A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity 𝜔. At time 𝑡 = 0, the vertical position of

Q. A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity 𝜔. At time 𝑡 = 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(𝑡) is given by            (A) 𝑒 sin 𝜔𝑡          (B) 𝑒(1 + cos 2𝜔𝑡)          (C) 𝑒(1 − cos 𝜔𝑡)      (D) 𝑒 sin 2𝜔𝑡

Ans: e(1−cosωt)

Sol:

Displacement of follower
y=OB′−OB(OB′will be parallel to PC)

=CM−OB

=(PC−PM)−OB(OB′=CM)

=R−ecosθ−(R−e)

=R−ecosθ−R+e

=e(1−cosθ)∴[ln time(t)θ=ωt]

=e(1−cosωt)