Question

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 B 12 in 10 in 10 rad/s VA 6 in Ilve 6 in** 16 in - 6 in

Answer 1

5 red la Given that WAB VA = Vo = (9 We know VB (AB) X WAB: وامت:0 [v=rw] velocity of point. 'B? (12)2 + (0)2)x5 [UB - 67.08203.in/sed Draw Velocity triangle ( Not to scale) Anton वव 1 90- 90- Ore 90-2 [ velocity diagram) 6 tan (0,12 0 - 63:43| Q = 59.03] 125] tan (&) 10 6 tan (B) B:7:125 2. 16 B с. A Configuration (equivalent) diagłam to show angle fig 2

Applying sine Rule in figure ③ Vdc since+B) Voc Sin (180 -- Vab sin (x-6) Vic = sin(180 - 59.03 - 63.43.) x67.08203 Sin (59 03-7. 125) 71 921 واحن Wbc = Vbc 71.921 √(16)2 + (222 4.4 603 had S Bc Angular Velocity of Ber WBC -4.460.3 rad S Vdc sin (63.43 +7:125) 67.08 203 Sin ( 59.03 - 7.125) Vdc = 80.376 in s Woc Vdc 30.376 co)2 + (6) 2 Angular Velocity of Da' wpc = 6:8921 sred's Ans © To find Wr. we know that it will be equal to gear periphery Velocity VR (G) x6.8921 VR. 241-3531 ins) () = 91W - And