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
CAM-FOLLOWER MECHANISM Base Circle Rb Prime Circle Return spring Lift (h) phi Pressure Angle omega Cam Follower MOTION PROFILE COMPARISON Displacement (s) Velocity (v) Acceleration (a) Infinite! Jerk Characteristics Uniform: INFINITE at ends Parabolic: INFINITE at midpoint Harmonic: INFINITE at ends Cycloidal: FINITE everywhere Motion Profile Legend Uniform (Cv=1.0) Parabolic (Ca=4.0) Harmonic (Cv=1.57) Cycloidal (Smooth) Application Guidance Low speed: Uniform or Parabolic High speed, low vibration: Cycloidal (preferred)
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 rotation angle during rise motion

Position within rise phase for analysis

For inertia force calculation

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 Velocity1.0INFINFVery slow
Parabolic2.04.0INFLow accel
Simple Harmonic1.574.93INFModerate
Cycloidal2.06.2839.5High 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)