Question

K7. Parameters of the mechanism: C,3 T1 2 cm, R14 cm, r22 cm, R2 4 cm, I3 12 cm, R3 16 cm. Equation for the angle of pulley 2: O3-2(t2-3t) rad. Find: 5 01, 81, ac, as at the instant tı 2 sec V4,

V4 velocity , w1 angular velocity, Ac acceleration at point c, a5 acceleration, E1 angular acceleration

Answer 1

4'3-2(t2-3t)rad

$\dot \psi= (4t-6r)ad/s$

$\ddot \psi= 4rad/s^2$

$v_4 = r_3\dot \psi_3$

4- 0.12b

velocity of 4:

0.12 (4t-6)m/s

Point C has two components of acceleration:

Tangential:

$a_{c_t} = R_3\ddot \psi$

0.64m/s2 0.16 * 4 ac,

Radial:

$a_{c_N} = R_3\dot \psi^2$

$\frac{\dot \psi}{w_2} = \frac{R_2}{R_3}$

$\frac{4t-6}{w_2} = \frac{4}{16}$

angular velocity of 2: $\Rightarrow w_2 = 4*(4t-6)rad/s$

2 T2 W1 Ri

4 * (4-6) au 1

angular velocity of 1: $\Rightarrow w_1 = 8*(4t-6)rad/s$

$\varepsilon _1 = \dot w_1$

angular acceleration of 1: $\Rightarrow \varepsilon _1 = 32rad/s^2$

$a_5 = r_1\varepsilon _1$

acceleration of 5 :
a50.64m