Dividing Plate

Part of Gear Making

Making and using a dividing plate to accurately index gear blanks for consistent tooth spacing.

Why This Matters

The dividing plate (also called an indexing plate) is the most important tool for gear cutting. It is a disc with precisely drilled holes arranged in concentric circles, each circle containing a different number of equally spaced holes. By indexing from hole to hole, the gear blank is rotated by exactly the right angle for each tooth space — eliminating the cumulative error that builds up with compass-step methods alone.

With a dividing plate, a craftsman can divide a circle into any number of parts covered by the hole circles on the plate, and through simple gear ratios between the plate and the workpiece, can divide into many more numbers beyond what the plate circles directly cover. This is the pre-industrial solution to the precision division problem that every gear maker faces.

Making a dividing plate is itself a gear-making bootstrapping problem: the first plate must be made without the benefit of a plate. The solution is to make the first plate using geometric methods and iteration for a small number of commonly needed hole circles, then use that plate to make better plates with more circles. This bootstrapping approach is how the precision machine tool industry historically developed.

Dividing Plate Geometry

A dividing plate is a disc (typically 200–400 mm diameter, 10–20 mm thick, cast iron, brass, or hardwood for light use) with multiple concentric circles of drilled holes. Each circle contains a different number of evenly spaced holes.

A typical plate might have circles of: 24, 30, 36, 40, 48, 54, 60 holes. These numbers were chosen to cover common gear tooth counts through the indexing arithmetic (explained below).

The holes in each circle must be equally spaced in angle. The angular position of each hole is n × (360°/N) for n = 0, 1, 2, … N-1, where N is the number of holes in that circle.

Drilling the First Dividing Plate

The first plate is drilled using the compass-arm geometric method:

1. Mark the blank disc with center and pitch circles for each planned hole circle.
2. For the 24-hole circle: use the compass-step method to divide the pitch circle into 24 parts (using the chord calculation: chord = 2R sin(180°/24)). The iterative compass method, done carefully, achieves the ±0.1 mm accuracy needed.
3. Center-punch and drill each hole — typically 3–4 mm diameter, drilled through to the back face.
4. Verify by stepping around with the compass: the accumulated error after 24 holes should be less than 0.3 mm.
5. Repeat for each additional hole circle, using different pitch circle diameters to separate the circles.

For circles of 24, 30, 36 holes: compass-step methods work well (18 seconds step, 15 seconds step, 12 seconds step). For other numbers, use the chord calculation.

Using the Dividing Plate

The plate is mounted on a spindle that also holds the gear blank. An indexing pin (a spring-loaded pin or a manually inserted peg) engages the holes. To rotate the blank by the correct angle for each tooth:

Simple direct indexing. If the gear has N teeth, and the plate circle has exactly N holes, move the pin exactly one hole for each tooth. This is only possible when N matches a hole circle directly.

Plate-ratio indexing. If no hole circle matches N exactly, mount the plate on a worm-gear-reduced spindle so that the plate must be moved multiple holes for each tooth of the gear. The most common arrangement uses a 40:1 worm gear: one full revolution of the plate spindle = 40 teeth advanced on the gear.

With a 40:1 worm: holes moved per tooth = (40 × holes per circle) / N. For a 30-tooth gear using the 24-hole circle: 40 × 24 / 30 = 32 holes per tooth. Move 32 holes on the 24-hole circle for each tooth.

This requires checking that the result is a whole number — adjust the calculation if needed, or use a different hole circle.

Making the Sector Arms

Counting holes one by one for each tooth space is tedious and error-prone. Sector arms (two adjustable radial arms that straddle the correct number of holes) make the process faster and more reliable.

The sector arms are two flat strips hinged at the center. Set them to span exactly the correct number of holes per tooth (plus one, since you count the hole the pin is in as the starting position). Advance the pin from the last hole of one tooth cut to the first hole of the next — always to the leading edge of the sector. Then swing the sector forward to the new pin position. This completely eliminates hole-counting per tooth.

Sector arms can be made from flat sheet metal (brass or iron) with a center hole that fits over the plate spindle boss, and a locking friction screw to hold the angular setting.

Dividing Plate Accuracy and Errors

The accuracy of gears made with a dividing plate is limited by:

• The accuracy of the hole positions in the plate itself
• Any looseness or play in the indexing pin fit
• Any backlash in the worm drive (if used)
• The accuracy of the cutting setup (see metal gear cutting article)

For a well-made plate with holes within ±0.1 mm of true position on a 200 mm pitch circle, the angular error per tooth space is approximately ±0.1/100 × (360°/N per tooth) — negligibly small. The limiting factor in most hand-built systems is the gear cutting setup, not the plate accuracy.

Error check: After cutting all teeth, mesh the finished gear with a known-good gear and rotate slowly by hand. Listen and feel for cyclic irregularities — a tooth space that is slightly too wide or narrow will give a distinct catch or loose spot once per revolution. If found, compare the affected tooth to adjacent ones by measurement.

Expanding Coverage with a Basic Plate

A single plate with circles of 15, 16, 17, 18, 19, 20 holes (the prime-number and awkward-number circles) combined with a 40:1 worm gives access to gear tooth counts of any number from about 8 to 127 that can be expressed as a ratio with these denominators — which covers virtually all practical gear counts. The 17- and 19-hole circles are particularly useful because 17 and 19 are prime numbers not easily obtained by other means.