buletinul institutului politehnic din iaşi - Universitatea Tehnică ...

232 Victor Cotoros and Emil Budescu
iii) a new force denoted with F * , is considered in ankle joint, as being the
resultant of all the forces exerted by muscles, tendons, ligaments and bones in
contact, like previous F, but translated in the articulation;
iv) for system balance, that is, to cancel the new introduced force F * , the
force -F * is considered, which has the same application point, the same direction
but inverse sense with respect to force F * ;
v) the couple of forces (F, - F * ) is representing a muscular moment Mg
acting on the ankle joint. The muscular moment Mg takes into account both
agonist and antagonist muscles;
vi) the resultant force F * , with the application point at the rotation center
of the ankle, is decomposed on the directions Ox, Oy and Oz , into R , R
and respectively R , for the 3D structural model.
g z
6
x5
x2
5
z4
x1
4
x2
ϕ
1
x1
z5
ϕ 4
8'
D
8
ϕ 4
A
3
x4
O 1
z1 z2
ϕ
1
Fig. 2 – Definition of geometrical variable parameters (ϕ1 and ϕ4).
C
z2
O 2
B
y5
2
7
7'
1
y2
y1
y2
g x g y
Using this method of force reducing, all the forces are reduced to a
unique resultant force and resultant moment into a certain point. This is the
preliminary stage for writing and solving the equations of static or dynamic
balance, for the biomechanical system shank-ankle-foot. In Fig. 3 there is
presented, in successive images, the method of force reducing for the ankle. In
this figure, the notations represent: F are the forces in the muscles acting
m1,2,3..n
on the foot; F are the forces acting in tendons; Fo is the force acting in
t 1,2,3..n
bone structures (tibia, fibula and talus), including the joint ligaments; RSxyz
are
the reaction forces of the ground on the foot along the directions Ox, Oy,Oz; GP is the weight force of the foot; F is the resultant of all forces previously