KEVOS® MAKEOS · Quality
Taper and Angle Gauges with Discs
What angle or taper do these two discs set, or where must they be placed for a required taper?
Angle and taper per foot set by two discs at a centre distance, the centre distance for a required angle or taper (on the centre-line or from one side), and the disc size for a given angle, using the handbook’s disc gauge rules.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Calculate | choice | What to calculate. |
| Large disc diameter | in | Diameter of the larger disc. |
| Small disc diameter | in | Diameter of the smaller disc. |
| Centre distance | in | Distance between disc centres. |
| Included angle | ° | Required included angle. |
| Taper per foot (on diameter) | in/ft | Required taper per foot (change in diameter over 12 in), measured on the centre-line or from one side as selected. |
Method and formulas
- K = (D − d) ÷ 2C; included angle = 2 arcsin K; taper per foot = 24K ÷ √(1 − K²); from one side T = 24K √(1 − K²) ÷ (1 − 2K²).
- Centre distance for taper T: C = (D − d)/2 × √(1 + (T/24)²) ÷ (T/24); for an angle: C = (D − d) ÷ 2 sin(α/2).
- Centre distance for a taper from one side: C = (D − d) ÷ √(2 − 2 ÷ √(1 + (T/12)²)). Disc to touch at an angle: D = d (1 + sin(α/2)) ÷ (1 − sin(α/2)).
- Example (handbook case): 1.5 and 1 in discs at 5 in give 5.732° and 1.2015 in/ft.
Limitations
- Inch units with taper per foot as in the handbook rules; convert metric tapers to the same basis.
- Discs must be round and of known diameter.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set up a disc gauge for checking tapers
- Find the taper given by a disc set-up
- Size a disc to contact a reference disc at an angle
Who it is for
- Quality inspectors
- Toolmakers
- Metrology technicians
What you get
- Included angle
- Taper per foot (centre-line and from one side)
- Centre distance or disc diameter
Interpreting the result
- Use gauge blocks between disc centres or a sine bar to set the centre distance accurately.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 684–685. Topic reference; no source tables or recommended settings are reproduced.
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