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= VD = 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 GP VR 6 in 16 in 6 in-

Answer 1

we draw a velocity diagram for finding the velocities.

step 1: draw a line (ab) perpendicular to link AB from the fix point a of 5cm as per our scale.

step 2: now draw a line perpendicular to link BC from point b and also draw a line perpendicular to link CD from fixpoint d. intersection of this two line is a point c.

measure the line and multiplay by scale and do the calculatioan as per below picture to get answers.
Scale 1cm= 2in B. y lorad/s AB=13.6 in BC= 16.2 in CD = 11.6 in Wbu= lo sails You = Wbux(BA) 10x13-6=136 in/S Velocity diagram Scales 1cm= 27.2 in/s t TYCb a, Voce Ved= dC = 5.9 x 27.2 Ved = 160.48 in's Vcb=bC= 5.3x27.2=1144.16 in /s

→ In The Velocity of Bpint B. (Vou) Vba = Wbu x(BA) = 10 x 13.6 bu = 136 inls - angular Velaity of link B2 W bc = Vebx BL = 144.16 16.2 18.8988 raas - angular velocity of link e D Wed = Ved 160.48 CD led = 13.8345 Juals! Vertical Velocity of Juck VR. Rack is conected with gear of D due to more bes angular motion of ultimal Hy Rack link CD. Wed=13-8345 radle Wat => VR Wod x6 = 13.8345 x6 =183.00 in/s)