A two-member Curvic indexing coupling locates a rotary member at discrete tooth-aligned positions. Separate the faces before rotating, advance a whole number of tooth pitches, then re-engage and clamp. Enter a tooth count and a requested number of index steps to calculate angular travel and watch the face teeth separate, rotate and re-engage.
Curvic Coupling Indexing Interactive Calculator
Calculate tooth pitch and an integer-pitch index move. See the actual tooth count around an annular curved-tooth face, with a separate enlarged view of release and engagement.
Equation Used
- Equal angular spacing with an integer number of teeth.
- Index move is an integer number of tooth pitches.
- Rotation occurs only after separation; engagement occurs at a tooth-aligned orientation.
- No tooth-load, manufacturing-tolerance or clamp-capacity calculation.
Angular pitch is not accuracy or repeatability. Tooth contours, lift distance and timing are illustrative.
Curved face teeth, discrete angular positions
Gleason describes Curvic teeth as curved when viewed along the coupling axis, with mating concave and convex forms. They are face teeth distributed around an annulus. The drawing uses illustrative hourglass tooth outlines; manufacturing dimensions and grinding-wheel settings are not specified.
The circular view shows every entered tooth. The lower diagram is an enlarged sector of the engagement, with vertical clearance exaggerated. It is a side section, not a second straight-tooth coupling.
Separate, index, and clamp
For the simple two-ring arrangement, axial separation releases the teeth before the movable member rotates. Once the requested whole number of pitches is complete, the teeth align for re-engagement. The animation repeats this sequence and continues to the next position instead of jumping back after each move.
The explanatory cycle timing is not a machine cycle-time prediction. For moves exceeding a turn, the duration is lengthened to keep rotation visible.
Index-angle calculation
For N equally spaced teeth, the angular pitch is 360/N degrees. A move of k tooth pitches has an unwrapped angle k×360/N. Multiply the pitch in degrees by 3600 to express the same spacing in arcseconds.
There are N possible tooth-aligned orientations in a revolution. Repeating one selected step k does not necessarily visit them all: it visits N/gcd(N,k) distinct orientations. The result box reports all available positions, not the number reached by that repeated step.
72 teeth and one-pitch indexing
With 72 teeth, one pitch is 5 degrees, or 18,000 arcseconds. A one-pitch move advances 5 degrees; a seven-pitch move advances 35 degrees. Both finish at a tooth-aligned position.
A 72-pitch move makes one complete revolution. The unwrapped move remains 360 degrees even though the final angular orientation matches the starting orientation.
Spacing is not positioning accuracy
The tooth-count arithmetic does not determine repeatability, backlash, runout, stiffness or allowable torque. Those require tooth manufacture, mounting, loading and measurement information absent from these two inputs.
The illustrated ring outlines and enlarged section are explanatory geometry. Neither is a production tooth profile, clamp-force calculation or collision-clearance specification.
Indexing questions
Why must the ring lift before rotating?
The mating teeth constrain relative rotation while engaged.
Why show a separate enlarged section?
It makes the axial engagement sequence visible while the circular view preserves the annular curved-tooth form.
Does a small pitch mean equal accuracy?
No. Pitch is nominal spacing. Accuracy and repeatability require measurements and a complete design.
Can a move exceed one revolution?
Yes. The move result keeps complete revolutions; the final orientation is that angle modulo 360 degrees.
References
Gleason Works, Curvic Coupling Design, Gear Technology, November/December 1986, printed pages 34–35, for curved annular tooth form and indexing applications.
US4015487A, Index mechanism, background description of conventional two-member tooth-index coupling separation and integer-pitch indexing. This calculator shows that basic arrangement, not the patent’s differential three-member invention.
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