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 6 in [VR 6 in- 16 in 6 in

Answer 1

Answer -

As no specific method is asked , this problem is solved by Graphical method.

If any query , please ask in a comment section

Solution : - By Graphical Method CONFIGURATION DIAGRAM SCALE: 1cm = 4 in B A lo rad/sec A no D 8.6cm Vcd V CB 7.6cm ad VBA b 6.7cm VELOCITY DIAGRAM SCALE: Ich = 20 in/sec

A] The Velocity of Point B : o = tans (2) = 63.43° sino = 12 AB ri AB = 12 12 sino = = 13.42 in sin63.43 VBA = Vo = ABX WBA = 13.42 x 10 VB = 134.2 rain/sec Ans B] The angular velocity of BC & DC : - To calculate WEB and Wed draw velocity Diagram,

To draw velocity diagram :- One velocity ; VBA VBA is known = 134.2 in's : Decide scale by using UBA. Scale - Ich = 20 in/sec Therefore rector ab = 134-2 = 6.7 cm 20 Now; To calculate length BC & CD B BIT xa C A 022 D x ac tano = Bze Bx'-xx' = 12-10 2c xc 16 Oi tan ( (+) = 7.12° !

2 BC= Bx sino, = 16.12 inch sin 7.12 Now; tan Oz cy YD 10 6 O2 = tant (0) 59.03 CD = 10 cy sin da = 11.66 in sin 59.03 Now: Results from from Velocity Velocity Diagram V co = Vector cb X Scale (7.6 cm) x (20 in/sec) VcB 152 in /sec e Vco = Vector cd x Scale 8.6 x 20 VCD = 172 in /sec

" Angular Velocity of CB :- WEB Vcs 152 9.43 CB 16.12 WEB = 9.43 rad/sec - Ang Angular Velocity of co :- Wed VCD - 172 11.66 = 14.75 co Wed = 14.75 rad /sec - Ang c] The velocity of Rack cve) VR WCD X Radius of pinion - 14.75 X 6 VR = 88.51 inch / sec - Ans