BIZOMAT MAKEOS · Quality
Polar Hole Position Check (Nominal X–Y from Radius and Angle, Position Error, Bonus Tolerance)
For holes dimensioned by radius and angle and measured in X and Y, how far is each hole from its true position, and does it pass with the bonus tolerance from its size?
Inspection of up to four holes dimensioned in polar coordinates: the nominal X and Y of each hole from its radius and angle (as the polar coordinates tool), the distance from nominal to the measured centre (as the distance between two points tool), the position error as a diameter, and the position tolerance allowed at the measured hole size including bonus tolerance from maximum material condition, with the hole size checked against its limits.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of holes | holes | Number of holes to check. |
| Hole 1 | ||
| Nominal radius | mm | Radius of hole 1 from the datum centre. |
| Nominal angle from +X | ° | Angle of hole 1 from +X, anticlockwise. |
| Measured X | mm | Measured X of hole 1. |
| Measured Y | mm | Measured Y of hole 1. |
| Measured hole diameter | mm | Measured diameter of hole 1. |
| Hole 2 | ||
| Nominal radius | mm | Radius of hole 2. |
| Nominal angle from +X | ° | Angle of hole 2. |
| Measured X | mm | Measured X of hole 2. |
| Measured Y | mm | Measured Y of hole 2. |
| Measured hole diameter | mm | Measured diameter of hole 2. |
| Hole 3 | ||
| Nominal radius | mm | Radius of hole 3. |
| Nominal angle from +X | ° | Angle of hole 3. |
| Measured X | mm | Measured X of hole 3. |
| Measured Y | mm | Measured Y of hole 3. |
| Measured hole diameter | mm | Measured diameter of hole 3. |
| Hole 4 | ||
| Nominal radius | mm | Radius of hole 4. |
| Nominal angle from +X | ° | Angle of hole 4. |
| Measured X | mm | Measured X of hole 4. |
| Measured Y | mm | Measured Y of hole 4. |
| Measured hole diameter | mm | Measured diameter of hole 4. |
| Tolerances | ||
| Position tolerance at MMC (diameter) | mm | Diameter of the position tolerance zone at maximum material condition. |
| Smallest hole size (MMC) | mm | Smallest allowed hole size. |
| Largest hole size (LMC) | mm | Largest allowed hole size. |
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: Number of holes
- What it is
- How many of the four hole entries the tool checks, starting from hole 1. Entries beyond this number are ignored.
- Units and format
- Enter a number in holes: holes. The form accepts 1 holes to 4 holes. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 holes as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Fill the holes in order from hole 1; a hole entered as hole 4 is skipped if this is set to 3.
Hole 1
What this means: Nominal radius
- What it is
- The radius from the datum centre to the true position of hole 1, as dimensioned on the drawing (half the pitch circle diameter for holes on a circle).
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the radius, not the pitch circle diameter.
What this means: Nominal angle from +X
- What it is
- The angle on the drawing from the positive X axis to hole 1, measured anticlockwise about the datum centre.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Make sure the measuring machine’s X axis and angle direction match the drawing’s.
What this means: Measured X
- What it is
- The X coordinate of the measured centre of hole 1, from the datum centre, as reported by the measuring machine or found by inspection.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50.02 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure from the same datum origin and orientation as the nominal positions.
What this means: Measured Y
- What it is
- The Y coordinate of the measured centre of hole 1, from the datum centre.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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.
- Get it right
- Keep the sign: below the X axis is negative.
What this means: Measured hole diameter
- What it is
- The measured diameter of hole 1, checked against the size limits and used for the bonus tolerance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.05 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger hole within its limits adds bonus tolerance equal to its size above MMC.
- Get it right
- Use the actual mating size (largest pin that fits) where possible, not a single two-point reading.
Hole 2
What this means: Nominal radius
- What it is
- The radius from the datum centre to the true position of hole 2, as dimensioned on the drawing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the radius, not the pitch circle diameter.
What this means: Nominal angle from +X
- What it is
- The angle on the drawing from the positive X axis to hole 2, measured anticlockwise about the datum centre.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Make sure the measuring machine’s X axis and angle direction match the drawing’s.
What this means: Measured X
- What it is
- The X coordinate of the measured centre of hole 2, from the datum centre.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -0.015 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure from the same datum origin and orientation as the nominal positions.
What this means: Measured Y
- What it is
- The Y coordinate of the measured centre of hole 2, from the datum centre.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50.02 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign: below the X axis is negative.
What this means: Measured hole diameter
- What it is
- The measured diameter of hole 2, checked against the size limits and used for the bonus tolerance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.04 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger hole within its limits adds bonus tolerance equal to its size above MMC.
- Get it right
- Use the actual mating size where possible, not a single two-point reading.
Hole 3
What this means: Nominal radius
- What it is
- The radius from the datum centre to the true position of hole 3, as dimensioned on the drawing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the radius, not the pitch circle diameter.
What this means: Nominal angle from +X
- What it is
- The angle on the drawing from the positive X axis to hole 3, measured anticlockwise about the datum centre.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 180° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Make sure the measuring machine’s X axis and angle direction match the drawing’s.
What this means: Measured X
- What it is
- The X coordinate of the measured centre of hole 3, from the datum centre.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -49.99 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure from the same datum origin and orientation as the nominal positions.
What this means: Measured Y
- What it is
- The Y coordinate of the measured centre of hole 3, from the datum centre.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -0.02 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign: below the X axis is negative.
What this means: Measured hole diameter
- What it is
- The measured diameter of hole 3, checked against the size limits and used for the bonus tolerance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.06 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger hole within its limits adds bonus tolerance equal to its size above MMC.
- Get it right
- Use the actual mating size where possible, not a single two-point reading.
Hole 4
What this means: Nominal radius
- What it is
- The radius from the datum centre to the true position of hole 4, as dimensioned on the drawing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the radius, not the pitch circle diameter.
What this means: Nominal angle from +X
- What it is
- The angle on the drawing from the positive X axis to hole 4, measured anticlockwise about the datum centre.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 270° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Make sure the measuring machine’s X axis and angle direction match the drawing’s.
What this means: Measured X
- What it is
- The X coordinate of the measured centre of hole 4, from the datum centre.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 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.
- Get it right
- Measure from the same datum origin and orientation as the nominal positions.
What this means: Measured Y
- What it is
- The Y coordinate of the measured centre of hole 4, from the datum centre.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -50.03 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign: below the X axis is negative.
What this means: Measured hole diameter
- What it is
- The measured diameter of hole 4, checked against the size limits and used for the bonus tolerance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.02 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger hole within its limits adds bonus tolerance equal to its size above MMC.
- Get it right
- Use the actual mating size where possible, not a single two-point reading.
Tolerances
What this means: Position tolerance at MMC (diameter)
- What it is
- The diameter of the cylindrical position tolerance zone in the feature control frame, which applies when the hole is at its smallest size (maximum material condition).
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.05 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger tolerance lowers the share of tolerance each hole uses.
- Get it right
- It is a diameter zone: the tool compares it with twice the radial deviation, so do not halve it.
What this means: Smallest hole size (MMC)
- What it is
- The smallest hole size allowed by the drawing, its maximum material condition. Bonus tolerance is the measured size minus this size.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a hole, MMC is the lower size limit, not the upper one.
What this means: Largest hole size (LMC)
- What it is
- The largest hole size allowed by the drawing, its least material condition. Holes above it fail the size check.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a hole, LMC is the upper size limit.
Method and formulas
- Nominal X = r cos θ, Y = r sin θ (as the polar coordinates tool).
- Deviation = √(Δx² + Δy²) (as the distance between two points tool); position error = 2 × deviation.
- Tolerance allowed = position tolerance + (measured size − MMC size) for a hole within its size limits.
- Example: the worst hole uses 90.351% of its allowed position tolerance.
Limitations
- Two-dimensional position from the datum centre; datum shift and perpendicularity are not included.
- Hole size as a single measured diameter.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a polar hole pattern from CMM X–Y results
- Apply bonus tolerance to hole positions
- Convert polar drawing dimensions for inspection
Who it is for
- Inspectors
- Quality engineers
- CNC programmers
What you get
- Nominal X and Y of each hole
- Position error and tolerance allowed
- Size and position decision
Interpreting the result
- Bonus tolerance means a hole made larger than its smallest size may be further out of position and still assemble.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 40–45, 615–627, 692–694. Topic reference; no source tables or recommended settings are reproduced.
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