Material Selection Decision Logic
| Application | Recommended Materials |
|---|---|
| Low-speed, light-load | Gray iron castings (Class 20–30) |
| Moderate-speed, moderate-load | Nodular iron or SAE 1020 steel |
| High-speed, high-load | Carburized SAE 1020 or induction-hardened SAE 4340 |
| Maximum endurance | SAE 4340, induction hardened to 50–55 Rc |
Design Modification Strategies: When the Numbers Don't Work
Sometimes your initial cam design produces pressure angles that are too large, radii of curvature that are too small, or contact stresses that exceed material limits. Here are the six primary modifications available to you:
| Modification | What It Fixes | Trade-Off |
|---|---|---|
| 1. Increase cam size | Decreases pressure angle, increases radius of curvature | Larger machine, more precise manufacturing, higher inertia |
| 2. Switch to offset or swinging follower | Reduces pressure angle | May increase cam complexity |
| 3. Reduce cam rotation speed | Reduces inertia forces directly | Lower machine throughput |
| 4. Increase rise angle β | Distributes rise over more degrees | Reduces available dwell time |
| 5. Increase cam thickness | Reduces contact stress (larger b) | Requires small follower deflections |
| 6. Change cam curve type | Addresses specific force or jerk issues | May affect other parameters |
The Factors That Influence Cam Forces
The five main factors driving cam forces:
- Displacement and cam speed → acceleration forces (often dominant at high speed)
- Dynamic forces from backlash and flexibility → impact and vibration
- Linkage dimensions → weight and weight distribution
- Pressure angle and friction → side thrust and guide loading
- Spring forces → constant load throughout the cycle
The Factors That Influence Cam Stresses
The two factors driving surface stresses:
- Radius of curvature of cam and roller
- Material properties (surface endurance limit)
Layout of Cylinder Cams
Not all cams are flat plates. Cylindrical cams (also called barrel cams or drum cams) use a groove cut into the surface of a cylinder to guide the follower.
Developing the Cam Curve
To lay out a cylindrical cam with uniformly accelerated motion:
- Divide the base circle of the cylinder into equal parts (typically 12)
- Set off these parts along a straight line (the development)
- Divide the total rise in the proportion 1 : 3 : 5 : 5 : 3 : 1 for uniformly accelerated motion
- Draw horizontal lines from the division points and vertical lines from the circumferential positions
- The intersections are points on the developed cam curve
- Project these points back onto the cylindrical surface
The second half of the cam (the return) is constructed in the same manner, except the curve falls instead of rising.
Shape of Rolls for Cylinder Cams
This is a detail that separates competent cam designers from the rest.
The rolls (followers) for cylindrical cams working in a groove should be conical, not cylindrical. Here's why:
| Roll Shape | Problem |
|---|---|
| Straight (cylindrical) | Varying surface speed between top and bottom of groove → excessive friction, scrubbing action |
| Curved (barrel) | Small bearing area wears quickly → creates grooves in cam surface → destroys accuracy and creates backlash |
| Conical | Permits true rolling action in the groove → minimal friction, maximum life |
The amount of taper depends on the spiral angle of the cam groove. Since this angle typically varies along the cam, design the taper for the section where the heaviest duty is performed.
Determining the cone angle:
- Find the circumferential distance b on the cam surface for the critical section
- Find the throw a for that section
- Line OU = development of roll movement at the top of the groove
- Line OV = development at the bottom of the groove
- Make the top width and bottom width of the groove proportional to OU and OV
Plate Cams on a Milling Machine
Plate cams with a constant rise (such as those used on automatic screw machines) can be cut on a universal milling machine using the spiral head set at an angle α.
The principle: When the spiral head is vertical, the cam's lead equals the machine's geared lead. By inclining the spiral head, you can produce any lead less than the geared lead.
The formula:
Where:
- α = angle to which the index head is set from horizontal
- r = rise of cam in the given portion of circumference
- L = spiral lead for which the milling machine is geared
- φ = angle (in degrees) over which the rise occurs
Example: A cam requires a rise of 0.125 units in 300° of rotation. The machine is geared for a lead of 0.670 units.
The spiral head and vertical milling attachment are both set to this angle so the finished cam edge is parallel to its rotation axis.
Multi-lobe cams: When a cam has several lobes with different leads, gear the machine for a lead slightly exceeding the greatest lead on the cam. Then mill all lobes by simply changing the spiral head angle for each—no regearing needed.
Practical tip: Mill on the underside of the cam whenever possible. This prevents chip interference and makes it easier to see any layout lines.
Simple Method for Cutting Uniform Motion Cams
For precision uniform-motion cams (such as heart cams), use the index-and-lower method:
- Mount the cam on an arbor between milling machine centers
- Set the indexing head to the required number of divisions (e.g., 200 for a heart cam)
- Calculate the incremental lowering per index division: divide the total throw by half the number of divisions
- Make the first cut, then lower the knee by the calculated increment and advance the index
- Repeat for each cut
Example: Heart cam with 1.1 unit throw, indexed for 200 divisions.
Each successive cut is 0.011 units lower and one index position advanced.
Improvement method and result
Let's return to where we started. the practitioner Engström stood over the wreckage of a constant-velocity cam and understood immediately what had gone wrong—and what needed to change.
Here is what she redesigned, step by step:
| Original Design | the practitioner's Redesign | Why |
|---|---|---|
| Constant velocity displacement | Cycloidal motion | Eliminates infinite acceleration at transitions; only 1.05× dynamic multiplier |
| R_min too small for speed | Recalculated R_min using pressure angle formula | Kept α_max below 30° for the translating follower |
| Gray iron cam, Class 20 | SAE 4340 steel, induction hardened | Increased allowable stress from 58,000 to 226,000 |
| No spring preload analysis | Full spring force calculation with preload | Ensured follower contact at all speeds |
| No manufacturing tolerance spec | Surface finish and tolerance callout | Prevented acceleration spikes from surface errors |
The result: four years of uninterrupted operation at 900 RPM, 22 hours per day.
Quick-Reference Design Checklist
Use this checklist for every cam design, whether you are a student completing your first assignment or a veteran engineer reviewing a critical production mechanism.
Phase 1: Displacement Diagram
Phase 2: Cam Geometry
Phase 3: Force Analysis
Phase 4: Stress and Material
Phase 5: Manufacturing
Comprehensive Formula Reference
Displacement Formulas
| Motion Type | Displacement y | Velocity v | Acceleration a |
|---|---|---|---|
| Constant Velocity | h(φ/β) | hω/β | 0 (∞ at ends) |
| Parabolic (1st half) | 2h(φ/β)² | 4hωφ/β² | 4h(ω/β)² |
| Parabolic (2nd half) | h[1−2(1−φ/β)²] | (4hω/β)(1−φ/β) | −4h(ω/β)² |
| Simple Harmonic | (h/2)(1−cos(180°φ/β)) | (hπω/2β)sin(180°φ/β) | (hπ²ω²/2β²)cos(180°φ/β) |
| Cycloidal | h(φ/β−sin(360°φ/β)/2π) | (hω/β)(1−cos(360°φ/β)) | (2πhω²/β²)sin(360°φ/β) |
Key Sizing Formulas
| Parameter | Formula |
|---|---|
| Angular velocity | ω = 6N (degrees/sec) |
| Effective weight | W = W_f + ⅓W_s + W_e |
| Acceleration force | R = Wa/g |
| Spring force | F_s = R(factor) − W_f − F_e − F_f |
| Spring constant | K_s = (F_s − preload)/y_a |
| Contact stress (steel/steel) | S_c = 2290√((F_n/b)(1/r_f ± 1/R_c)) |
| Contact stress (steel/cast iron) | S_c = 1850√((F_n/b)(1/r_f ± 1/R_c)) |
| Cam torque | T_o = (R_min + y)·F_n·sin α |
| Milling angle | sin α = 360°r/(φL) |
Dynamic Force Multipliers
| Curve Type | Multiplier for R |
|---|---|
| Cycloidal | 1.05 |
| Parabolic | ≥ 2.0 |
| Simple Harmonic | ~1.5 |
Maximum Pressure Angle Limits
| Follower Type | Conservative Maximum |
|---|---|
| Translating | 30° |
| Swinging | 45° |
Your Next Step
You now hold the complete engineering framework for designing, analyzing, and manufacturing cam mechanisms—from the first stroke of the displacement diagram to the final surface stress calculation.
Here is what separates engineers who build machines that run from those who build machines that break:
- They start with the displacement diagram, not the cam profile
- They choose the motion curve based on operating speed and force requirements, not convenience
- They calculate the pressure angle before committing to a cam size
- They verify the radius of curvature to prevent undercutting and surface failure
- They analyze forces including dynamic multipliers for real-world conditions
- They specify materials based on surface endurance data, not gut feeling
- They control manufacturing accuracy because they understand that a 0.001 unit bump at 900 RPM produces forces 10 times the design value
The question is not whether you understand cams. After reading this guide, you do.
The question is: what will you design next?
Pull out your displacement diagram. Choose your curve. Run the numbers. And build something that lasts.
If you found this guide valuable, share it with a colleague who designs mechanisms. The engineering in these pages has been validated across decades of industrial practice—it works today, and it will work a century from now.