An indexing head — also called a dividing head — is a precision workholding fixture that rotates a workpiece by exact angular increments through a worm-and-wheel drive coupled to an index plate. It solves the problem of cutting evenly spaced features like gear teeth, splines, flutes, or bolt circles on a manual milling machine, where simple rotary tables cannot hold tight angular accuracy across many divisions. The 40:1 worm ratio means 40 turns of the crank equal one full revolution of the spindle, giving you 9° per crank turn and the ability to divide a circle into thousands of unique counts using selectable hole circles on the index plate.
How the Indexing Head (dividing Head) Works
The mechanism is a brass worm wheel — almost always 40 teeth — driven by a single-start steel worm on a hand crank. Turn the crank 40 times and the spindle rotates exactly once. That ratio is the foundation. To index, say, 24 gear teeth around a blank, you divide 40 by 24 and get 1 and 16/24 turns per tooth, which simplifies to 1 turn plus 16 holes on a 24-hole circle of the index plate. The sector arms set the count so you don't have to recount holes each time.
Why a worm-and-wheel? Because it's self-locking and gives huge mechanical reduction in a small envelope, and the wheel's teeth average out small errors so cumulative pitch error stays well under 1 arc-minute on a quality Brown and Sharpe or Cincinnati universal dividing head. If the worm-to-wheel backlash exceeds about 0.05 mm at the pitch line — usually from worn brass or an over-loose eccentric — your divisions drift and you'll see uneven tooth thickness on a finished gear. The fix is the engagement eccentric: most heads let you swing the worm out of mesh for direct indexing off a 24-hole plate on the spindle nose, then back into mesh and lock for normal indexing. Skip that re-engagement step and you can shear a worm tooth on the first cut.
For counts that won't divide evenly into 40 — like 127 teeth for a metric translation gear on an imperial lathe — you use differential indexing. Change gears between the spindle and the index plate make the plate itself rotate slightly as you crank, adding or subtracting the fractional turn you can't reach with plain indexing. Universal dividing heads also tilt 0–90° for helical milling and bevel gear blanks, with the spindle driven by the leadscrew through a gear train so the workpiece rotates as the table travels.
Key Components
- Worm and Worm Wheel (40:1): A single-start hardened-steel worm meshes with a 40-tooth bronze worm wheel pressed onto the spindle. The 40:1 ratio is the industry standard — 40 crank turns = 1 spindle revolution. Pitch-line backlash should sit under 0.05 mm; above that, indexing accuracy degrades visibly on gear-cutting work.
- Index Plate: A hardened steel disc with multiple concentric hole circles — common Brown and Sharpe sets carry 15, 16, 17, 18, 19, 20, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49 holes. The plunger pin drops into a hole to lock the crank between cuts. Plate flatness must hold within 0.02 mm or the plunger will bind.
- Sector Arms: Two adjustable arms on the index plate set to span the exact number of holes required between cuts. They eliminate manual hole-counting between every division, which is where 90% of operator errors happen.
- Spindle and Direct Index Plate: The spindle nose carries a 24-hole direct indexing plate for fast division of 2, 3, 4, 6, 8, 12, or 24. With the worm disengaged via the eccentric, you index directly off this plate — quick for hex bolt heads or 6-flute end mills.
- Tilting Body and Tailstock: On a universal head the body swings −5° to +95° for cutting bevel gears or angled splines. A matching tailstock with adjustable height supports long shafts; centre alignment must hold within 0.01 mm TIR or you'll cut tapered teeth.
- Change Gear Quadrant: Bolts to the rear of the head and carries the gear train linking spindle to index plate for differential indexing, or spindle to leadscrew for helical milling. Standard gear sets run 24, 28, 32, 40, 44, 48, 56, 64, 72, 86, 100 teeth.
Real-World Applications of the Indexing Head (dividing Head)
Anywhere a manual mill needs to make a circular pattern of identical features, the indexing head shows up. It's not just gear cutting — splines, ratchets, knurled grips, polygon turning, drilling bolt circles on flanges, and milling reamer flutes all run on the same fixture. You'll find dividing heads in toolrooms, prototype shops, watchmaker benches, and university machine-shop courses where students learn gear theory hands-on before they touch a CNC.
- Gear manufacturing: Cutting spur gears on a Bridgeport Series 1 mill using a Vertex BS-0 dividing head and an involute gear cutter — typical job is a 32-tooth, module 1.5 replacement gear for vintage machinery.
- Toolmaking: Milling flutes on end-mill blanks and reamers, where a Cincinnati universal dividing head holds the blank tilted at the helix angle while the spindle is geared to the table leadscrew.
- Aerospace prototyping: Drilling 24-hole bolt circles on titanium flange prototypes at companies like small turbine-engine R&D shops, where one-off parts don't justify CNC fixturing.
- Firearms and shooting sports: Cutting rifling-style flutes into bolt-action barrels and milling 6-groove or 8-groove patterns on revolver cylinders using a Sherline or Phase II dividing head on a benchtop mill.
- Watchmaking and clockmaking: Cutting fine-pitch wheels with 60–180 teeth on a watchmaker's lathe-mounted dividing attachment, like the Schaublin 70 with its 60-position direct index plate.
- Education: MIT's Pappalardo Lab and similar university shops use Brown and Sharpe heads to teach gear cutting and helical milling — the manual workflow forces students to understand the math behind division.
The Formula Behind the Indexing Head (dividing Head)
The plain-indexing formula tells you how many crank turns plus how many holes on which circle to advance for each cut. The interesting range is in the divisor N. At low N — say 4 to 12 divisions — you get whole or half crank turns and the math is trivial; the head is overkill but accurate. At nominal N around 20 to 60, you land on the sweet spot where the 40:1 ratio gives clean fractional moves on standard hole circles. Above N ≈ 50, more divisors fall outside what plain indexing can hit, and you start needing the high-count plate or differential indexing. The formula below is the daily driver — when it returns a fraction whose denominator doesn't match any available hole circle, that's your signal to switch to differential mode.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| T | Crank turns required per division (whole turns plus a fraction expressed as holes / hole-circle) | turns | turns |
| N | Number of equal divisions required around the workpiece | divisions | divisions |
| Rw | Worm-to-wheel ratio (40 on standard heads, 60 or 90 on some watchmaker heads) | dimensionless | dimensionless |
| θ | Angular advance per crank turn (= 360° / R<sub>w</sub>) | degrees | degrees |
Worked Example: Indexing Head (dividing Head) in a 27-tooth bronze worm gear blank
You are cutting a 27-tooth bronze worm gear on a Bridgeport Series 1 mill using a Vertex BS-1 dividing head with a 40:1 worm ratio and a Brown and Sharpe #2 index plate (21, 23, 27, 29, 31, 33 hole circles). You need to know exactly how to index between each tooth cut, and you want a feel for how the same head behaves at the low and high ends of typical division counts.
Given
- Rw = 40 ratio
- N = 27 teeth
- Available hole circles on plate #2 = 21, 23, 27, 29, 31, 33 holes
Solution
Step 1 — apply the plain indexing formula at the nominal job, N = 27:
The 27-hole circle is right there on plate #2, so this works directly: 1 full crank turn plus 13 holes on the 27-hole circle. Set the sector arms to span 13 holes (count 14 holes including the start hole) and you index every tooth identically. This is the sweet spot — the divisor matches an available hole circle exactly, so you never deal with awkward fractions.
Step 2 — check the low end of typical operating range, N = 6 (a hex bolt head):
Six full crank turns plus 12 holes on an 18-hole circle gives 60° per division. At this low N you'd actually disengage the worm and use the 24-hole direct index plate — one tooth on the direct plate every 4 holes is faster and just as accurate. The formula still works, it's just slow.
Step 3 — check the high end, N = 127 (the metric-conversion gear count):
127 is prime and doesn't share a factor with any standard hole circle. Plain indexing fails here. You'd switch to differential indexing, picking change gears (typically a 24:127 ratio approximation using a 40T and a compound train) so the index plate rotates slightly as you crank, making up the irrational fraction. This is where the universal head earns its name — and where a beginner without the change-gear chart will give up and order a CNC rotary table.
Result
For the 27-tooth worm gear, advance 1 full crank turn plus 13 holes on the 27-hole circle between each cut — the sector arms span 13 holes so you don't recount. At the low end (N = 6) the head is overkill but the math is trivial and you'd use direct indexing for speed; at the high end (N = 127) plain indexing fails entirely and you must set up differential change gears, which adds an hour to setup. If you cut the gear and find tooth-thickness variation above ±0.02 mm, the usual culprits are: (1) sector arms slipping between divisions because the friction screw wasn't tight, (2) the index plate not seated flat against its register face leaving a 0.1 mm wobble that telegraphs into every cut, or (3) a sticky worm-engagement eccentric that lets the worm walk axially under cutting load. Check the plate seating first — it's the most common and the easiest to miss.
Choosing the Indexing Head (dividing Head): Pros and Cons
A dividing head is one of three common ways to index a workpiece on a milling machine. The choice comes down to division count, accuracy, setup time, and how often you do the job. Here's how the indexing head stacks up against a plain rotary table and a CNC rotary indexer.
| Property | Indexing Head (40:1) | Plain Rotary Table | CNC Rotary Indexer |
|---|---|---|---|
| Indexing accuracy (typical) | ±30 arc-seconds with quality plate | ±2 arc-minutes reading the vernier | ±10 arc-seconds with closed-loop encoder |
| Maximum practical division count | Effectively unlimited via differential indexing | Limited by vernier readability — ~360 reliable divisions | Unlimited, software-defined |
| Setup time per job | 10–20 minutes (plate selection, sector arms) | 5 minutes (zero the vernier) | 30–60 minutes (program, wire, home) |
| Cost (new, mid-range) | $400–$1,500 for BS-0 to BS-2 | $200–$800 for an 8–12 inch table | $2,500–$8,000 for a closed-loop unit |
| Tilting / helical milling capability | Yes on universal head, 0–90° | No (horizontal only) | 4th-axis units only; tilt requires 5-axis |
| Operator skill required | High — must understand division math and plate selection | Low — read the dial | Medium — G-code and fixturing knowledge |
| Best fit | One-off and small-batch gear, spline, flute work | Simple bolt circles and arc milling | Production runs and complex multi-axis features |
Frequently Asked Questions About Indexing Head (dividing Head)
This is almost always backlash takeup direction. If you back the crank up to recover an over-shoot on one division and then forward on the next, the worm engages the wheel from opposite flanks and you eat 0.02–0.08 mm of pitch-line backlash on every direction reversal. Always approach each division from the same direction — if you overshoot, back off a quarter turn and creep forward to the hole.
The other suspect is the spindle thrust bearing. On older Brown and Sharpe heads the thrust washer wears and lets the spindle shift axially under cutting load, which shows up as a periodic error every full revolution. Pull the spindle, check axial play with a dial indicator — anything over 0.01 mm needs new thrust faces.
Use differential indexing when the divisor is prime or has factors that don't appear on any of your hole circles — 127, 101, 97, 73 are the classic offenders. A high-count plate (often 49 or 53 holes on the back side) covers a few more cases but won't help with primes above the highest hole count.
Rule of thumb: if 40/N produces a fraction whose denominator doesn't simplify to match a hole circle you own, and N is above 50, set up the differential gears. Below 50, you can usually find a workaround — for instance, N = 51 = 17 × 3, and 17-hole circles are common on a B&S #1 plate.
Size by maximum workpiece diameter and weight, not by mill size. BS-0 swings about 130 mm and is the right pick for watchmaking, small gears under 100 mm, and benchtop mills. BS-1 swings about 175 mm and is the sweet spot for a Bridgeport Series 1 — it handles 90% of toolroom gear work and still fits on a 9 × 42 inch table with room to traverse.
BS-2 swings 225 mm or more and gets heavy — over 40 kg. Only worth it if you're cutting gears above 150 mm regularly. The bigger head also shifts the workpiece higher off the table, which eats Z travel on a knee mill.
Three causes, in order of frequency. First, swarf in the hole — a single chip of bronze or steel from gear cutting falls onto the plate and the pin won't seat. Always brush or air-blast the plate before each session and keep a chip shield over it during cuts.
Second, plunger pin wear. The pin tip should be a precise taper; if it's rounded over or mushroomed from being slammed home, it can't enter a clean-edged hole. Replace it — they're cheap. Third, plate-to-spindle register surface contamination. If the plate isn't seated dead flat, the hole circle is no longer concentric with the crank and the pin tries to enter at an angle.
Almost certainly the change-gear ratio between the leadscrew and the dividing head spindle. The helix angle depends on the lead of the helix relative to table travel, which you set with the gear train on the quadrant. A 1° error usually traces to picking the wrong pair of compound gears — the available ratios are discrete, so most published helix-cutting charts give you the closest achievable angle, not the exact one.
Check the chart for the next ratio up or down. Also verify the leadscrew pitch on your specific mill — a Bridgeport Series 1 with an imperial leadscrew and a metric workpiece needs a translation gear in the train, and that's where errors creep in.
Yes, but only as a static indexing fixture, not for live polygon turning. Mount the head on the cross-slide or a dedicated bracket, lock the workpiece, take a flat cut, index, repeat. This works fine for cutting hex or square shanks on shafts up to the head's swing capacity.
True polygon turning — where the tool and workpiece rotate at coupled speeds to generate a polygon in one continuous cut — needs a geared polygon attachment, not a dividing head. The dividing head's worm is self-locking by design and won't run at coupled spindle speed.
References & Further Reading
- Wikipedia contributors. Indexing head. Wikipedia
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