This calculator performs the simple-indexing arithmetic for an ideal worm dividing head. It reports the crank advance required per equal spindle division and the corresponding pitch on one entered hole circle.
Indexing Head Interactive Calculator
Explore ideal simple-indexing turns, whole turns, fractional hole-circle pitch and spindle step angle.
Equation Used
- Ideal worm reduction R:1 with no backlash, pitch error or compliance.
- N equal spindle divisions around 360 degrees.
- The entered hole circle contains H equally spaced holes and the crank plunger starts exactly in a hole.
- The required hole pitch must be an exact integer for the selected circle. Use the compatibility message rather than rounding the displayed decimal.
- No direct, compound or differential indexing, change gears, helical milling, workholding, cutting force, collision, strength, accuracy or safety model.
A physical plunger can land only on a hole. The displayed required hole pitch must therefore be an integer on the selected circle; a fractional result means that circle cannot execute the requested simple index. Differential or compound indexing is not calculated.
Ideal simple indexing
An R:1 worm head requires R crank turns for one spindle revolution. Dividing the spindle into N equal positions therefore requires R/N crank turns per index.
The schematic illustrates one crank advance and the corresponding 360/N spindle step. The wheel teeth and plate layout are symbolic; the drawing does not model worm contact or plunger engagement.
Use as a setup-arithmetic check
The result can help translate an already verified worm ratio and desired division count into an ideal crank move. It does not confirm that the selected plate can make the move, except by exposing whether the required hole pitch is integral.
Whole turns plus hole pitch
Let T=R/N. The crank advance is floor(T) whole turns plus frac(T) of a turn. On an H-hole circle, that fraction requires H frac(T) hole pitches.
If the pitch is not an integer, the plunger cannot land on a hole of that circle. Choose a compatible circle or use a separately designed compound or differential setup.
27-division example
With R=40, N=27 and H=27, T=40/27=1+13/27 turns. The move is one whole crank turn plus 13 hole pitches, and ideal spindle step is 13.333 degrees.
With H=24 instead, the required pitch is 11.556 holes, so that selected circle cannot perform the simple index.
What arithmetic cannot establish
Use the actual head ratio and available plate circles, following the manufacturer’s instructions for counting and backlash. An integer hole count establishes only the ideal angular move. It does not establish workholding, cutter clearance, machine capacity or finished-part accuracy.
Questions
Can I round a fractional hole pitch?
No. Rounding creates cumulative angular error.
Does the calculator perform differential indexing?
No. It does not calculate change gears or plate rotation.
Does exact arithmetic guarantee part accuracy?
No. Worm and plate error, backlash, setup, workholding, cutter position and machine condition still matter.
References & Further Reading
- Wikipedia contributors. Indexing head. Wikipedia
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