BIZOMAT 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). |
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: Degrees
- What it is
- The whole degrees part of the angle to be set, as written on the drawing in degrees, minutes and seconds.
- 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 12° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter only the whole degrees here; a decimal angle can be typed here with minutes and seconds left at 0.
What this means: Minutes
- What it is
- The minutes part of the angle, where one minute is one sixtieth of a degree.
- Units and format
- Enter a number in ′: ′. The form accepts 0 ′ to 59.999999 ′. 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
- Do not enter decimal fractions of a degree here: 0.5° is 30 minutes.
What this means: Seconds
- What it is
- The seconds part of the angle, where one second is one sixtieth of a minute.
- Units and format
- Enter a number in ″: ″. The form accepts 0 ″ to 59.999999 ″. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 ″ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Seconds and minutes both count in sixties, not hundredths.
What this means: Sine bar length (roller centres)
- What it is
- The distance between the centres of the two rollers of the sine bar, its nominal length. The gauge stack height is this length times the sine of the angle.
- 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
- A longer bar needs a taller stack but each micrometre of stack error moves the angle less.
- Get it right
- Use the roller centre distance marked on the bar, not its overall length.
What this means: Gauge-block set resolution
- What it is
- The smallest step in height your gauge block set can build. The tool rounds the exact stack height to a multiple of this step.
- 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.
- Effect on the result
- A coarser resolution can leave a larger rounding error in the angle.
- Get it right
- Take it from the smallest increment in your block set.
What this means: Stack tolerance (sum of block tolerances)
- What it is
- The combined size tolerance of all the gauge blocks in the stack, added up from the grade tolerance of each block.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0 µm to 50 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.25 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The angle error from the stack rises in proportion to it.
- Get it right
- Enter it in micrometres, not millimetres: 0.001 mm is 1 µm.
What this means: Angle tolerance (±)
- What it is
- The plus-or-minus tolerance on the angle from the drawing, in seconds of arc, against which the total set-up error is checked.
- Units and format
- Enter a number in arcsec: arcsec. The form accepts 0.1 arcsec to 3600 arcsec. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 arcsec as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Convert minutes to seconds: 1′ is 60″.
What this means: Measured stack height (0 = none)
- What it is
- The height of a gauge stack already built or measured under the sine bar, from which the tool gives the angle it sets. 0 skips this check.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be less than the bar length.
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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