Drawing cam profile for offset roller follower

Displacement data

Rise (UARM, $h = 30$ mm, $\beta = 90^\circ$). The first half (0 to $45^\circ$) is uniform acceleration, $s = 2h(\theta/\beta)^2$; the second half is uniform retardation, $s = h - 2h(1-\theta/\beta)^2$.

Return (SHM, $\beta = 120^\circ$). $s = \dfrac{h}{2}\left(1 + \cos\dfrac{\pi\phi}{120^\circ}\right)$, where $\phi$ is the angle from the start of the return and $s$ is the height above the lowest position.

Remaining angles: dwell at the top $45^\circ$, dwell at the bottom $105^\circ$. Check: $90 + 45 + 120 + 105 = 360^\circ$.

Drawing procedure

1. Choose a scale (full size). Mark the cam centre $O$.
2. Draw the base circle of radius 35 mm and the prime circle of radius $35 + 10 = 45$ mm (the roller centre is the trace point).
3. Draw the offset circle of radius 10 mm about $O$. The follower line is tangent to this circle, 10 mm to the right of the vertical through $O$. Mark the lowest trace point $A_0$ where this line meets the prime circle.
4. Draw the displacement diagram: a base line representing $360^\circ$ of cam rotation, divided into rise 90, dwell 45, return 120 and dwell 105. Plot the curve using the tables above (parabolic for the rise, cosine curve for the return).
5. Because the cam rotates clockwise, use inversion: keep the cam fixed and rotate the follower anticlockwise. Starting from $A_0$, divide the prime circle into the same angles (15 degree steps for the rise, 30 degree steps for the return) in the anticlockwise direction.
6. Through each division point on the prime circle, draw a tangent to the offset circle (the follower position lines). Along each tangent, measure the displacement from the table outward from the prime circle. This gives the roller-centre points $A_1, A_2, \dots$.
7. Join the points with a smooth curve: this is the pitch curve.
8. With each point as centre and radius 10 mm (the roller radius), draw circles. The inner envelope touching all the circles is the cam profile.
9. Draw the dwell portions as arcs of the prime circle (pitch curve) and of the base circle (profile).

Check

The pressure angle is greatest near mid-rise; measure it between the follower line and the normal at contact and confirm it is below about $30^\circ$. An offset on the correct side lowers the pressure angle during the rise.