In the cam-follower mechanism, the slotted bar rotates with constant angular vel

Question

In the cam-follower mechanism, the slotted bar rotates with constant angular velocity ?=10 rad/s and the radial position of the follower A is determined by the profile of the stationary cam.  The path of the follower is described by the polar equation r=1+0.5cos(2?) ft.  Determine the velocity of the cam follower when ?=30o

a) In terms of polar coordinates

b) in terms of cartesian coordinates

In the cam-follower mechanism, the slotted bar rotates with constant angular velocity ?=10 rad/s and the radial position of the follower A is determined by the profile of the stationary cam. The path of the follower is described by the polar equation r=1+0.5cos(2?) ft. Determine the velocity of the cam follower when ?=30 degree In terms of polar coordinates in terms of cartesian coordinates

Explanation / Answer

r=1+0.5cos(2?)

a) radial velocity V_r = dr/dt = d( 1+0.5cos(2?))/dt = 0.5 = 0

tangential velocity = r.d?/dt = ?r = ? . (1+0.5cos(2?))

? at ? =30, V_? = 10 x (1 + 0.5 cos 60) = 12.5 m/s

? total velocity = ? V_r2 + V_?2 = 12.5 et^ , where et^ represents the tangential direction.

b) Now V_x = V_? cos 30 = 12.5 x cos 30 = 10.825m/s

and V_y = V_?, sin 30 = 6m/s

? total V = V_x i+ V_y j = 10.825 i + 6 j m/s

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