The Ultimate Guide to Cam Design: Kinematics, Pressure Angles, and Manufacturing

The Heart of Automation: Mechanical Cam Design

Classes of Cams

Cams may, in general, be divided into two classes: uniform motion cams and accelerated motion cams. The uniform motion cam moves the follower at the same rate of speed from the beginning to the end of the stroke. However, as the movement starts from zero to full speed instantly and stops in the same abrupt way, there is a distinct shock at the beginning and end of the stroke if the movement is at all rapid.

In machinery working at a high rate of speed, therefore, it is important that cams are so constructed that sudden shocks are avoided when starting the motion or when reversing the direction of motion of the follower.

The uniformly accelerated motion cam is suitable for moderate speeds, but it has the disadvantage of sudden changes in acceleration at the beginning, middle, and end of the stroke. A cycloidal motion curve cam produces no abrupt changes in acceleration and is often used in high-speed machinery because it results in low noise, vibration, and wear. The cycloidal motion displacement curve is so called because it can be generated from a cycloid, which is the locus of a point of a circle rolling on a straight line.

Cam Follower Systems

The three most used cam and follower systems are radial and offset translating roller followers (Figs. 1a and 1b) and the swinging roller follower (Fig. 1c). When the cam rotates, it imparts a translating motion to the roller followers in Figs. 1a and 1b and a swinging motion to the roller follower in Fig. 1c.

The motion of the follower is, of course, dependent on the shape of the cam. The following section on displacement diagrams explains how a favorable motion is obtained so that the cam can rotate at high speed without shock.

The arrangements in Figs. 1a, 1b, and 1c show open-track cams. In Figs. 2a and 2b, the cam roller is forced to move in a closed track. Open-track cams build smaller than closed-track cams but, in general, springs are necessary to keep the roller in contact with the cam at all times. Closed-track cams do not require a spring and have the advantage of positive drive throughout the rise and return cycle. The positive drive is sometimes required, as in the case where a broken spring would cause serious damage to a machine.

Pressure Angle and Radius of Curvature

The pressure angle at any point on the profile of a cam may be defined as the angle between the direction where the follower wants to go at that point and where the cam wants to push it. It is the angle between the tangent to the path of follower motion and the line perpendicular to the tangent of the cam profile at the point of cam-roller contact.

The size of the pressure angle is important because:

1. Increasing the pressure angle increases the side thrust, and this increases the forces exerted on the cam and follower.
2. Reducing the pressure angle increases the cam size, and often this is not desirable because:
   • The size of the cam determines, to a certain extent, the size of the machine.
   • Larger cams require more precise cutting points in manufacturing and, therefore, an increase in cost.
   • Larger cams have higher circumferential speed, and small deviations from the theoretical path of the follower cause additional acceleration, the size of which increases with the square of the cam size.
   • Larger cams mean more revolving weight, and in high-speed machines, this leads to increased vibrations in the machine.
   • The inertia of a large cam may interfere with quick starting and stopping.

The maximum pressure angle α_m should, in general, be kept at or below 30 degrees for translating-type followers and at or below 45 degrees for swinging-type followers.

These values are on the conservative side and in many cases may be increased considerably, but beyond these limits, trouble could develop and an analysis is necessary.

Radius of Curvature

The minimum radius of curvature of a cam should be kept as large as possible:

1. To prevent undercutting of the convex portion of the cam.
2. To prevent too high surface stresses.

Figs. 3(a), (b), and (c) illustrate how undercutting occurs.

Undercutting cannot occur at the concave portion of the cam profile (working surface), but caution should be exerted in not making the radius of curvature equal to the radius of the roller follower. This condition would occur if there is a cusp on the displacement diagram which, of course, should always be avoided.

To enable milling or grinding of concave portions of a cam profile, the radius of curvature of concave portions of the cam must be larger than the radius of the cutter to be used:

R_c = ρ_min + r_f

Cam Forces, Contact Stresses, and Materials

After a cam and follower configuration has been determined, the forces acting on the cam may be calculated or otherwise determined. Next, the stresses at the cam surface are calculated and suitable materials to withstand the stress are selected. If the calculated maximum stress is too great, it will be necessary to change the cam design.

Such changes may include:

1. Increasing the cam size to decrease pressure angle and increase the radius of curvature.
2. Changing to an offset or swinging follower to reduce the pressure angle.
3. Reducing the cam rotation speed to reduce inertia forces.
4. Increasing the cam rise angle, β, during which the rise, h, occurs.
5. Increasing the thickness of the cam, provided that deflections of the follower are small enough to maintain uniform loading across the width of the cam.
6. Using a more suitable cam curve or modifying the cam curve at critical points.

Although parabolic motion seems to be the best with respect to minimizing the calculated maximum acceleration and, therefore, also the maximum acceleration forces, nevertheless, in the case of high-speed cams, cycloidal motion yields the lower maximum acceleration forces.

Thus, it can be shown that owing to the sudden change in acceleration (called jerk or pulse) in the case of parabolic motion, the actual forces acting on the cam are doubled and sometimes even tripled at high speed. Whereas with cycloidal motion, owing to the gradually changing acceleration, the actual dynamic forces are only slightly higher than the theoretical.

Therefore, the calculated force due to acceleration should be multiplied by at least a factor of 2 for parabolic and 1.05 for cycloidal motion to provide an allowance for the load-increasing effects of elasticity and backlash.

The main factors influencing cam forces are:

1. Displacement and cam speed (forces due to acceleration).
2. Dynamic forces due to backlash and flexibility.
3. Linkage dimensions which affect weight and weight distribution.
4. Pressure angle and friction forces.
5. Spring forces.

The main factors influencing stresses in cams are: 1) radius of curvature for cam and roller; and 2) materials.

Cam Materials: In considering materials for cams it is difficult to select any single material as being the best for every application. Often the choice is based on custom or the machinability of the material rather than its strength. However, the failure of a cam or roller is commonly due to fatigue, so that an important factor to be considered is the limiting wear load, which depends on the surface endurance limits of the materials used and the relative hardnesses of the mating surfaces. You can find data on material properties in the Machinery's Handbook.

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Modern Cam Manufacturing: The CNC Revolution

In the past, cams were manufactured by tracing a master template. Today, the process is fully digital, bridging the gap between design and manufacturing (CAD/CAM).

1. From SolidWorks to G-Code

Modern engineers use parametric software like SolidWorks or Autodesk Inventor to generate the cam profile automatically.

• Motion Analysis: You define the follower displacement (Rise-Dwell-Fall), and the software generates the cam geometry.
• CNC Grinding: This geometry is exported to a 5-Axis CNC Grinder. This eliminates the "Undercutting" issues seen in manual machining, as modern software can detect collisions before the metal is cut.

Search for CNC Programming Handbooks

2. The "Electronic Cam" (Servo Motion)

In modern high-speed packaging, mechanical cams are often being replaced by "Electronic Cams."

Instead of a physical metal disc, a Servo Motor is programmed to follow a specific motion profile. This allows you to change the "Cam Shape" instantly by modifying the software code, without stopping the machine to change parts. This is a key feature of Industry 4.0 flexible manufacturing.

Search for Motion Control & Servo Guides

3. Maintenance: Checking Cam Wear

Even the best-designed cams wear out. A common maintenance task is checking the Runout and surface profile.
Engineers use precision Dial Indicators with magnetic bases to measure the lift of the cam at specific intervals to ensure it still meets the timing diagram requirements.

Shop Professional Dial Indicators (Mitutoyo)

Recommended Articles on Cam Timing

• Timing Diagram (Part 1 - No Overlap Movement)
• Timing Diagram (Part 3 - Cycloid Cam Profile Analysis)
• Polynomial Cam Function (Fifth-degree polynomial)