KEVOS® MAKEOS · Threads
Compound Indexing on a Dividing Head (Exact and Approximate Movements, Error at the Work)
Simple indexing cannot give the number of divisions I need. Which two-circle (compound) movement on my index plates gives it exactly, or, if none does, which approximate movement over several workpiece revolutions comes closest, and how large is the error at my workpiece diameter?
Indexing movements for a plain dividing head with Brown & Sharpe plates 1–3 or the two-sided Cincinnati standard plate, by the method the handbook describes: simple indexing when a hole circle divides the crank turns exactly, compound indexing (two movements on two circles of the same plate, added or subtracted) when that is exact, and otherwise approximate compound movements that fill in the divisions over several workpiece revolutions. Each movement is given with the precise number of divisions it produces, the handbook’s measure of closeness (the diameter at which the error equals 0.001) and the error at your workpiece diameter against the error you accept. A movement taken from an indexing table can be checked the same way.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Show | choice | Search for the best movements for the number of divisions, or check one movement read from an indexing table. |
| Job | ||
| Number of divisions wanted | divisions | Number of equally spaced divisions (teeth, flutes, holes) wanted around the work. |
| Worm ratio (crank turns per spindle turn) | :1 | Crank turns for one turn of the spindle; 40 for most plain dividing heads. |
| Index plates on the head | choice | The standard index plates available: Brown & Sharpe plates 1–3 (six circles each) or the Cincinnati standard plate (eleven circles on each side). Compound movements use two circles of the same plate or side. |
| Most workpiece revolutions accepted for an approximate movement | rev | Approximate movements fill in the divisions over several revolutions of the work; more revolutions give closer approximations but longer, more error-prone indexing. |
| Accuracy | ||
| Workpiece diameter (pitch diameter for a gear) | mm | Diameter at which the position error matters, normally the pitch diameter of a gear or the diameter of the feature being divided. |
| Position error accepted at that diameter | mm | Largest position error at that diameter you accept from an approximate movement. |
| Movement to check | ||
| Whole turns of the crank | turns | Whole turns of the crank in each indexing movement. |
| Holes moved on the first circle | holes | Holes moved on the first (crank pin) circle. |
| Holes in the first circle | holes | Number of holes in the first circle. |
| Second movement | choice | Whether the second movement is in the same direction (added) or the opposite direction (subtracted). |
| Holes moved on the second circle | holes | Holes moved on the second (stationary pin) circle, moving plate and crank together. |
| Holes in the second circle | holes | Number of holes in the second circle. |
| Workpiece revolutions for the full set of divisions | rev | Revolutions the work makes before all divisions are cut, as listed beside the movement in the table. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Show
- What it is
- Whether to search for the best movements or to check one movement from an indexing table.
- Units and format
- Choose one of 2 options from the list: Best movements for the number of divisions; Check a movement taken from a table.
- Example
- The form opens with “Best movements for the number of divisions” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Search lists the best movements; check reports only the movement you enter.
- Get it right
- Search first; use the check to confirm a movement someone has written on the job card.
Job
What this means: Number of divisions wanted
- What it is
- Number of equally spaced divisions wanted around the work, such as gear teeth or flutes.
- Units and format
- Enter a number in divisions: divisions. The form accepts 2 divisions to 1000 divisions. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 127 divisions as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the crank movement per division; prime numbers above 50 rarely index simply.
- Get it right
- Count the teeth or features on the drawing, not the spaces between them.
What this means: Worm ratio (crank turns per spindle turn)
- What it is
- Crank turns for one turn of the dividing head spindle (the worm ratio).
- Units and format
- Enter a number in :1: a ratio to one (type 3 for 3:1). The form accepts 1 :1 to 200 :1. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 :1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Scales every crank movement.
- Get it right
- Most plain dividing heads are 40:1; some are 60:1 or 5:1. It is stamped on the head or in its manual.
What this means: Index plates on the head
- What it is
- Which standard index plates are available on the dividing head.
- Units and format
- Choose one of 2 options from the list: Brown & Sharpe standard plates 1, 2 and 3; Cincinnati standard plate, sides 1 and 2.
- Example
- The form opens with “Brown & Sharpe standard plates 1, 2 and 3” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Sets the hole circles searched; compound movements use two circles of the same plate or side.
- Get it right
- Brown & Sharpe heads have plates 1, 2 and 3; Cincinnati heads have one two-sided standard plate.
What this means: Most workpiece revolutions accepted for an appr…
- What it is
- Most revolutions of the work you accept before all divisions are cut.
- Units and format
- Enter a number in rev: rev. The form accepts 1 rev to 30 rev. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 13 rev as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More revolutions allow closer approximations.
- Get it right
- Keep it low for manual indexing: each revolution adds a full set of movements and chances of a miscount.
Accuracy
What this means: Workpiece diameter (pitch diameter for a gear)
- What it is
- Diameter at which the position error matters, usually the pitch diameter of the gear.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The error of an approximate movement grows in direct proportion to the diameter.
- Get it right
- For a gear use the pitch diameter; for holes or slots use the diameter they sit on.
What this means: Position error accepted at that diameter
- What it is
- Largest position error at that diameter you accept from an approximate movement.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.01 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the accuracy check and the choice of revolutions.
- Get it right
- Take a small share of the spacing tolerance on the drawing, since the cutting adds its own errors.
Movement to check
What this means: Whole turns of the crank
- What it is
- Whole turns of the crank in each indexing movement of the movement being checked.
- Units and format
- Enter a number in turns: a number of turns. The form accepts 0 turns to 200 turns. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 turns as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Adds whole turns to the movement per division.
- Get it right
- In tables a movement such as 7 41/47 means 7 whole turns and 41 holes in the 47 circle.
What this means: Holes moved on the first circle
- What it is
- Holes moved on the first circle, the circle the crank pin follows.
- Units and format
- Enter a number in holes: holes. The form accepts 0 holes to 400 holes. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 42 holes as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the first fractional part of the movement.
- Get it right
- Count from the hole the pin is in as hole zero, as the handbook describes.
What this means: Holes in the first circle
- What it is
- Number of holes in the first circle used by the crank pin.
- Units and format
- Enter a number in holes: holes. The form accepts 2 holes to 400 holes. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 47 holes as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the size of each hole step on the first circle.
- Get it right
- Read it from the plate; it must be one of the circles on the plate mounted.
What this means: Second movement
- What it is
- Whether the second movement is in the same direction as the first or the opposite one.
- Units and format
- Choose one of 2 options from the list: Added (positive compounding); Subtracted (negative compounding).
- Example
- The form opens with “Added (positive compounding)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Adds or subtracts the second fractional movement.
- Get it right
- Tables show a plus sign for positive and a minus sign for negative compounding.
What this means: Holes moved on the second circle
- What it is
- Holes moved on the second circle, the one followed by the stationary pin.
- Units and format
- Enter a number in holes: holes. The form accepts 0 holes to 400 holes. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 holes as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the second fractional part of the movement.
- Get it right
- For this movement the crank and plate turn together while the stationary pin is out.
What this means: Holes in the second circle
- What it is
- Number of holes in the second circle used by the stationary pin.
- Units and format
- Enter a number in holes: holes. The form accepts 2 holes to 400 holes. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 39 holes as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the size of each hole step on the second circle.
- Get it right
- Use a circle on the same plate as the first; enter any circle when there is no second movement.
What this means: Workpiece revolutions for the full set of divis…
- What it is
- Revolutions the work makes before all the divisions of the checked movement are cut.
- Units and format
- Enter a number in rev: rev. The form accepts 1 rev to 50 rev. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 rev as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The precise number of divisions is the worm ratio times this, divided by the movement.
- Get it right
- Tables list it beside each approximate movement; exact movements need one revolution.
Method and formulas
- Crank movement per division for an exact result = worm ratio × R ÷ N, where R is the number of workpiece revolutions (1 for exact movements).
- Simple indexing is exact when worm ratio × circle ÷ N is a whole number of holes; the circle with the fewest holes to count is preferred.
- A compound movement is w + a ÷ A ± b ÷ B crank turns, with A and B two circles of the same plate; the movement for each circle pair is searched hole by hole.
- Precise number of divisions N′ = worm ratio × R ÷ (w + a ÷ A ± b ÷ B); R must have no factor in common with N so the later revolutions fill the spaces left by the earlier ones.
- Diameter at which the error equals 0.001 = 0.001 N ÷ (π |N − N′|), which reproduces the handbook table; error at a diameter d = (d ÷ that diameter) × 0.001 = π d |N − N′| ÷ N.
- Example: 127 divisions with a 40:1 head has no exact movement on the Brown & Sharpe plates; the handbook’s movement 42/47 + 2/39 over 3 revolutions gives 127 divisions and an error of 0.0058642 mm at 200 mm.
Limitations
- Compound indexing needs an index plate able to turn on the worm shaft and a stationary pin on the head frame; the second movement turns crank and plate together.
- In negative compounding take up the worm backlash by backing off a few holes before each movement.
- Only the standard plates are searched; the Cincinnati high-number plates and differential indexing (the differential indexing tool) are other ways to reach divisions simple indexing cannot.
- The error measure is the handbook’s; it describes how far the last division misses after the full set of movements.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Index a prime or awkward number of divisions without differential change gears
- Choose between approximate movements by the error they leave at the workpiece
- Check a movement taken from an indexing table before cutting
Who it is for
- Machinists
- Toolmakers
- Gear cutters
What you get
- Simple indexing movement when one is exact
- Exact compound movement when one exists
- Best approximate movement for each number of workpiece revolutions
- Precise number of divisions of each movement
- Diameter at which the error equals 0.001
- Position error at your workpiece diameter
Interpreting the result
- Prefer simple indexing, then an exact compound movement, then the approximation with the fewest workpiece revolutions that meets your accuracy: every extra revolution adds movements and chances of a miscount.
- For an approximate movement, the error grows in proportion to the diameter: a movement good enough for a small gear can be too coarse for a large one.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2079–2086. Topic reference; no source tables or recommended settings are reproduced.
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