KEVOS® MAKEOS · Quality
Compound-Angle Sine Plate Set-up (True Angle and Stack Heights)
For a surface with two apparent slopes, what true compound angle and direction does it have, and what gauge-block stacks set a compound sine plate to it?
Set-up of a compound (double) sine plate for a surface sloping in two perpendicular directions: true compound angle and its direction (as the compound angle tool), the lower plate angle equal to the first slope, the upper plate angle measured in the tilted plane, tan B′ = tan B cos A, the stack heights for each plate (as the sine bar tool), the stacks rounded to the block set, and the check of each plate angle against its limit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Slope in the first vertical plane | ° | Angle of the surface from horizontal seen in one vertical plane (the lower plate axis). |
| Slope in the second vertical plane (at 90°) | ° | Angle of the surface from horizontal in the vertical plane at right angles (the upper plate axis). |
| Lower plate roller centres | mm | Distance between the rollers of the lower plate. |
| Upper plate roller centres | mm | Distance between the rollers of the upper plate. |
| Gauge-block set resolution | mm | Smallest step the gauge-block set can build. |
| Largest angle for one plate | ° | Largest angle you set on one plate (sine plates lose accuracy above about 45°). |
Method and formulas
- True angle = tan⁻¹ √(tan² A + tan² B); direction = tan⁻¹(tan B ÷ tan A) (as the compound angle tool).
- Lower plate set to A; upper plate set to B′ with tan B′ = tan B cos A.
- Stack height H = L sin(angle) (as the sine bar tool), rounded to the block set resolution.
- Example: 20° and 30° make a true 34.314° slope; set the lower plate with 68.404 mm and the upper with 95.374 mm (B′ = 28.481°).
Limitations
- Both slopes must be measured from horizontal in vertical planes at right angles.
- Plate, roller and stack errors add as for a single sine bar.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set up a compound sine plate for grinding or inspection
- Convert drawing slopes to a true angle
- Check whether a compound angle is within a plate’s range
Who it is for
- Toolmakers
- Inspectors
- Machinists
What you get
- True compound angle and direction
- Plate angles and stack heights
- Rounded stacks and angle checks
Interpreting the result
- The upper plate angle is always smaller than the drawing slope B, because the lower plate already tilts its frame.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 119–121, 676–682. Topic reference; no source tables or recommended settings are reproduced.
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Open the Compound-Angle Sine Plate Set-up (True Angle and Stack Heights) calculator
