This calculator reports the ideal geometric step and input-rotation index/dwell fractions of a standard external Geneva mechanism. The adjustable cycle span is a reporting scale; one physical driver revolution is 360 degrees.
Indexing Motion Interactive Calculator
Explore standard external-Geneva step geometry and scale its index/dwell fractions over an entered reference cycle span.
Equation Used
- Standard external Geneva with N equally spaced radial slots and one driving pin.
- Ideal centre distance C and crank radius a satisfying a/C=sin(pi/N).
- The entered cycle angle is an abstract reference span used to scale the geometric phase fractions; the physical driver revolution remains 360 degrees.
- No pin/slot clearance, locking-disk geometry, undercut/interference, contact force, acceleration/jerk, inertia, torque, stress, wear, lubrication, backlash, manufacturing tolerance, speed or safety model.
For N equally spaced slots, a standard external Geneva has output step 360/N and ideal input engagement span 180−360/N degrees per 360-degree driver revolution. Values of the reference span other than 360 degrees merely scale those phase fractions; they are not a different physical driver revolution.
Standard external-Geneva geometry
A continuously rotating crank pin enters one radial slot, turns the star by exactly one station pitch, then leaves it for the dwell portion of the driver revolution. With N slots, the ideal crank-radius ratio is a/C=sin(pi/N).
The animation aligns a radial direction with the pin during the theoretical index interval. Its fixed slot lengths, wheel outline and omitted locking disks are schematic; they do not establish a buildable mechanism.
Use as an ideal phase-ratio check
The calculator can verify output pitch and the ideal index/dwell split for a textbook external Geneva. It cannot select a mechanism, determine attainable speed or accuracy, or establish loads and life.
One physical input revolution
For N slots, output step is 360/N degrees. The ideal input engagement span is 180−360/N degrees, so index fraction is 1/2−1/N and dwell fraction is 1/2+1/N.
The adjustable reference span Aref multiplies those fractions for reporting only. Set Aref=360 degrees to read the physical input-rotation angles directly.
Four-slot example
For N=4 and Aref=360 degrees, output step is 90 degrees, ideal index span is 90 degrees, dwell span is 270 degrees and index fraction is 25%. If Aref is changed to 720 degrees, the displayed spans double but the physical mechanism has not acquired a 720-degree driver revolution.
Limits of the phase calculation
These phase fractions do not determine speed, torque or service life. A working Geneva needs compatible pin, slot and locking geometry with sufficient clearance. Loads, inertia, contact forces and material strength require separate analysis.
Questions
Does station count alone determine safe speed?
No. Geometry, motion derivatives, inertia, loads, stiffness, clearance, lubrication and materials are required.
Is the dwell perfectly motionless in a real machine?
The ideal geometry has dwell, but real output motion and repeatability are affected by clearance, backlash, compliance and wear.
Can this formula be applied to a cam indexer or ratchet?
No. Their phase laws are defined by different geometry.
References & Further Reading
- Wikipedia contributors. Indexing (motion). Wikipedia
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