buletinul institutului politehnic din iaşi - Universitatea Tehnică ...

234 Victor Cotoros and Emil Budescu
where
for the dynamic balance of the initial contact on the heel (Fig. 4),
⎧RSx
− Rgx = mpax, ⎪
⎪RSy
− Rgy = mpay, ⎪
⎨
⎪RSz
+ Rgz − Gp= mpaz, ⎪
i
⎪⎩ + ( R ) + ( G ) + ( F ) = J ,
M M M M ε p
g C s C p C p
i j k
M ( R ) = r × R = x 0 − z = i( zR ) + j( −xR− zR ) + k xR ,
C S A S A A A Sy A Sz A Sx A Sy
R R R
Sx Sy Sz
i j k
M ( G ) = r × G = x y − z = i( − z G ) + k( −x
G ) ,
C p O p O O O O p O p
0 −G
0
i j k
p
i i
M ( F ) = r × F = x y − z = i(
m a y + m a z ) +
C O O O O p z O p y O
ma ma ma
p x p y p z
+ j( −max − maz ) + k(
max −may
).
p z O p x O p y O p x O
mp, Jp – the mass and respectively the mass inertia moment of the foot, εp –
angular acceleration of the foot, F i – inertia force of the foot, yielding the
expressions to calculate the unknowns:
⎧ Rgx = RSx −mpa,
⎪
⎪ xRgy = RSy −mpay,
⎪
⎪ Rgz =− RSz + Gp+ mpa, ⎨
y
⎪Mgx
=− zARSy + zOGp+ Jpxε px −may p z O −maz
p y O,
⎪
Mgy = RSx yA+ RSz xA+ Jpyε py + max p z O + maz p x O,
⎪
⎪
⎪⎩ Mgy =− RSyxA+ GpxO+ Jpzε pz − max p y O + may p x O.
For the dynamic balance of total support of the foot on the ground (Fig. 5),
(1)
(2)