PhD Fekete - SZIE version - 2.2 - Szent István Egyetem

Literature review
They applied the following simplifications:
Figure 2.53. Numerical model [Ling et al., 1997]
a) The model is planar, created in the sagittal plane,
b) Ligaments are one-dimensional bodies without mass,
c) Ligaments can change in length, but only in case of tension,
d) No penetration of the tibia or femur is allowed,
e) No friction is assumed.
As an incompleteness of the earlier models, the authors appointed that the articular surfaces of
the femur are often assumed circular. To improve this problem, they used fourth order and root
functions to describe the connecting surfaces (denoted by f i parameter). The authors determined
the sliding-rolling ratio by calculating the arc lengths travelled on the surface of the tibia and
femur between each simulation step:
s =
upper
∫
lower
2
⎛ dfi
⎞
1 + ⎜ ⎟ dx
(2.12)
⎝ dx ⎠
If i = 1, then it is the curve of the tibia, if i = 2, then it is the curve of the femur. The slidingrolling
ratio is defined as the difference between the larger distance (s l ) and the smaller distance
(s s ) travelled on the femur and tibia over the smaller of the two arc lengths travelled (s s ).
sliding
s − s
s
l s
/ rolling =
(2.13)
The problem with this definition is that e.g.: s l equals to 6 mm and s s equals to 2 mm, then if we
calculate the sliding-rolling ratio from Eq. (2.13), we obtain 2. By knowing s l and s s , then by
common sense it is obvious that the sliding-rolling ratio is distributed as 66% sliding and 33%
of rolling. However, from the above-mentioned formula (Eq. (2.13)), we can only obtain the
number of two, which grants no clear physical interpretation about the ratio.
s
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