Cam Design Calculator
Design cam mechanisms with multiple motion profiles. Calculate follower displacement, velocity, acceleration, pressure angle, and base circle sizing for packaging machines, engine valves, indexing mechanisms, and more.
How It Works - Cam Motion Theory
Cam Motion Profiles
- Constant Velocity (Uniform): Follower moves at constant speed. Simple but causes infinite acceleration at start/end (shock loading). Only suitable for very slow speeds or with modified transitions.
- Parabolic (Constant Acceleration): Provides minimum peak acceleration for a given rise. Acceleration is constant during each half of the motion, reversing at midpoint. Has infinite jerk at transitions.
- Simple Harmonic: Follows a cosine displacement curve. Smooth velocity profile but has discontinuous acceleration at ends. Good for moderate speeds.
- Cycloidal: Zero velocity, acceleration, and jerk at both ends. Smoothest motion profile - ideal for high-speed applications where vibration must be minimized.
Pressure Angle
- The pressure angle is the angle between the follower motion direction and the normal to the cam profile
- It determines side loading on the follower guides and affects mechanical efficiency
- Maximum recommended: 30 degrees for translating followers
- Higher pressure angles cause increased guide wear and potential jamming
- Pressure angle can be reduced by: increasing base circle radius, reducing lift, or using different motion profiles
- For oscillating followers, the maximum pressure angle can be higher (up to 45 degrees)
Base Circle
- The base circle is the smallest circle that can be drawn tangent to the cam profile
- Determines the minimum size of the cam and affects pressure angle throughout the motion
- Larger base circle = smaller pressure angle = smoother operation but larger cam
- Base circle radius must be chosen to keep pressure angle within acceptable limits
- Typical starting point: base circle radius = 1.5 to 3 times the total lift
- Prime circle = base circle + roller radius (for roller followers)
Motion Profile Characteristics
- Cv (Velocity coefficient): v_max = Cv * h * omega / beta
- Ca (Acceleration coefficient): a_max = Ca * h * omega^2 / beta^2
- Cj (Jerk coefficient): j_max = Cj * h * omega^3 / beta^3
- Lower Ca means lower peak acceleration (less inertia force)
- Finite Cj means smoother motion (no shock at transitions)
Follower Types
- Knife-edge: Simplest, but high contact stress - only for light loads
- Flat-faced: Good load distribution, self-adjusting for wear
- Roller: Low friction, handles high speeds - most common
- Spherical: Accommodates misalignment, used in precision applications
Cam Mechanism Geometry & Motion Profiles
Quick-Select Presets
Motion Profile Type
Constant Velocity
Cv=1.0, Ca=INF
Parabolic
Cv=2.0, Ca=4.0
Simple Harmonic
Cv=1.57, Ca=4.93
Cycloidal
Cv=2.0, Ca=6.28, Smooth
Cam Parameters
Cam rotation angle during rise motion
Position within rise phase for analysis
For inertia force calculation
Geometry Parameters
mm
Set to 0 for knife-edge or flat-faced follower
mm
Horizontal distance from cam center to follower axis
50%
Position within rise motion (0-100%)
12.5
mm
Displacement at Position
CYCLOIDAL - SMOOTH
Velocity
--
Acceleration
--
Jerk
--
Inertia Force
--
Max Velocity
--
Max Acceleration
--
Rise Time
--
Position
--
Motion Curves
Displacement
Velocity
Acceleration
Motion Profile Coefficients
| Profile | Cv | Ca | Cj | Best For |
|---|---|---|---|---|
| Constant Velocity | 1.0 | INF | INF | Very slow |
| Parabolic | 2.0 | 4.0 | INF | Low accel |
| Simple Harmonic | 1.57 | 4.93 | INF | Moderate |
| Cycloidal | 2.0 | 6.28 | 39.5 | High speed |
v_max = Cv * h * omega / beta | a_max = Ca * h * omega^2 / beta^2 | j_max = Cj * h * omega^3 / beta^3
Key Formulas
Cycloidal Displacement:
s = h * [theta/beta - sin(2*pi*theta/beta)/(2*pi)]
Pressure Angle (in-line follower):
tan(phi) = (ds/dtheta) / (Rb + s)
With Offset:
tan(phi) = (ds/dtheta - e) / sqrt((Rb+s)^2 - e^2)