1 Crank DC is connected to link CB which is in turn connecte

1) Crank DC is connected to link CB which is in turn connected to crank BA. A gear is attached to crank BA which engages rack G. If crank DC is turning at a constant angular velocity of 10 rad s in the clockwise direction as shown, find: a) The velocity of the rack, G. b) The acceleration of the rack, G. Note: The rack, G, is constrained so it can only move vertically (up and down). 12 in 10 in 6 in 16 in 6 in

Solution

from the figure

Length of link CD = Underroot(36+144)

CD = 13.416 in

Velocity of link CD = r x w

since Velocity at point B and C will be same

Vcd = 13.416 x 10 = 134.16 in/sec

Vc = Vb

Distance of AB

lab = Underroot(36+100) = 11.66 in

angular velocity of AB = Wab = 134.16/11.66

Wab= 11.50 rad/sec

Velocity of rack = Wab x radius of gear

Vrack = 11.50 x 6 = 69 inch/sec

Assume time as 10 sec

acceleration for 10 sec

Acc(rack)10 = 69/10 =6.9 inch/sec²