For the same instant in time, calculate the
muscle moments and reaction forces at
the knee joint. The leg segment is 43.5
cm long.
Ways to Measure Force
• Transducers
• Force Platforms
• Pressure Distribution Sensors
• Internally applied force sensors
» Buckle transducers
» Fiber Optics
• Isokinetic Devices
Force Transducers
Operating Principles
• Resistive (piezoresistive) Elements
• Deformation (very small, micro) causes an
electrical change in resistance that is measured as
a voltage change
• Based upon semiconductive material (i.e. silicon)
• Piezoelectric Elements
• Naturally occurring mineral that produces electric
charge in response to deformation
Force Platforms
•
•
Most common transducer used in
biomechanics
Two types
(1) strain-gauge: less expensive, good for static
measurement, less of a range
(2) Piezoelectric: more expensive, highfrequency response
Force Platforms
• Any single 3-D force vector applied to the
force plate can be described by 9
quantities:
(1) 3 Forces: Fx, Fy, Fz
(2) Force Vector Location: x, y, z
(3) 3 Orthogonal Moments: Mx, My, Mz
Force Platform Outputs: Vertical
Fy1
Fy4
Fy2
Fy3
y
z
X
Fy = Fy1 + Fy2 + Fy3 + Fy4
Force Platform Outputs: Shear Forces
y
Fx4
Fx1
z
X
Fx3
Fx2
Fx = (Fx1 + Fx4) + (Fx2 + Fx3)
Force Platform Outputs: Shear Forces
Fz4
Fz1
y
z
X
Fz3
Fz = (Fz1 + Fz2) + (Fz3 + Fz4)
Fz2
Force Platform Calculations:
The Center of Pressure (no shear forces)
Fy1
Fy4
Fy
Fy2
Fy3
y
CPz
z
CPx
X
2a
Measured Reaction Moments:
Mx = (Fy2 + Fy3)*b - (Fy1 + Fy4)*b
Thus:
Mz = (Fy3 + Fy4)*a – (Fy1 + Fy2)*a
Cpx = Mz/Fy
Calculated Reaction Moments:
Mx = -(Fy*Cpz)
Mz = -(-Fy*Cpx)
Cpz = -Mx/Fy
2b
Force Platform Calculations:
Effect of Origin Location with Shear Forces
y
Fx
d
x
Additional Shear Force Contribution to Reaction Moment Mz = -Fx*d
Y
Fz
d
Z
Additional Shear Force Contribution to Reaction Moment Mx = Fz*d
Final Center of Pressure
Calculation:
• CPx = (Mz-Fx*d)/Fy
• CPz = -(Mz+Fz*d)/Fy
Center of Pressure
• Misconceptions:
– COP gives no insight into the pressure at any of the
contact points under the foot
» During stance both your heel and the ball of feet in contact
with ground
» Use a pressure measurement system to get insight on the
pressure underneath all contact areas
» Tekscan
– COP relative to the foot can not be determined from
force plate output alone. You need to know where the
foot is placed relative to the force plate CS
Internal vs External Joint Moments
• Internal  produced from soft tissues (muscles, ligaments, etc)
• External  produced about a joint by some force external to
the body (ex. GRF, weight of segment)
W
Data Synchonization
Kinetic & Kinematic Data
• Kinetic and kinematic come from different
sources
• Same event MUST be captured at the
same time
• Examples
» Vertical channel of Force Plate triggers a LED
• Sampling frequencies must be at an even multiple
Research Article (handout)
• Influence of a custom foot orthotic
intervention on lower extremity dynamics
in healthy runners
» MacLean et al. (2006)