When a follower moves with simple harmonic motion, its maximum acceleration during outstroke will be: (where S strike of the follower, θ_o - angular displacement of the cam during outstroke of the follower, ω -angular velocity of the cam in rad/sec.)

Concept:

When a follower moves with simple harmonic motion, its maximum acceleration during the outstroke can be derived using the principles of simple harmonic motion (SHM). The relevant parameters given are:

• S: Stroke of the follower
• \(\theta_o\): Angular displacement of the cam during the outstroke of the follower
• \(\omega\): Angular velocity of the cam in rad/sec

Calculation:

From the SHM equation:

Displacement of the follower is given by:

\( x = A \cos(\omega t) \)

Where A is the amplitude of motion, which is half of the stroke:

\( A = \frac{S}{2} \)

Velocity is given by:

\( v = - A \omega \sin(\omega t) \)

Acceleration is given by:

\( a = - A \omega^2 \cos(\omega t) \)

Maximum acceleration occurs when \(\cos(\omega t) = 1\), giving:

\( a_{\text{max}} = A \omega^2 \)

Substituting \(A = \frac{S}{2}\) , we get:

\( a_{\text{max}} = \frac{S}{2} \omega^2 \)

Using the relation for angular displacement:

\( \omega = \frac{\pi}{\theta_o} \)

We substitute into the acceleration equation:

\( a_{\text{max}} = \frac{S}{2} \left( \frac{\pi}{\theta_o} \right)^2 \)

Simplifying:

\( a_{\text{max}} = \frac{\pi^2 \omega^2 S}{2 \theta_o^2} \)