Machine Design #80: Supplementary Dimension Symbols — One Wrong Symbol Can Change the Process
The supplementary dimension symbol must be readable, manufacturable, inspectable, maintainable, and safe when the boundary changes.
Start with the function
Write the input condition, expected result, acceptance limit, failure symptom, and measurement method before choosing a view, symbol, feature, or note. Do not hide unknowns behind a large factor; assign an owner and a test.
Core checks
- Function of the symbol and affected process: know what each symbol commits the shop to, because a symbol chooses a process as surely as a note does.
- Reference edge, datum, and measurement direction: state the reference edge, the datum and the direction of measurement; a symbol without a reference can be read two ways.
- Machining, forming, welding, or inspection meaning: check what the symbol means to cutting, forming, welding and inspection, since the same mark carries a different cost in each.
- Supplier interpretation and confirmation: confirm the supplier reads the symbol the way you meant it, in writing, before the first part is cut.
- Consistency with standards and model: keep the symbol consistent with the standard named in the title block and with the 3D model.
- Review evidence before release: keep the review record: who checked the symbols, against which standard, and on which revision.
Failure modes
| Failure mode | Symptom | Verification |
|---|
| Ambiguous meaning | Wrong process or inspection | Review standard and evidence |
| Omitted interface | Assembly or maintenance error | Walk the real route |
| Documents out of sync | Correct name, wrong revision | Baseline all references |
A symbol is not decoration: it tells the shop what kind of shape this is
A number on a drawing only means something when the reader knows what it measures. The symbol placed before the value is the part that says so, and putting the wrong one changes both the machining method and the measuring instrument.
| Symbol | Meaning | Where confusing it hurts |
|---|
| ⌀ diameter | A dimension across the centre of a cylinder or a hole | Omitted, the reader takes it as a straight length and the shape comes out wrong |
| R radius | A circular arc, measured from its centre | Confusing R with ⌀ makes the size wrong by a factor of two |
| S⌀ / SR spherical | A sphere, not a cylinder or a flat arc | A different instrument is needed; confusing it produces the wrong shape |
| □ square | A square section, one value for both sides | Omitted, the shop queries it or dimensions it twice |
| t thickness | Thickness of a sheet or a wall | Not stated, it has to be inferred from the views and is easily misread |
| C chamfer | A 45-degree chamfer, the value being the leg length | Confusing it with R gives the wrong edge shape |
| ( ) reference dimension | For reference only, not an acceptance criterion | Used as an inspection criterion it creates duplicate checks and disputes |
| [ ] theoretically exact dimension | Goes with a geometric tolerance, carries no plus-minus tolerance | Adding a plus-minus tolerance contradicts the geometric tolerance frame |
| n× quantity | The number of identical features | Missing, the reader has to count on the view and easily misses one |
The chamfer and radius symbols and the traps when they are confused are covered in Machine Design #106. Reading this same symbol set on a Japanese drawing is in Technical Japanese #03.
Three groups that go wrong most often
Reference dimensions. Brackets mean "provided so the reader can picture it", not an acceptance requirement. If a dimension matters enough to inspect, dimension it normally and give it a tolerance; if it is only a consequence of other dimensions, bracket it and do not ask QC to measure it. Stating the same relationship twice in two ways is the classic source of contradictions between drawing and inspection report.
Theoretically exact dimensions. They locate a feature when its positional variation is controlled by a geometric tolerance. They carry no plus-minus tolerance — the tolerance lives in the frame. Adding a plus-minus tolerance creates two rules for one feature. Allocating tolerance by function is covered in Machine Design #97.
Stepped holes. A drilled hole with a counterbore for a screw head, with a countersink for a flat-head screw, or with a thread depth, is a chain of several pieces of information. Writing them on one line in a clear order — diameter, depth, then the secondary feature — works far better than scattering the numbers around the view and leaving the reader to assemble them.
Where to put the symbol, and how to avoid dimensioning twice
- The symbol goes before the value, not after, and is not moved into a general note.
- A feature should have one place where it is defined. If the overall length is already fixed by
the sum of the segments, then the overall length must be a reference dimension, or the other way round.
- Dimension a feature on the view that shows its shape most clearly — hole diameter on the view
where the hole appears round, depth on the section.
- The reading direction of text and numbers has to be consistent across the drawing, because
drawings in the shop get rotated.
Four ways to state a tolerance, each saying something different
The symbol says what the number measures; the tolerance says how far it may deviate. There are four ways to state it and they are not interchangeable.
| Form | Example | Use when |
|---|
| Symmetric | 50 plus or minus 0.1 | Deviation is equally acceptable both ways, no functional preference |
| Asymmetric | 50 +0.2 / −0.05 | The function tolerates more deviation on one side than the other |
| Unilateral | 50 +0.3 / 0 | Deviation is permitted on one side only; common for depths and minimum clearances |
| Limit dimensions | 50.3 / 50.0 | The inspector reads the two limits directly instead of adding and subtracting |
The last form is worth using where sign errors are easy: the inspector simply compares the reading against two limits with no mental arithmetic. Every piece of mental arithmetic on the shop floor is a chance to get it wrong.
Asymmetric tolerancing is an under-used cost saver. If a hole must not be undersize but may be oversize, writing +0.3 / 0 is considerably easier to make than plus or minus 0.15 — the same functional guarantee, with the acceptance zone opened on the side that does no harm.
General tolerances: what applies to every dimension without its own
The corner of the drawing should always carry a general tolerance class, with separate classes for linear dimensions, for angles, and for radii or chamfers. Without it, every dimension without an individual tolerance becomes undefined, and each shop applies its own default.
Three things commonly left out of that line:
- The class for angles, which is separate from the one for linear dimensions; omit it and angles
become free dimensions.
- Non-machined dimensions (as-cast surfaces, laser-cut edges) need their own, wider class.
- Dimensions after surface treatment — say whether the general tolerance applies before or after
coating.
Do not stack tolerances on the same feature
A feature should be controlled by one mechanism. Three overlaps come up often:
| Overlap | Why it is wrong |
|---|
| A basic dimension in a box with a plus-minus added | The tolerance already lives in the geometric tolerance frame |
| Both a dimension chain and an overall dimension, each toleranced | The overall will contradict the chain; one of them has to be a reference dimension |
| An individual tolerance where the general tolerance is already tight enough | Redundant, and it adds another line to inspect |
A quick pre-release check: for every dimension carrying its own tolerance, ask "if this line were removed, what would still control the feature?". If the answer is "it would still be controlled adequately", that line is redundant.
MINATA release checklist
- [ ] Function, boundary, and failure symptom are written.
- [ ] Interfaces, ownership, and mistake-proofing are clear.
- [ ] Six topic checks have evidence and pass/fail limits.
- [ ] Manufacturing, assembly, inspection, and maintenance were tried.
- [ ] Revision, supplier, and configuration records agree.
Good engineering is a chain of explicit assumptions that survives manufacture, operation, maintenance, and change. For supplementary dimension symbol, evidence that the result continues to work is the MINATA standard.
Frequently asked questions
Does a dimension in brackets have to be measured?
No. It is a reference dimension, given only so the reader can picture the part. If it matters enough to check, dimension it normally with a tolerance — but then remove one of the dimensions that defines the same relationship, so one feature does not have two rules.
How does a boxed dimension differ from an ordinary one?
It is a theoretically exact dimension used together with a geometric tolerance. It has no plus-minus tolerance of its own; the tolerance lives in the geometric tolerance frame. Adding a plus-minus tolerance creates a contradiction.
What happens if the diameter symbol is omitted?
The reader may take the number as a straight length and the part comes out the wrong shape. It is a cheap mistake to prevent and an expensive one to fix, which is why it belongs in the mandatory pre-release review list.
Should a chamfer be given as C or as two dimensions?
Use C when the chamfer really is 45 degrees. A chamfer at any other angle has to be given as a leg length and an angle, because the C symbol cannot describe it.
How should a stepped hole be dimensioned compactly?
On one line in order — hole diameter, depth, then the counterbore diameter and depth — rather than scattering the numbers around the view. This reduces the chance of the reader mixing up information belonging to two different holes.
Frequently asked questions, continued
When should an asymmetric tolerance be used?
When the function only fears deviation in one direction. If a hole must not be undersize but may be oversize, +0.3 / 0 is far easier to produce than plus or minus 0.15 while giving the same functional guarantee. It is an under-used way to reduce machining cost.
What is gained by stating limit dimensions instead of plus-minus?
The inspector reads the two limits directly instead of calculating. Where sign errors are easy or the tolerance is asymmetric, this removes a calculation step — and every piece of shop-floor arithmetic is a chance to get it wrong.
What happens without a general tolerance note?
Every dimension without an individual tolerance becomes undefined and each shop applies its own default. Two batches from two suppliers can then differ while both follow the same drawing.
Does the general tolerance cover angles?
Only if a separate class for angles is stated. The class for linear dimensions does not automatically apply to angles. Many drawings omit this and angles quietly become free dimensions.
How do you know a tolerance line is redundant?
Ask what would still control the feature if the line were removed. If it would still be adequately controlled — by the general tolerance, by a geometric tolerance frame, or by another dimension chain — the line is redundant and only adds an inspection point.
Conclusion
Supplementary Dimension Symbols is not paperwork done to make a file look tidy. It is how intent becomes a result that can be manufactured, assembled and measured repeatedly. A good drawing does not need the designer standing beside it to explain it; the structure of the information has to do that work.
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