Presets
Playback
Driver and wheel
The crank turns at constant speed. While the pin is in a slot the wheel turns; for the rest of the revolution a locking disc holds it still (dwell). The pin enters tangentially, so the wheel starts and stops with zero speed.
Model checks
The science
What is modelled
A driver of crank radius r turns about the origin; the wheel centre is at distance A. With N slots the tangent-entry condition fixes r = A sin(π/N). While the pin is in a slot the wheel angle is the direction of the pin seen from the wheel centre.
Equations
φ(t) = atan2(r sin t, A + r cos t), engaged for a driver window ofπ - 2π/N.- Speed ratio
ωout/ωin = r (A cos t + r) / (A² + r² + 2 A r cos t). - Peak ratio
sin(π/N) / (1 - sin(π/N))(2.414 for four slots); moving fraction1/2 - 1/N.
Checks run in the page
- The indexing angle per revolution is 360/N.
- Zero wheel speed at engagement and release, and the closed form against a numerical derivative.
- The peak speed ratio for 3, 4, 6 and 8 slots.
- The moving share of each revolution.
Honest simplifications
Pure kinematics with a rigid pin and slot: no clearance, friction, impact loads or wear. The drawing of the locking disc and slots is schematic. Acceleration is large at entry, which is why real Geneva drives wear at high speed.
What to try
- Drag the scrub slider through one revolution and watch the speed ratio rise to its peak mid-stroke.
- Pick Three-slot: a long stroke, with a peak speed ratio of about 6.5 times the driver speed.
- Pick Eight-slot: a short stroke and a long dwell.