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) B 12 in 10 in 10 rad/s VA 6 in IVR 6 in 16 in - 6 in --

Answer 1

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- Ans: - Given: Wag = 5 rad/s. NA = Vg =0 - * (a) The velocity of point B: -VB = VA + WAR XYBIA = 0 + 8 WART R x C 6i + 12 h 2 5² x ( 67 + 12 72 = |- 60 ? + 30 7 mcs : Resulterant, Vq = V 60 ²+ 30² =/67.08 in's (6 The angular velouty of BC and DC: - U = UB + Wo be a rub = (-601 +30f) + WBct lx ( 16 ? - 29 ) = (-60 î 1307) + (20g ? + 160 BL Å = (2W BC-60) î +(30+16 Wood ĵ - Vo = V t Web a roll (2 WB -80 ↑ + (30 +16 WBC û + WDCA (6) - 10 ) = (2 COBL-60 H10 Woc) i +(30 + 16 W BE G Woden to (2.), (1) Since VD=0, 2 00 BL-60+10 Woc=0 30+16 BL + 6 Woc=0 Multiplying by -8 and adding o 480 - 16 O BE +16 WBC to wo bc =0 510 74 obc=0 6.8919 rad is 8o W Dc = 0 30 => wr Dc=

From (1), 2W BL-60 + 10x 6.8919 0 2 WBC = 60-1086.8919 & W Be=-8.919 2 =%-4.4595 rad/s (counter clockwise) (c) vertical relocity up of the rack! and pinion: - Up = W =6.8919 x 6 = 41,3514 mois in's Cupwards). IDE x r