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240 Victor Cotoros and Emil Budescu where ⎧RSx − Rgx = mpax, ⎪ RSy − Rgy = mpay, ⎪ ⎨ ⎪RSz + Rgz − Gp= mpaz, ⎪ ⎪⎩ g + C( Rs) + C( Gp) = Jp , M M M ε p i j k MC( RS ) = rE× RS= xE0 zE= i( − zER Sy ) + j( − xERSz + zERSx ) + kxER Sy , R R R Sx Sy Sz i j k MC( Gp) = rO× Gp = xO yO − zO = i( − zOGp) + k ( −x OG p ) , 0 −G 0 p i j kk i i MC( F ) = rO× F = xO yO − zO = i( mpazyO + mpay O) + ma ma ma z r p x p y p z + j( −max− maz ) + k( max−may ), p z O p x O p y O p x O yielding the expressions to calculate the unknowns ⎧Rgx = RSx −mpax, ⎪ ⎪ Rgy = RSy −mpay, ⎪ Rgz = Gp− RSy+ mpaz, ⎪ ⎨ Mgx = zERSy + zOGp+ Jpxε px −may p z O −maz p y O , ⎪ ⎪ Mgy = xERSz − zERSx + Jpyε py + max p z O + maz p x O, ⎪ ⎪ ⎩ Mgz =− RSy xE+ GpxO+ Jpzεpz − max p y O + may p x O , For the dynamic balance of the start of support on the tips of fingers (Fig. 6), the equations are given by Eqs. (5) and (6) (7) (4)
Bul. Inst. Polit. Iaşi, t. LVIII (LXII), f. 4, 2012 241 From Eqs. (2), (4) and (6), (7) there can be seen that the unknowns Rgx, Rgy, Rgz and Mgx, Mgy, Mgz are linearly depending on the components of the reaction with the ground Sx R , Sy R and Sz R the weight force of the foot Gp, the linear and angular accelerations of the foot but, at the same time, they are depending on the anthropometrical data of the foot, geometrical position of the contact point between the foot and ground, as well as the angles of dorsal – plantar and inversion – eversion flexions. 4. Conclusions 1. From Eqs. (2), (4) and (6), (7) there can be determined the reaction forces and moments in ankle joint, which are necessary to evaluate the mechanical stresses loading tibia, fibula or astragal. Function of the value of these stresses, there can be analyzed various osteosynthesis techniques and can be made recommendations regarding the gait during bone healing (osteosynthesis) as simultaneous technique of articular rehabilitation. 2. In case of tibial malleolus fracture, the mechanical load of the osteosynthesis assembly during the gait should not exceed the critical values for fracture fragments displacement. Thus, on the basis of reaction forces and moments in ankle, there can be analyzed the distribution of mechanical stresses in tibia and certain features of the gait can be recommended to patient, for a correct healing and articular rehabilitation. REFERENCES Budescu E., Iacob I., Bazele biomecanicii în sport. Ed. Univ. “Al. I. Cuza” Iaşi, 2005. Papilian V., Anatomia omului. Vol. 1, Aparatul locomotor. Ed. Didactică şi Pedagogică, Bucureşti, 1982. Poteraşu V.F., Popescu D., Curs de mecanică teoretică. Vol. 1 şi 2, Ed. Universităţii Tehnice “Gheorghe Asachi”, Iaşi, 1995. ASPECTE PRIVIND BIOMECANICA ARTICULARĂ: ARTICULAŢIA GLEZNEI (Rezumat) Lucrarea prezintă modelul dinamic tridimensional al articulaţiei gleznei, considerând ca mişcări independente flexia dorsală-plantară şi inversia-eversia. Forţele interne care acţionează asupra piciorului au fost reduse în centrul articulaţiei la o forţă şi un moment unice. Folosind analiza dinamică inversă, au fost scrise ecuaţiile de mişcare ale piciorului, pentru patru poziţii distincte ale contactului dintre picior şi sol în timpul mersului. Ecuaţiile pot fi folosite pentru determinarea forţei şi momentului articular din gleznă, fiind necesare valori ale caracteristicilor antropometrice, forţei şi momentului de inerţie şi forţei de contact dintre picior şi sol.
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