Question

8. In the Figure below, bar AB rotates with a clockwise angular velocity of 5 rad/s. Points A and D are fixed (VA=Vp=0). Find: a) The velocity of point B b) The angular velocity of BC and DC c) The vertical velocity VR of the rack in the rack-and-pinion gear (35 points) 12 in 10 in 10 rad/s NAAM ||VR mm 6 in 16 in 6 in

Answer 1

Given data ! - WAB s radls ((w) Solution of la) volocity volocity of Point B. Vo = WAB X IBIA -SÂ x 10.5 i + i) fus B = -2.5 its Hence ; lis) = (5)+42072 = 5.59 fils (Ans) So Magnitude of veloutj of point B is 5.59 ft/s Part(3) angular veb city of BC and DC Vc = VB + WBC X VIB = (s î -2.5f) + WBL Â x 1133 ? – 0.167 ſ) Vc = = (5+0.167 Wor) î + 1-25 + 1-33 WBC) F write expression for the velocity at D. Vc VD + Wia x Voic = 0 + -UCD Â x l-os î+0.833 Î WID Ve +0.833^ ît as Wed Í from canation 0 and 2 % compare Coefficients of î and f. s40.167 WBC = 0.83344, IWBC = 610-83360-5) (2) -2.5 + 1.33 WBC = +0.5 WCD 1.33 WBC = 2.5 tous WCD (3

Sojving equation @ and 3 Wco 6.92 radls Ans) WBC - 4.48 gadis Part (c) The vertical Velouty (VR) 6.4 the Year VR = Valeo VR = (0.5) (6-92) = 3.46 ftis - (Ang)
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