Question

Given: Figure 3, r, = 6.0 cm, r,-ro3C= 6.0 cm, r,-5.0 cm, r5-ro = 9.0cmO2 10°, co2- 80 rpm CW. Find: Draw vector loops. Write the vectors loop equations in vector form, then polar form and then in Cartesian form. Underline scalar variables that change with time. Solve the position equations for r4, Ogr, θ. where r is the distance of B2 from O3 and rs is the distance of D from O3. Derive and solve the velocity equations for cos, dr4/dt, cos, drs/dt. 3. B, on 2 B3 on 3 Figure 3

Answer 1

W_2 = 2 pi N_2 pi N_2/60 = 2 times pi times 80/60 = 8.3775 rad/s r_2 = 6 cm, r_O_3 B = 2, r_1 e^I theta_2 = 10 degree theta_3 = 2 theta_1 = 90 degree therefore Vector loop eqn, R^bar_1 + R^bar_2 = R^bar_3 r_1 e^I theta 1 + r_2e^I theta_2 = r_03/e^I theta_3 real pant 5 cos 90 + 6 cos 10 = r_o 3B cos theta_3 = > 6 cos 10 = r_o_3B cos theta_3 imaginary part, 5 sin 90 + 6 cos 10 = r_03B sin theta_3 5.90884 = r_03B cos theta_3 & 6.04188 r_03 B = 71.4188 r_o3B = 8.450g cm & cos theta_3 = 5.90884/8.4509 = > theta_3 = 45.6378 degree Now deviating equation (1) wrt . t, r_1, theta, r_2 are constants r_03B = r_4 therefore 0 + r_2 w_2 I e^I 10 degree = 8.4509 times w_3 I e^145.6378 + dr_4/dt e^I 45.6378 real part -50.2655 sin 10 = -8.4509 w_3 sin 45.6378 + dr_4/dt cos 45.6378