A cam converts pure rotation into a prescribed reciprocating motion at the follower. The cam's edge profile, expressed as radius r(θ) measured from the rotation axis, is designed so the follower traces exactly the displacement diagram s(θ) the machine needs — this cam uses a classic 4-stroke cycle: dwell (0–90°, follower at rest on the base circle), rise (90–180°, follower lifts by L), dwell (180–270°, follower held at full lift), fall/return (270–360°, follower drops back to the base circle).
Within the rise and fall strokes, the motion law — how displacement varies with angle — determines the follower's velocity and acceleration profile, which in turn determines vibration, noise, wear and the spring force needed to keep the follower in contact with the cam at speed:
Let x = (θ − θ_start) / β, β = stroke angle (90° here), L = lift
Uniform velocity: s = L·x — constant velocity, but
acceleration jumps to
±∞ at both ends (shock)
Simple harmonic: s = L/2·(1 − cos(πx)) — smooth, but nonzero
(SHM) acceleration at the
stroke's start/end
Cycloidal: s = L·(x − sin(2πx)/2π) — zero displacement,
velocity AND
acceleration at both
ends: the smoothest,
most widely used law
for high-speed cams
- Motion-law buttons — pick which law governs the rise and fall strokes; the cam's physical profile is rebuilt immediately from r(θ) = base circle + L·(law-specific fraction).
- Cam speed (RPM) — angular velocity ω of the cam shaft; θ = ω·t sets how fast the profile sweeps past the follower.
- Lift L / Base circle radius — the two defining dimensions of the profile, redrawn live.
- Readouts — displacement s(t) is read directly off the rotating profile; velocity and acceleration are the live numerical derivatives ds/dt and d²s/dt², matching what a real accelerometer on the follower would report.
Real-world relevance: this exact mechanism — plus the SHM/cycloidal trade-off — governs the intake/exhaust valve trains in most piston engines, indexing tables, textile looms and packaging machinery.