Please show all work. Design the cam Derive the s v a j functions of the followe

Question

Please show all work.

Design the cam Derive the s v a j functions of the follower motion knowing that it rises from 0 to 3" between 0degree and 45degree, falls from 3" to 1" between 45degree and 120degree, dwell at 1" between 120degree and 180degree, falls to zero between 180degree and 210degree, and dwell at zero for the remainder of the cycle. Assume that the follower is moving along the vertical axis, and there is no eccentricity. What is the surface area of the cam if the roller radius r = 0.25" and the prime circle radius Rp = 1". (Hint: you need to find coordinates of the cam surface) blue = cam surface area

Explanation / Answer

Dispacement function:

For 0 <= theta <= 45 deg, Displacement of follower s = 3/45*theta

For 45 <= theta <= 120 deg, s = 3 + (1-3)/(120-45)*(theta - 45)

For 120 <= theta <= 180, s = 1

For 180 <= theta <= 210, s = 1 - (theta - 180) / (210 - 180)

For 210 <= theta <= 360, s = 0

Velocity function:

For 0 <= theta <= 45 deg, Velocity of follower v = ds/dt = 3/45

For 45 <= theta <= 120 deg, v = ds/dt = (1-3)/(120-45) = -2/75

For 120 <= theta <= 180, v = ds/dt = 0

For 180 <= theta <= 210, v = ds/dt = - 1 / (210 - 180) = -1/30

For 210 <= theta <= 360, v = ds/dt = 0

Acceleration function:

For 0 <= theta <= 45 deg, Acceleration of follower a = dv/dt = 0

For 45 <= theta <= 120 deg, a = dv/dt = 0

For 120 <= theta <= 180, a = dv/dt = 0

For 180 <= theta <= 210, a = dv/dt = 0

For 210 <= theta <= 360, a = dv/dt = 0

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