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Geometric dimensioning and tolerancing

Geometric dimensioning and tolerancing is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Geometric dimensioning and tolerancing rather than just read about it. In short: Geometric dimensioning and tolerancing (GD&T) is a system for defining and communicating engineering tolerances via a symbolic language on engineering drawings and computer-generated 3D models that describes a physical object's nominal geometry and the permissible variation thereof. GD&T is used to define the nominal (theoretically perfect) geometry of parts and assemblies, the allowable variation in size, form, ori…

Geometric dimensioning and tolerancing — main illustration
Geometric dimensioning and tolerancing — illustration

Key takeaways

  • Geometric dimensioning and tolerancing belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Geometric dimensioning and tolerancing to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Geometric dimensioning and tolerancing from memory before moving on to harder problems.

Reference excerpt

Geometric dimensioning and tolerancing (GD&T) is a system for defining and communicating engineering tolerances via a symbolic language on engineering drawings and computer-generated 3D models that describes a physical object's nominal geometry and the permissible variation thereof. GD&T is used to define the nominal (theoretically perfect) geometry of parts and assemblies, the allowable variation in size, form, orientation, and location of individual features, and how features may vary in relation to one another such that a component is considered satisfactory for its intended use. Dimensional specifications define the nominal, as-modeled or as-intended geometry, while tolerance specifications define the allowable physical variation of individual features of a part or assembly. There are several standards available worldwide that describe the symbols and define the rules used in GD&T. One such standard is American Society of Mechanical Engineers (ASME) Y14.5. This article is based on that standard. Other standards, such as those from the International Organization for Standardization (ISO) describe a different system which has some nuanced differences in its interpretation and rules (see GPS&V). The Y14.5 standard provides a fairly complete set of rules for GD&T in one document. The ISO standards, in comparison, typically only address a single topic at a time. There are separate standards that provide the details for each of the major symbols and topics below (e.g. position, flatness, profile, etc.). BS 8888 provides a self-contained document taking into account a lot of GPS&V standards.

Origin The origin of GD&T is credited to Stanley Parker, who developed the concept of "true position". While little is known about Parker's life, it is known that he worked at the Royal Torpedo Factory in Alexandria, West Dunbartonshire, Scotland. His work increased production of naval weapons by new contractors. In 1940, Parker published Notes on Design and Inspection of Mass Production Engineering Work, the earliest work on geometric dimensioning and tolerancing. In 1956, Parker published Drawings and Dimensions, which became the basic reference in the field.

Fundamental concepts

Dimensions A dimension is defined in ASME Y14.5 as "a numerical value(s) or mathematical expression in appropriate units of measure used to define the form, size, orientation, or location, of a part or feature." Special types of dimensions include basic dimensions (theoretically exact dimensions) and reference dimensions (dimensions used to inform, not define a feature or part).

Units of measure The units of measure in a drawing that follows GD&T can be selected by the creator of the drawing. Most often drawings are standardized to either SI linear units, millimeters (denoted "mm"), or US customary linear units, decimal inches (denoted "IN"). Dimensions can contain only a number without units if all dimensions are the same units and there is a note on the drawing that clearly specifies what the units are. Angular dimensions can be expressed in decimal degrees or degrees, minutes, and seconds.

Tolerances Every feature on every manufactured part is subject to variation, therefore, the limits of allowable variation must be specified. Tolerances can be expressed directly on a dimension by limits, plus/minus tolerances, or geometric tolerances, or indirectly in tolerance blocks, notes, or tables. Geometric tolerances are described by feature control frames, which are rectangular boxes on a drawing that indicate the type of geometric control, tolerance value, modifier(s) and/or datum(s) relevant to the feature. The type of tolerances used with symbols in feature control frames can be:

equal bilateral unequal bilateral unilateral no particular distribution (a "floating" zone) Tolerances for the profile symbols are equal bilateral unless otherwise specified, and for the position symbol tolerances are always equal bilateral. For example, the position of a hole has a tolerance of .020 inches. This means the hole can move ±.010 inches, which is an equal bilateral tolerance. It does not mean the hole can move +.015/−.005 inches, which is an unequal bilateral tolerance. Unequal bilateral and unilateral tolerances for profile are specified by adding further information to clearly show this is what is required.

Datums and datum references

A datum is a theoretically exact plane, line, point, or axis. A datum feature is a physical feature of a part identified by a datum feature symbol and corresponding datum feature triangle, e.g.,

◻ A − − ◂ | {\displaystyle {\displaystyle \Box }\!\!\!\!{\scriptstyle {\mathsf {A}}}\!-\!\!\!-\!\!\!\blacktriangleleft \!\!\!|}

These are then referred to by one or more 'datum references' which indicate measurements that should be made with respect to the corresponding datum feature. The datum reference frame can describe how the part fits or functions.

Purpose and rules The purpose of GD&T is to describe the engineering intent of parts and assemblies. GD&T can more accurately define the dimensional requirements for a part, allowing over 50% more tolerance zone than coordinate (or linear) dimensioning in some cases. Proper application of GD&T will ensure that the part defined on the drawing has the desired form, fit (within limits) and function with the largest possible tolerances. GD&T can add quality and reduce cost at the same time through producibility. According to ASME Y14.5, the fundamental rules of GD&T are as follows,

… excerpt ends here. Continue reading the full article.

Illustrations

Geometric dimensioning and tolerancing: Example of true position geometric control defined by basic dimensions and datum features
Example of true position geometric control defined by basic dimensions and datum features

Worked examples

Example 1 — a first encounter with Geometric dimensioning and tolerancing

Start with the simplest possible case. Write down what Geometric dimensioning and tolerancing claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Geometric dimensioning and tolerancing before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Geometric dimensioning and tolerancing ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Geometric dimensioning and tolerancing

In research
Geometric dimensioning and tolerancing appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Geometric dimensioning and tolerancing in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Geometric dimensioning and tolerancing is common in secondary-school and first-year university syllabi. It links to neighbouring topics Applied geometry, Geometric measurement, Technical drawing, so understanding it makes those chapters shorter.
In everyday life
Look for Geometric dimensioning and tolerancing outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Geometric dimensioning and tolerancing in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Geometric dimensioning and tolerancing means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Geometric dimensioning and tolerancing out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Geometric dimensioning and tolerancing in simple terms?

Geometric dimensioning and tolerancing (GD&T) is a system for defining and communicating engineering tolerances via a symbolic language on engineering drawings and computer-generated 3D models that describes a physical object's nominal geometry and the permissible variation thereof. GD&T is used to…

Why does Geometric dimensioning and tolerancing matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Geometric dimensioning and tolerancing?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Geometric dimensioning and tolerancing.

Tags

  • Applied geometry
  • Geometric measurement
  • Technical drawing

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