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Cam-Follower Harmonic Motion Kinematics Calculator

Cam-and-follower mechanisms in internal combustion engines, automation indexing tables, and packaging machinery convert constant camshaft rotation into controlled reciprocating follower motion.

Total linear displacement during the rise event (typically 5 to 50 mm).

Camshaft rotation angle over which the full lift occurs (typically 60° to 120°).

Operating rotational velocity of the camshaft.

Total mass of the reciprocating assembly (follower, pushrod, spring half-mass).

Calculated Result
789.6 m/s²

Peak Follower Acceleration

Max Follower Acceleration

789.6 m/s² (80.5 g)

Peak Dynamic Inertia Force

671.1 N

Max Follower Velocity

3.14 m/s

Cam Rise Stroke Duration

12.5 ms

Cam Rotational Speed

1200 RPM

Calculation Breakdown

  1. Simple Harmonic Motion Rise ProfileLift h = 25 mm, Rise Angle β = 90°, ω = 2π × 1200 / 60 = 125.7 rad/s
  2. Peak Harmonic Acceleration & Follower Inertiaa_max = (π² × h × ω²) / (2 × β²) = 789.6 m/s² (80.5 g) → F = m × a = 671.1 N

Cam Dynamics Metrics

Interactive visualization based on your current inputs

Value
0.017345067Lift (mm)Max Vel (m/s)Max Accel (g/10)Inertia Force (N/10)Rise Time (ms)ParameterValue

What Is the Cam-Follower Harmonic Motion Kinematics Calculator?

The Cam-Follower Harmonic Motion Kinematics Calculator calculates velocities, accelerations, and inertia forces for reciprocating cam followers.

How Does the Cam-Follower Harmonic Motion Kinematics Calculator Work?

It converts camshaft RPM into angular velocity (rad/s) and evaluates the first and second time derivatives of the simple harmonic rise profile.

Cam-Follower Harmonic Motion Kinematics Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

V_{max} = \frac{\pi h \omega}{2 \beta}, \quad a_{max} = \frac{\pi^2 h \omega^2}{2 \beta^2}, \quad F_{in} = m \cdot a_{max}

Simple harmonic rise kinematics relating angular cam velocity to linear reciprocating derivatives.

How to Use the Cam-Follower Harmonic Motion Kinematics Calculator

  1. Enter follower total lift stroke in mm.
  2. Specify the rise angle of rotation in degrees.
  3. Input operating camshaft RPM and reciprocating follower mass.

Step-by-Step Example Calculation

1,200 RPM Automation Cam Profile

Input Values:

camLiftStrokeMm:25
riseAngleDeg:90
camRotationalSpeedRpm:1200
followerMassKg:0.85
Worked Steps: Generates 3.14 m/s max velocity, 789.6 m/s² (80.5 g) max acceleration, and 671.1 N peak inertia force.

Understanding Your Result

Max Follower Velocity: Peak speed reached at the midpoint of the lift stroke.

Max Acceleration: Peak acceleration occurring at the beginning and end of rise.

Peak Inertia Force: Dynamic load exerted on cam profile and return spring.

Factors That Affect the Result

  • Narrower rise angles β compress the event into fewer degrees, sharply elevating acceleration.
  • Follower mass directly scales the dynamic inertial load.

When Should You Use This Calculator?

  • Automotive valve trains, industrial pick-and-place arms, textile machinery, and high-speed indexing.

Assumptions & Limitations

  • Assumes rigid follower assembly and pure Simple Harmonic Motion without profile fabrication deviation.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Based on Norton Design of Machinery and Shigley Mechanical Engineering Design principles.

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