Calculate the ideal step and index/dwell fractions of an external Geneva from its slot count. An equally spaced multi-pin comparison flags overlapping engagement intervals; passing that check does not establish a physically compatible mechanism.
Intermittent Motion Interactive Calculator
Explore external-Geneva step angle, total index share and dwell share for ideal equally spaced driver pins.
Equation Used
- Standard external Geneva with N equally spaced radial slots.
- P driver pins are equally spaced and each pin produces one 360/N star step.
- Ideal crank-radius/centre-distance relation a/C=sin(pi/N).
- Reported multi-pin phase shares are physically meaningful only when P(1/2−1/N)<=1.
- No pin/slot and locking-disk interference beyond the phase-overlap check, clearance, backlash, contact ratio, acceleration/jerk, load inertia, torque, strength, wear, lubrication, speed, tolerances or safety model.
For N slots, one pin engages over input angle 180−360/N degrees, so its index fraction is 1/2−1/N—not 1/N except at N=4. With P equally spaced pins, total fraction is P(1/2−1/N) only while engagement windows do not overlap; P(1/2−1/N)>1 is not feasible in this ideal arrangement.
External-Geneva timing
For N slots, the ideal driver-pin engagement angle is 180−360/N degrees. During each engagement, the star advances one step of 360/N degrees. The rest of the input rotation is dwell.
The drawing uses a/C=sin(pi/N) and one radial direction follows the first pin during its index interval. Additional pins are displayed, but their separate indexing motions are not simulated. Slot lengths and locking geometry also remain schematic.
Use as an ideal geometry check
The outputs can check the textbook phase fractions and star step for a proposed slot and pin count. They cannot establish a buildable multi-pin layout, speed, accuracy, load capacity or service life.
One-pin fraction and multi-pin feasibility
One-pin index fraction is (180−360/N)/360=1/2−1/N. For P equally spaced pins with nonoverlapping windows, total index fraction is P times that value and total dwell is the complement.
If P(1/2−1/N)>1, engagement windows overlap and this ideal multi-pin interpretation is infeasible; the displayed share is capped at 100% rather than implying negative dwell.
Six-slot example
For N=6 and P=1, star step is 60 degrees, engagement spans 120 degrees of input, index share is 33.33%, dwell share is 66.67%, and dwell input angle is 240 degrees.
What the phase comparison does not establish
Nonoverlapping engagement intervals are only one requirement. A multi-pin Geneva also needs compatible pin, slot and locking geometry throughout the cycle. Loads, inertia, clearance and stiffness determine practical speed and accuracy; the phase percentages alone cannot establish them.
Frequently asked questions
Why does each pin’s engagement fraction depend on slot count?
For the standard external geometry, the driver engagement angle is 180−360/N degrees. Dividing by 360 gives 1/2−1/N.
Does nonoverlapping timing prove a multi-pin drive can be built?
No. The actual pins, slots and locking features can still interfere. The illustration does not simulate each additional pin’s index.
Does dwell angle guarantee usable process time?
No. Driver speed, settling, compliance, backlash and control timing are not included.
References & Further Reading
- Wikipedia contributors. Geneva drive. Wikipedia
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
