KEVOS® MAKEOS · Quality
Sine Bar Set-Up from Degrees, Minutes and Seconds (Gauge Stack, Set Angle, Error)
For an angle given in degrees, minutes and seconds, what gauge block stack goes under the sine bar, what angle does it actually set, and is the set-up error within tolerance?
Sine bar set-up for a drawing angle in degrees, minutes and seconds: the angle converted to decimal degrees and radians (as the degrees, minutes and seconds tool), then the exact height difference, the gauge block stack rounded to the set’s resolution, the angle the stack sets, the rounding error, the angle change per micrometre and the total error with the stack tolerance (as the sine bar set-up tool), with the set angle shown back in degrees, minutes and seconds, and the angle given by a measured stack.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Degrees | ° | Whole degrees of the angle. |
| Minutes | ′ | Minutes of the angle. |
| Seconds | ″ | Seconds of the angle. |
| Sine bar length (roller centres) | mm | Distance between the sine bar roller centres. |
| Gauge-block set resolution | mm | Smallest step the gauge block set can build. |
| Stack tolerance (sum of block tolerances) | µm | Combined tolerance of the blocks in the stack. |
| Angle tolerance (±) | arcsec | Tolerance on the angle in seconds of arc. |
| Measured stack height (0 = none) | mm | Height of a stack already built, to find the angle it gives (0 to skip). |
Method and formulas
- Decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3600 (as the degrees, minutes and seconds tool).
- Height = L sin θ; stack rounded to the set’s resolution; set angle = asin (stack ÷ L); error per micrometre = 0.001 ÷ (L cos θ) (as the sine bar set-up tool).
- Set and measured angles converted back to degrees, minutes and seconds.
- Example: 12° 30′ 15″ is 12.504°; build a 43.302 mm stack (error 0.39331″).
Limitations
- Bar, rollers and surface plate taken as perfect.
- Angles above 45° are better set as their complement on an angle plate.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set a sine bar to a drawing angle in degrees and minutes
- Check the angle a built stack gives
- Convert set-up angles for an inspection report
Who it is for
- Inspectors
- Toolmakers
- Machinists
What you get
- Angle in decimal degrees
- Gauge block stack and set angle
- Set-up error and decision
Interpreting the result
- On a 200 mm bar one micrometre of stack is about one second of arc at small angles.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 103–104, 676–682, 705–708. Topic reference; no source tables or recommended settings are reproduced.
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