PhD Fekete - SZIE version - 2.2 - Szent István Egyetem

Results
4. RESULTS
4.1. Results regarding the analytical-kinetical model
4.1.1. Effect of the center of gravity – Standard squat model
Since the required parameters and variables are available, the analytical-kinetical model of
subsection 3.2 can be evaluated and compared to the results of other authors. However, let us
first investigate the effect of the horizontally moving center of gravity on the standard squat
model described by Mason et al. [Mason et al., 2008] from subsection 2.2.
As it has been proven by other authors [Cohen et al., 2001, Mason et al., 2008], the
patellofemoral forces directly depend on the net knee moment in case of the standard squat.
Therefore, it is interesting to see how this moment depends on the position of the center of
gravity. As it was mentioned earlier, the standard squat model is based on the following three
assumptions:
1. During squatting the line of action of the center of gravity does not change its position
horizontally,
2. The femur and tibia are symmetrically positioned (their rotation during the movement
is equivalent),
3. The net knee moment can be derived as a simple function of the flexion angle
(Eq. (2.4) and Eq. (2.5)).
The movement of the center of gravity has been described empirically as a linear function of the
flexion angle (Eq. (3.28) and Eq. (3.29)). In subsection 3.3, an equation has been created
(Eq. (3.37)) to define the moment arm for the net knee moment. This equation, as an
amendment, includes the horizontal movement of the center of gravity (λ 3 ) and the rotation of
the tibia (γ).
Let us substitute Eq. (3.37) into Eq. (2.5) in order to determine the net knee moment with
horizontally moving center of gravity:
M
k
( α)
= 0.5⋅
BW ⋅Ys
( α)
= 0.5⋅
BW ⋅l30 ⋅ λ3(
α)
⋅sin(
α − γ )
(4.1)
After analytically deriving this net knee moment with the moving center of gravity, and
considering that the femur and tibia are not symmetrically positioned, a new calculation was
carried out. In Figure 4.1, two net knee moments are compared: the original net knee moment
without the effect of the horizontally moving center of gravity, and a modified (non-standard)
net knee moment described in Eq. (4.1).
– 119 –