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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°). |
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: Slope in the first vertical plane
- What it is
- The slope of the surface from horizontal as seen in the first vertical plane, which is the axis of the lower sine plate. The lower plate is set to this angle.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 80°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Slope in the second vertical plane (at 90°)
- What it is
- The slope of the surface from horizontal as seen in the vertical plane at right angles to the first, along the upper plate axis.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 80°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The upper plate is not set to this angle: the tool converts it to B′ in the tilted plane.
What this means: Lower plate roller centres
- What it is
- The centre-to-centre distance between the two rollers of the lower sine plate, marked on the plate.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 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 lower stack height is proportional to it.
What this means: Upper plate roller centres
- What it is
- The centre-to-centre distance between the two rollers of the upper sine plate, marked on the plate.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 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 upper stack height is proportional to it.
What this means: Gauge-block set resolution
- What it is
- The smallest step in height that your gauge-block set can build. Both stack heights are rounded to a whole number of these steps.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.0001 mm to 0.01 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.0005 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type the step in millimetres, as given for the gauge-block set.
What this means: Largest angle for one plate
- What it is
- The largest angle you are willing to set on either plate. The tool checks the lower plate angle and the upper plate angle B′ against it.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 80°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from your inspection procedure or the plate maker’s guidance.
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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