KEVOS® MAKEOS · Manufacturing
Locating Three Holes by the Disk Method (Disk Diameters from Centre Distances)
To locate three precision holes on the lathe or for checking by three disks whose rims touch, what diameter must each disk be so that its centre falls on its hole, given the three centre distances between the holes?
Disk method of locating holes in small precision work, by the handbook rule: three carefully centred disks are made to such diameters that when their rims touch, each disk centre lies on a hole position; the disks are then clamped to the work and each in turn is indicated true with the lathe spindle. From the centre distances A–B, B–C and A–C the radii are r_A = (AB − BC + AC) ÷ 2, r_B = AB − r_A and r_C = BC − r_B, with the triangle of the hole positions for checking the layout.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Centre distance hole A to hole B | mm | Distance between the centres of holes A and B from the drawing (dimension x in the handbook). |
| Centre distance hole B to hole C | mm | Distance between the centres of holes B and C (dimension y). |
| Centre distance hole A to hole C | mm | Distance between the centres of holes A and C (dimension z). |
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: Centre distance hole A to hole B
- What it is
- Centre distance between hole A and hole B from the drawing.
- 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 23.622 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer A–B distance enlarges disks A and B.
- Get it right
- Use the basic dimension; label the holes so A–B, B–C and A–C go round the triangle.
What this means: Centre distance hole B to hole C
- What it is
- Centre distance between hole B and hole C from the drawing.
- 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 18.288 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer B–C distance enlarges disks B and C.
- Get it right
- Calculate it from the drawing coordinates when it is not dimensioned.
What this means: Centre distance hole A to hole C
- What it is
- Centre distance between hole A and hole C from the drawing.
- 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 21.844 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer A–C distance enlarges disks A and C.
- Get it right
- Each distance must be less than the sum of the other two.
Method and formulas
- x − y is the difference between the radii of disks A and C; adding z gives the diameter of disk A, so r_A = (x − y + z) ÷ 2.
- r_B = x − r_A; r_C = y − r_B; check r_A + r_C = z.
- Angles of the triangle by the law of cosines; hole C at ((x² + z² − y²) ÷ 2x, √(z² − that²)) from hole A with B on the x axis.
- Example: centre distances 23.622, 18.288 and 21.844 mm need disks of 27.178, 20.066 and 16.51 mm diameter.
Limitations
- Each disk must have a positive radius, which needs each centre distance to be less than the sum of the other two.
- The accuracy of the hole positions depends on the disk diameters, their roundness and the centring of their holes; grind and measure them.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Make locating disks for three holes bored on the lathe
- Check the layout of three holes from their centre distances
- Plan a toolroom job without a jig borer
Who it is for
- Toolmakers
- Toolroom machinists
- Model engineers
What you get
- Diameter of each disk
- Radius of each disk
- Angles of the hole triangle
- Position of hole C with A at the origin and B on the x axis
Interpreting the result
- A very small disk means one hole is close to the line through the other two; consider locating that hole from a different pair.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3481–3482. Topic reference; no source tables or recommended settings are reproduced.
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