---
title: "Drawing cam profile for offset roller follower"
subject: "Theory of Mechanism and Machine I"
chapter: 3
key: "semester_6/theory_of_mechanism_and_machine_i:offset-roller-follower-cam-profile"
source: https://www.bctengineer.com/q/semester_6/theory_of_mechanism_and_machine_i/offset-roller-follower-cam-profile
site: BCT Engineering
---

# Drawing cam profile for offset roller follower

Theory of Mechanism and Machine I · Chapter 3: Cams and Followers

- Asked in: year not given, 8 marks
- Video: [HOW TO DRAW THE CAM PROFILE II OFFSET FOLLOWER II MOVES WITH SHM](https://www.youtube.com/watch?v=XiWXcKRwtqc) — TECH CAD
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/theory_of_mechanism_and_machine_i/offset-roller-follower-cam-profile
- Whole chapter: https://www.bctengineer.com/md/semester_6/theory_of_mechanism_and_machine_i/chapter-3

## Question

Draw (describe step by step) the profile of a disc cam rotating clockwise with an offset roller follower, given: base circle radius 35 mm, roller diameter 20 mm, offset of the follower axis 10 mm to the right of the cam axis; the follower rises 30 mm with uniform acceleration and retardation during 90 degrees, dwells for 45 degrees, returns with SHM during 120 degrees and dwells for the remaining 105 degrees. Also tabulate the follower displacement at each 15 degrees of the rise and each 30 degrees of the return.

## Short answer

Draw base circle R35, prime circle R45, offset circle R10. With cam clockwise, rotate follower anticlockwise; divide prime circle, draw tangents to offset circle. Plot displacement from tables: rise (15° steps) 0, 1.67, 6.67, 15, 23.33, 28.33, 30 mm (UARM); return (30° steps) 30, 25.61, 15, 4.39, 0 mm (SHM). Connect points for pitch curve; cam profile is inner envelope of roller circles.

## Answer

#### 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, $s = h - 2h(1-\theta/\beta)^2$.

| Cam angle (deg) | Displacement (mm) |
|---|---|
| 0 | 0.00 |
| 15 | 1.67 |
| 30 | 6.67 |
| 45 | 15.00 |
| 60 | 23.33 |
| 75 | 28.33 |
| 90 | 30.00 |

**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.

| Return angle (deg) | Follower height above lowest position (mm) |
|---|---|
| 0 | 30.00 |
| 30 | 25.61 |
| 60 | 15.00 |
| 90 | 4.39 |
| 120 | 0.00 |

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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For base circle radius 35 mm and roller diameter 20 mm, the prime circle radius used for the construction is:
   A. 35 mm
   B. 25 mm
   C. 55 mm
   D. 45 mm
   Answer: D. Prime circle radius = base radius + roller radius = 35 + 10 = 45 mm, since the roller centre is the trace point. (Key point: Prime circle radius)

2. For a cam rotating clockwise, the construction by inversion uses:
   A. Cam fixed, follower rotated anticlockwise
   B. Cam fixed, follower rotated clockwise
   C. Follower fixed, cam rotated anticlockwise
   D. Both rotating in the same direction
   Answer: A. Keeping the cam fixed, the follower is given the opposite rotation, anticlockwise, and the division points are marked in that direction. (Key point: Inversion for clockwise cam)

3. With an offset follower, the follower position lines through each division point are drawn:
   A. Radially from the cam centre
   B. Tangent to the offset circle
   C. Perpendicular to the base circle
   D. Parallel to the horizontal
   Answer: B. The follower line is always tangent to the offset circle (10 mm radius), and displacement is measured along each tangent from the prime circle. (Key point: Follower lines for offset)

4. How is the cam profile obtained from the pitch curve for a roller follower?
   A. The pitch curve itself is the profile
   B. Draw roller circles at each pitch point and take the inner envelope
   C. Shift the pitch curve outward by the offset
   D. Join the points on the base circle
   Answer: B. Circles of roller radius (10 mm) are drawn about each roller-centre point, and the inner envelope touching them is the cam profile. (Key point: Cam profile from pitch curve)

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