Question

V. At the instant shown roller B on link AB is moving a circular path of radius 85 mm at angular position of 75 deg while slider A is moving in a linear path at the rates of 1.5 m/s and 2.7 m/s/s. If the length of AB is 240 mm, determine the angular velocities of (a) of roller B and (b) of link AB in rad/s aA αω

Answer 1

V_A = 1.5 m Vertical-bar Phi a_A = 2.7 m Vertical-bar Phi^2 V_A^vector = 1.5 L degrees V_B^vector = V_B cos 15 degrees L degrees - V_B sin 15 degrees j 0.966 V_B i - 0.259 V_B j. V_A^vector = V_B^vector + wkx r_A/B^vector: r_A/B^vector = 0.226 I + 0.0821 j Therefore 1.5 i = (0.966 V_B i - 0.259 V_B j) + wkx (0.226 i + 0.0821 j) = (0.966 V_B i - 0.259 V_B j) + 0.226 w_j - 0.0821 w_i \r\n 1.5 i = (0.966 V_B - 0.0821 w) i + (0.226 w - 0.259 V_B) j i rightarrow 1.5 = 0.966 V_B - 0.0821 w equation (1) j rightarrow 0 = 0.226 w - 0.259 V_B equation (2) Solving (1) and (2) w = 1.97 rad Vertical-bar Phi V_B = 1.72 m Vertical-bar Phi Acceleration by B: - Normal component (directed along B0) a_eta = V_B^2/OB = (1.72)^2/0.085 = 34.8 m/sec and tangential component directed along V_B: at now a_B^vector = a_A^vector - w^2 r_B/A^vector + alpha Vertical-bar alpha r_B/A^vector a_B^vector