Plate Cam Mechanism with Reciprocating Roller Follower

Plate cam mechanisms are widely used in various mechanical systems to convert rotary motion into reciprocating motion. They consist of a cam mounted on a rotating shaft and a follower that moves in a reciprocating motion according to the profile of the cam. One type of follower commonly used in plate cam mechanisms is the reciprocating roller follower.

Constant Acceleration of the Follower

In the given question, it is stated that the follower has a constant acceleration. This means that the rate of change of velocity of the follower remains constant throughout its motion. Let's analyze the different motion profiles and determine which one satisfies this condition.

a) Cycloidal Motion
Cycloidal motion is a smooth and continuous motion profile that results in a constant velocity of the follower. However, the acceleration of the follower is not constant in cycloidal motion. It changes throughout the motion, resulting in acceleration variations.

b) Simple Harmonic Motion
Simple harmonic motion is a periodic motion where the acceleration of the follower is directly proportional to its displacement from the equilibrium position. The acceleration is not constant in simple harmonic motion, as it varies with the displacement.

c) Parabolic Motion
Parabolic motion is a motion profile where the acceleration of the follower is constant. This means that the rate of change of velocity remains constant, satisfying the condition given in the question. The follower undergoes uniformly accelerated motion, resulting in a parabolic motion profile.

d) 3-4-5 Polynomial Motion
The 3-4-5 polynomial motion is a motion profile that can be described by a third-degree polynomial equation. This motion profile does not have a constant acceleration. The acceleration changes throughout the motion, resulting in acceleration variations.

Conclusion
Based on the analysis above, it can be concluded that the follower in a plate cam mechanism with a reciprocating roller follower has a constant acceleration in the case of parabolic motion. The parabolic motion profile satisfies the condition given in the question, where the follower has a constant rate of change of velocity, resulting in a constant acceleration.