Dividing Head Converter

The Dividing Head Converter calculates indexing turns and hole selections for equal divisions on milling machine dividing heads.

About the Dividing Head Converter

A dividing head converts a fixed amount of crank motion into precise rotation at the spindle. The usual worm gear ratio is 40 to 1, but some heads use 60 to 1 or other values. That fixed ratio allows you to index to any angle or to split a circle into equal divisions.

This converter bridges your design intent and the hardware at your mill. Enter the number of divisions or the angle you need. The tool suggests suitable hole circles and the holes to move each time. If a simple index will not work, it points to differential indexing or angular indexing as a backup.

Because shop setups vary, you can choose plate sets, ratio, and movement direction. The converter’s output includes whole turns, hole counts, and suggestions for sector arm positions. It also flags backlash concerns and gives notes on approaching holes from one side only.

How the Dividing Head Method Works

A crank turns the worm. The worm turns the worm wheel attached to the spindle. This multiplies precision by the gear ratio. For most heads, one crank revolution rotates the spindle by one-fortieth of a revolution, or nine degrees.

• Simple indexing uses fixed hole circles in the index plate. You move the crank by a set number of holes each step.
• One crank revolution equals 1 divided by the worm ratio at the spindle, so 1/40 of a turn for a 40 to 1 head.
• To make N equal divisions, you need a spindle rotation of 1/N per step. Translate that into crank turns.
• Sector arms frame the number of holes you move each time to reduce counting errors.
• Differential indexing gears the index plate to the worm. The plate moves slightly as you crank, enabling divisions simple indexing cannot reach.
• Angle indexing treats the target as degrees instead of divisions. Convert angle to crank turns and then to holes.

With the right hole circle, the crank move becomes whole turns plus a fraction of a turn. That fractional part converts to a whole number of holes on a chosen circle. When no circle fits, you either use differential indexing or split the move into mixed turns and partial-hole moves carefully controlled by a gear train.

Dividing Head Formulas & Derivations

All indexing starts from the worm ratio, R. For most shop heads, R is 40. Some are 60. The basic quantities are the number of divisions N, the angle A in degrees, and the selected index plate hole count P. From these, you compute crank turns and hole moves.

• Turns per division for equal spacing: Turns = R divided by N. Derivation: You need 1/N of a spindle turn. One crank turn makes 1/R of a spindle turn. So crank turns = (1/N) divided by (1/R) = R/N.
• Angle indexing: Turns for angle A degrees: Turns = R times A divided by 360. Derivation: A/360 is the fraction of a circle. Multiply by R to convert to crank turns.
• Simple indexing with a plate: If the required Turns is T, choose a hole circle with P holes and express T as whole turns plus h/P. That is, T = t + h/P. Then each step is t full turns plus h holes on the P-hole circle.
• Alternate fractions: If T has a fractional part f, find P such that P × f is an integer h. Use the smallest P available that makes h an integer to minimize counting error.
• Differential indexing (conceptual): If no P yields integer h, a gear train rotates the index plate during cranking. The effective fraction becomes f adjusted by the plate motion. Manuals express this as adding or subtracting a small correction term linked to the gear ratio and the chosen hole circle. The sign depends on the train direction.
• Angular resolution: One hole on a P-hole circle equals (1/P) of a crank turn, which equals (1/P) × (1/R) of a spindle turn. In degrees at the spindle, that is 360 divided by (P × R) degrees per hole.

These relations let you mix whole turns and hole counts with confidence. When the converter flags differential indexing, it gives a gear train ratio target and notes on plate rotation direction. Always verify the sign and direction with a test mark before cutting.

What You Need to Use the Dividing Head Converter

Before you start, gather a few details about your head and plates. This ensures the options shown match what you can do in your shop. You can also add notes about preferred circles or movement direction if your setup is constrained.

• Worm ratio R (commonly 40 or 60).
• Target: number of divisions or gear teeth N, or a specific angle A in degrees.
• Available index plate hole circles P (for example: 15, 16, 17, 18, 19, 20, and so on).
• Simple indexing or differential indexing selection.
• Direction of approach and backlash preference (always advancing or always backing into position).

The calculator handles ranges from 2 divisions up to several hundred. Edge cases include prime numbers that are not factors of your hole circles and very small angles. For those, expect the output to suggest differential indexing or a different plate. If your head uses uncommon plates, check that P values in the tool match your set.

How to Use the Dividing Head Converter (Steps)

Here’s a concise overview before we dive into the key points:

1. Select the worm ratio for your head from the ratio options.
2. Enter either the number of divisions or the exact angle you need.
3. Choose your available index plate hole circles, or pick a standard set.
4. Decide on simple indexing first; enable differential indexing only if needed.
5. Generate the output and review the suggested whole turns and hole counts.
6. Read the notes on approach direction, sector arm spacing, and backlash control.

These points provide quick orientation—use them alongside the full explanations in this page.

Example Scenarios

Cutting a 24-tooth spur gear on a 40 to 1 head. You need N = 24 equal divisions. Turns per division = R/N = 40/24 = 1 + 16/24 = 1 + 2/3 of a turn. Choose an 18-hole circle so 2/3 of a turn equals 12 holes, or a 15-hole circle where 2/3 equals 10 holes. The converter’s output may say: move 1 full turn plus 10 holes on the 15-hole circle each tooth, approach in one direction. What this means: set the sector arms 10 holes apart on the 15 circle, make 1 turn plus 10 holes between each cut.

Drilling 57 equally spaced holes around a flange. With a 40 to 1 head, Turns = 40/57, which cannot be expressed as t + h/P using common circles. The converter flags this and offers differential indexing with a suggested gear ratio and a suitable P. If your shop has a 60 to 1 head, the alternate option is Turns = 60/57 = 1 + 1/19, which works on a 19-hole circle as 1 turn plus 1 hole. What this means: either use a differential train on the 40 to 1 head as instructed, or switch to a 60 to 1 head and index 1 turn plus 1 hole on the 19 circle.

Accuracy & Limitations

Indexing accuracy depends on the worm gear, the plate, and your technique. The converter assumes ideal plate hole spacing and zero backlash unless you choose the backlash option. Real machines need consistent approach and careful locking.

• Backlash in the worm and gears can shift positions if you overshoot a hole and reverse.
• Index plate hole spacing has manufacturing tolerance; errors can accumulate over many steps.
• Differential indexing adds a gear train. Each gear adds small clearance and potential error.
• Thermal changes and clamping forces can slightly twist long workpieces.
• Rounded fractional recommendations can produce small residual angle errors if you ignore notes.

To improve results, always approach the mark from the same direction, keep the sector arms tight, and lock the spindle before cutting. For critical parts, scribe a test circle, index a few positions, and measure the spacing before you commit.

Units Reference

Indexing blends angle and rotation. You will see divisions, turns, holes, and degrees in the same plan. The table below shows how these units relate, so you can read the results and convert between them as needed.

Use R and N to find crank turns, then pick a P that turns the fractional part into whole holes. When the tool shows degrees, remember that 1 degree equals 60 minutes and 1 minute equals 60 seconds, which the converter expands automatically when helpful.

Tips If Results Look Off

If the numbers you see do not match your plate or seem hard to follow, you likely chose a hole circle that is not in your set or you rounded too early. The notes field highlights these issues, but you can also check the following.

• Confirm your worm ratio on the nameplate; 60 to 1 heads are common in some regions.
• Verify the exact hole counts on your plates; sets differ by maker.
• Try another hole circle that yields smaller hole moves and reduces counting error.
• Switch to angle indexing if it gives a cleaner move for your setup.
• For primes and large N, enable differential indexing and follow the gear-train suggestion.

Make a dry run with a felt-tip mark on a scrap part. Index five steps, then measure the chord distances. If they match evenly, you are ready to cut.

FAQ about Dividing Head Converter

Can I use this for any brand of dividing head?

Yes. Enter your worm ratio and available plates. The math is brand-agnostic, and the output adapts to your hole circles.

What if I only know the angle, not the number of divisions?

Use angle indexing. The converter multiplies your angle by the worm ratio and returns crank turns and hole moves.

Do I need differential indexing often?

Only when simple indexing cannot produce an integer hole move, such as with many prime division counts. The tool will tell you.

How do I handle backlash?

Always approach the hole from the same direction, set sector arms tight, and lock the spindle before cutting. The notes remind you of this.

Dividing Head Terms & Definitions

Dividing Head

A fixture that rotates a workpiece by precise increments using a worm gear and an index plate, often mounted on a milling machine.

Worm Ratio

The number of crank turns required for one full spindle revolution, commonly 40 or 60.

Simple Indexing

A method using only the index plate holes and the worm ratio to step the crank by whole turns plus a fixed number of holes.

Differential Indexing

A method that gears the index plate to the crank, letting the plate rotate slightly during cranking to achieve otherwise impossible divisions.

Index Plate

A disk with concentric circles of holes used to define precise fractions of a crank turn.

Sector Arms

Adjustable arms that enclose the required number of holes so the operator can repeat the same count without mistakes.

Backlash

Free play between mating gears and screws that can cause position error if motion reverses during a move.

Crank

The hand lever or handle connected to the worm shaft, turned by the operator to index the work.

Sources & Further Reading

Here’s a concise overview before we dive into the key points:

• Wikipedia: Dividing head overview and principles
• Wikipedia: Indexing in machining, including simple and differential methods
• Wikipedia: Worm drive fundamentals and ratios
• Wikipedia: Gear cutting methods and setups
• Wikipedia: Milling operations and tooling context for dividing heads

These points provide quick orientation—use them alongside the full explanations in this page.