Question

In cam and follower mechanism; if the rise motion is given by an equation: $S = \frac{h}{2} \left\{ 1 - \cos\left(\frac{\pi\theta}{\phi}\right) \right\}$, then the motion is called:

• A. Simple Harmonic Motion
• B. Uniform Acceleration and Retardation Motion
• C. Cycloidal Motion
• D. Constant Velocity Motion

Hint:

To identify this motion quickly, look for the Cosine term. Simple Harmonic Motion is always defined by sinusoidal (sine or cosine) functions. If the equation has a "1 - cos" structure, it's definitely SHM.

Answer 1

The Correct Option is A

1. Analyzing the Equation: The equation $S = \frac{h}{2} \left\{ 1 - \cos\left(\frac{\pi\theta}{\phi}\right) \right\}$ is the standard displacement equation for

Simple Harmonic Motion (SHM).

• h: Total rise or stroke of the follower.

• $\phi$: Total angle of rise.

• $\theta$: Angle turned by the cam at any instant.

2. Characteristics of SHM in Cams:

• Displacement: Follows a cosine curve, starting at zero when $\theta = 0$ and reaching $h$ when $\theta = \phi$.

• Velocity: Follows a sine curve, being zero at the beginning and end of the stroke and maximum at the middle.

• Acceleration: Follows a cosine curve. Crucially, there is a sudden change in acceleration at the start and end of the stroke, which can cause "jerk" in high-speed applications.

3. Comparison with Other Motions:

• Constant Velocity: $S$ is linear with respect to $\theta$ ($S \propto \theta$).

• Cycloidal: The equation involves both a linear term and a sine term to ensure zero acceleration at the start and end, making it suitable for high speeds.