Question

2.) The mechanism shown has link lengths as follows: OA-30 mm, BC-90 mm, AD-168 mm, AB- 1120 mm. Crank OA rotates 100 rad/s CCW. Find: DATA 90 a. Velocities of points A, B, D. b. Angular velocities of ABD and BC REQ'D

Answer 1

Given The mechanism shown has link lengths as, OA = 30 mm BC = 90 mm AD = 168 mm AB = 1120 mm Crank OA rotates 100 rad/s CCW \r\n By the relative velocity method V_OA = V_A = (OA)V_b = 30 times 100 v_a = 3000 mm/sec velocity polygon (a) By the sine rule v_a/sin 90 = v_ba/sin 30 = v_cb/sin 60 implies v_ba = v_a sin (30) & v_cb = v_a sin (60) = (3000) times 0.5 = 3000 times 0.866 v_ba = 1500 mm/sec v_cb = 2598.076 \r\n implies v_ba = v_b - v_d implies v_b = v_a + v_bc = 3000 + 2598.076 = 5598.076 mm/sec v_c = v_b implies v_ba = v_b - v_a v_b = v_ba + v_a = 1500 + 3000 v_b = 4500 mm/sec By scale ratio v_ab/v_ab = AB/AD = v_ad = (v_ab/AB)(AD) = 1500/1120 (1120 + 168) = 1.339 (1288) = 1724.6 mm/s = 1725 mm/s \r\n implies v_d = v_ad + v_a