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A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity πœ”. At time 𝑑 = 0, the vertical position of

A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity πœ”. At time 𝑑 = 0, the vertical position of

Q. A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity πœ”. At time 𝑑 = 0, the vertical position of the follower is 𝑦(0) = 0, and the system is in the configuration shown below.

The vertical position of the follower face, 𝑦(𝑑) is given byΒ Β Β Β Β Β Β Β Β Β Β  (A) 𝑒 sin πœ”π‘‘Β Β Β Β Β Β Β Β Β  (B) 𝑒(1 + cos 2πœ”π‘‘)Β Β Β Β Β Β Β Β Β  (C) 𝑒(1 βˆ’ cos πœ”π‘‘)Β Β Β Β Β  (D) 𝑒 sin 2πœ”π‘‘

Ans: e(1βˆ’cosΟ‰t)

Sol:

Displacement of follower
y=OBβ€²βˆ’OB(OBβ€²will be parallel to PC)

=CMβˆ’OB

=(PCβˆ’PM)βˆ’OB(OBβ€²=CM)

=Rβˆ’ecosΞΈβˆ’(Rβˆ’e)

=Rβˆ’ecosΞΈβˆ’R+e

=e(1βˆ’cosΞΈ)∴[ln time(t)ΞΈ=Ο‰t]

=e(1βˆ’cosΟ‰t)

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