Geometric dimensioning and tolerancing

Example of true position geometric control defined by basic dimensions and datum features

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:

1. equal bilateral
2. unequal bilateral
3. unilateral
4. 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

Main article: Datum reference

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.,

${\displaystyle \Box }\!\!\!\!{\scriptstyle {\mathsf {A}}}\!-\!\!\!-\!\!\!\blacktriangleleft \!\!\!|$

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,

1. All dimensions must have a tolerance. Plus and minus tolerances may be applied directly to dimensions or applied from a general tolerance block or general note. For basic dimensions, geometric tolerances are indirectly applied in a related feature control frame. The only exceptions are for dimensions marked as minimum, maximum, stock or reference.
2. Dimensions and tolerancing shall fully define each feature. Measurement directly from the drawing or assuming dimensions is not allowed except for special undimensioned drawings.
3. A drawing should have the minimum number of dimensions required to fully define the end product. The use of reference dimensions should be minimized.
4. Dimensions should be applied to features and arranged to represent the function and mating relationship of the part. There should only be one way to interpret dimensions.
5. Part geometry should be defined without explicitly specifying manufacturing methods.
6. If dimensions are required during manufacturing but not the final geometry (due to shrinkage or other causes) they should be marked as non-mandatory.
7. Dimensions should be arranged for maximum readability and should be applied to visible lines in true profiles.
8. When geometry is normally controlled by gauge sizes or by code (e.g. stock materials), the dimension(s) shall be included with the gauge or code number in parentheses following the dimension.
9. Angles of 90° are assumed when lines (including center lines) are shown at right angles, but no angle is specified.
10. Basic 90° angles are assumed where center lines of features in a pattern or surfaces shown at right angles on a 2D orthographic drawing are located or defined by basic dimensions and no angle is specified.
11. A basic dimension of zero is assumed where axes, center planes, or surfaces are shown coincident on a drawing, and the relationship between features is defined by geometric tolerances.
12. Dimensions and tolerances are valid at 20 °C (68 °F) and 101.3 kPa (14.69 psi) unless stated otherwise.
13. Unless explicitly stated, dimensions and tolerances only apply in a free-state condition.
14. Unless explicitly stated, tolerances apply to the full length, width, and depth of a feature.
15. Dimensions and tolerances only apply at the level of the drawing where specified. It is not mandatory that they apply at other levels (such as an assembly drawing).
16. Coordinate systems shown on drawings should be right-handed. Each axis should be labeled and the positive direction should be shown.

Symbols

List of geometric characteristics

Geometric characteristic reference chart

Application	Type of control	Characteristic	Symbol	Unicode character	Relevant feature		Virtual condition affected	References datum	Modified by		Affected by
					Surface	Of size			Ⓜ	Ⓢ	Bonus	Shift
Individual features	Form	Straightness		⏤ U+23E4	Yes	Yes	Of size	No	Of size	No	Ⓜ	No
		Flatness		⏥ U+23E5	Yes	No	No	No	No	No	No	No
		Circularity		○ U+25CB	Yes	No	No	No	No	No	No	No
		Cylindricity		⌭ U+232D	Yes	No	No	No	No	No	No	No
Individual or related features	Profile	Profile of a line		⌒ U+2312	Yes	No	No	Yes	No	No	No	Datum, Ⓜ
		Profile of a surface		⌓ U+2313	Yes	No	No	Yes	No	No	No	Datum, Ⓜ
Related features	Orientation	Perpendicularity		⟂ U+27C2	Yes	Yes	Of size	Yes	Of size	No	Ⓜ	Datum, Ⓜ
		Angularity		∠ U+2220	Yes	Yes	Of size	Yes	Of size	No	Ⓜ	Datum, Ⓜ
		Parallelism		∥ U+2225	Yes	Yes	Of size	Yes	Of size	No	Ⓜ	Datum, Ⓜ
	Location	Symmetry		⌯ U+232F	No	Yes	Yes	Yes	No	No	No	No
		Position		⌖ U+2316	No	Yes	Yes	Yes	Yes	Yes	Ⓜ	Datum, Ⓜ
		Concentricity		◎ U+25CE	No	Yes	Yes	Yes	No	No	No	No
	Run-out	Circular run-out		↗ U+2197	Yes	Yes	Of size	Yes	No	No	No	No
		Total run-out		⌰ U+2330	Yes	Yes	Of size	Yes	No	No	No	No