Cam Profile Calculator
Calculate cam profiles for follower displacement, velocity, and acceleration. Enter values for instant results with step-by-step formulas.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Harmonic: s = (h/2)(1 - cos(pi*theta/beta)) | Cycloidal: s = h(theta/beta - sin(2*pi*theta/beta)/(2*pi))
Where s = follower displacement, h = total stroke, theta = current cam angle, beta = rise/return angle. Velocity and acceleration are obtained by successive differentiation with respect to time, introducing angular velocity omega.
Worked Examples
Example 1: Harmonic Motion Cam for Packaging Machine
Problem:Design a cam with 30 mm base radius, 20 mm stroke, 120 deg rise, 60 deg dwell, 120 deg return, running at 600 RPM with harmonic motion.
Solution:Angular velocity = 600 x 2pi/60 = 62.83 rad/s\nMax displacement = 20 mm (at top of rise)\nMax velocity (harmonic) = h x pi x omega / (2 x beta_rise)\n= 20 x pi x 62.83 / (2 x 2.094) = 942.5 mm/s\nMax acceleration = h x pi^2 x omega^2 / (2 x beta_rise^2)\n= 20 x pi^2 x 62.83^2 / (2 x 2.094^2) = 89,134 mm/s^2\nMax cam radius = 30 + 20 = 50 mm\nRemaining dwell = 360 - 120 - 60 - 120 = 60 deg
Result:Max Velocity: 942.5 mm/s | Max Accel: 89,134 mm/s^2 | Cam Radius: 30-50 mm
Example 2: Cycloidal Motion for High-Speed Application
Problem:Same parameters but using cycloidal motion to reduce jerk at transitions for operation at 1200 RPM.
Solution:Angular velocity = 1200 x 2pi/60 = 125.66 rad/s\nCycloidal max velocity = 2 x h x omega / beta_rise\n= 2 x 20 x 125.66 / 2.094 = 2400 mm/s\nCycloidal max accel = 2pi x h x omega^2 / beta_rise^2\n= 2pi x 20 x 125.66^2 / 2.094^2 = 452,216 mm/s^2\nBenefit: Zero jerk at transitions (vs infinite jerk with harmonic)\nTrade-off: 27% higher peak acceleration than harmonic
Result:Max Velocity: 2400 mm/s | Max Accel: 452,216 mm/s^2 | Zero jerk discontinuity
Frequently Asked Questions
What is a cam mechanism and how does it convert motion?
A cam mechanism is a mechanical device that converts rotary motion into linear or oscillating motion through a specially shaped rotating profile. The cam is a rotating element with a contoured surface that pushes against a follower, which moves in a defined path as the cam rotates. The shape of the cam profile determines the displacement, velocity, and acceleration of the follower at every point of rotation. Cam mechanisms are fundamental components in internal combustion engines (valve actuation), textile machinery, packaging equipment, printing presses, and automated manufacturing systems. Their ability to produce precisely controlled, repeatable motion patterns makes them indispensable in mechanical engineering design.
What is the pressure angle in cam design and why is it critical?
The pressure angle is the angle between the direction of the follower motion and the normal force exerted by the cam on the follower at any given point. It is a critical design parameter because it determines the side loading on the follower guide and the efficiency of force transmission. A large pressure angle means more force is directed sideways rather than along the desired follower direction, increasing guide friction and wear. The maximum allowable pressure angle for translating followers is typically 30 degrees for roller followers and 20 to 25 degrees for flat-faced followers. Pressure angle can be reduced by increasing the base circle radius, but this makes the cam physically larger. Balancing pressure angle constraints against cam size is a fundamental design challenge.
How does base circle radius affect cam performance?
The base circle is the smallest circle that can be drawn tangent to the cam profile, and its radius is the most influential geometric parameter in cam design. A larger base circle reduces the pressure angle throughout the cam rotation, improving force transmission efficiency and reducing follower guide loads. However, a larger base circle also increases the overall cam size, weight, and the space required for installation. The minimum base circle radius is determined by the maximum allowable pressure angle constraint, typically calculated iteratively or using analytical methods for each motion type. For high-speed applications, larger base circles also reduce the cam surface curvature, which decreases contact stress and improves durability. Engineers typically start with the minimum acceptable base circle and increase it if space permits.
What is cam jerk and why does it matter for high-speed applications?
Jerk is the rate of change of acceleration with respect to time (the third derivative of displacement). In cam design, jerk discontinuities cause sudden changes in the inertial forces acting on the follower, which excite vibrations in the follower system and produce noise, impact loading, and accelerated wear. Simple harmonic motion has infinite jerk at the transition points where acceleration changes instantaneously, making it unsuitable for high-speed applications. Cycloidal motion has finite jerk throughout the cycle, producing smoother operation at high speeds. Modified sinusoidal and modified trapezoidal motions offer even better jerk characteristics by carefully shaping the acceleration profile. For applications above approximately 1000 RPM, selecting a motion type with controlled jerk becomes essential for reliable operation and acceptable noise levels.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy