Details of each component parts of a machine vice is shown in Fig1. Draw half full size in first angle projection.

Draw a horizontal axis representing the cam angle from $0^\circ$ to $360^\circ$. Draw a vertical axis representing the follower displacement from $0 \text{ mm}$ to $40 \text{ mm}$.

For uniform acceleration/retardation, the acceleration phase is from $0^\circ$ to $75^\circ$ and the retardation phase is from $75^\circ$ to $150^\circ$.
Divide the $150^\circ$ into an even number of equal intervals (e.g., 6 intervals of $25^\circ$ each).
The displacement $S$ for uniform acceleration is given by $S = 2L \left(\frac{\theta}{\beta}\right)^2$ for the first half, and for uniform retardation by $S = L - 2L \left(1 - \frac{\theta}{\beta}\right)^2$ for the second half, where $L = 40 \text{ mm}$ and $\beta = 150^\circ$.
Alternatively, graphically, divide the $150^\circ$ into 6 equal parts. For the first 3 parts (acceleration), the displacements are proportional to $1^2, 2^2, 3^2$. For the next 3 parts (retardation), the displacements are proportional to $3^2, 2^2, 1^2$ from the peak.
For example, at $25^\circ$: $S = 2(40) \left(\frac{25}{150}\right)^2 = 80 \left(\frac{1}{6}\right)^2 = 80 \times \frac{1}{36} \approx 2.22 \text{ mm}$.
At $75^\circ$: $S = 2(40) \left(\frac{75}{150}\right)^2 = 80 \left(\frac{1}{2}\right)^2 = 80 \times \frac{1}{4} = 20 \text{ mm}$.
At $150^\circ$: $S = 40 \text{ mm}$.
Plot these points and draw a smooth curve.

Draw a horizontal line at $40 \text{ mm}$ displacement from $150^\circ$ to $210^\circ$.

For simple harmonic motion (SHM), the displacement $S$ from the maximum lift is given by $S = \frac{L}{2} \left(1 + \cos\left(\pi \frac{\theta}{\beta}\right)\right)$, where $L = 40 \text{ mm}$ and $\beta = 150^\circ$. Here $\theta$ is the angle measured from the start of the fall phase.
Divide the $150^\circ$ into an even number of equal intervals (e.g., 6 intervals of $25^\circ$ each).
For example, at $25^\circ$ into the fall (i.e., $210^\circ + 25^\circ = 235^\circ$ cam angle):
$S = \frac{40}{2} \left(1 + \cos\left(\pi \frac{25}{150}\right)\right) = 20 \left(1 + \cos\left(\frac{\pi}{6}\right)\right) = 20 \left(1 + \frac{\sqrt{3}}{2}\right) \approx 37.32 \text{ mm}$.
This is the displacement from the base circle. So the follower position is $37.32 \text{ mm}$.
At $75^\circ$ into the fall (i.e., $210^\circ + 75^\circ = 285^\circ$ cam angle):
$S = 20 \left(1 + \cos\left(\frac{\pi}{2}\right)\right) = 20(1+0) = 20 \text{ mm}$.
At $150^\circ$ into the fall (i.e., $210^\circ + 150^\circ = 360^\circ$ cam angle):
$S = 20 \left(1 + \cos(\pi)\right) = 20(1-1) = 0 \text{ mm}$.
Plot these points and draw a smooth curve connecting them to $0 \text{ mm}$ at $360^\circ$.

The list radius (base circle radius) is $25.4 \text{ mm}$.
The roller follower diameter is $25.4 \text{ mm}$, so the roller radius is $12.7 \text{ mm}$.
The prime circle radius is the base circle radius plus the roller radius: $25.4 \text{ mm} + 12.7 \text{ mm} = 38.1 \text{ mm}$.
Draw a circle with radius $25.4 \text{ mm}$ (base circle) and another concentric circle with radius $38.1 \text{ mm}$ (prime circle). Mark the cam center.

Since the cam rotates anticlockwise, the angles for drawing the cam profile are measured clockwise from the starting position of the follower.
Divide the $360^\circ$ into sectors corresponding to the intervals used in the displacement diagram (e.g., $25^\circ$ intervals). Mark these radial lines clockwise from the vertical line representing the follower's initial position.

For each angular position on the cam, measure the corresponding displacement from the displacement diagram.

• For a roller follower with the line of action through the cam center, these displacements are measured radially outwards from the prime circle.
• Mark these points along the radial lines. These points represent the centers of the roller follower at different cam angles.

At each marked point (roller center), draw a small circle with the roller radius ($12.7 \text{ mm}$).
Draw a smooth curve that is tangent to all these roller circles. This curve represents the final cam profile.