Presets
Playback
Mechanism
More slots means smaller steps and a shorter engaged phase fraction 1/2 - 1/n.
Model checks
The science
What is modelled
A crank of radius r = a sin(π/n) carries a pin that enters a radial slot of an n-slot wheel at centre distance a. The pin is engaged while the crank turns through π - 2π/n; the wheel advances by 2π/n and then rests, locked by the crank's disc. The 3D page shows the four-slot case (90 degrees of motion per revolution, 270 degrees of dwell); this page generalises to n slots.
Equations
- Follower angle:
φ = atan2(λ sinθ, 1 - λ cosθ), λ = r/a = sin(π/n). - Speed ratio:
dφ/dθ = λ(cosθ - λ)/(1 - 2λ cosθ + λ²); peak λ/(1 - λ) on the line of centres. - Acceleration ratio at pin entry:
|φ''| = tan(π/n)(a finite jump, hence a shock load).
Checks run in the page
- Engaged crank angle and the integrated index step.
- Peak speed ratio against the closed form.
- Entry acceleration against tan(π/n).
- Closure: n steps make one wheel turn, and the pin stays on the slot axis.
Rigid, frictionless parts; the torque readout is J · |φ''| ω² for the entered inertia.
What to try
- Go from 4 to 8 slots: the step halves and the shock at entry drops from tan 45 to tan 22.5 degrees.
- Raise the crank speed: the entry torque grows with the square of the speed.
- Watch the pin colour: yellow while engaged, red while the wheel is locked.