### Geometric Dimensioning and Tolerances

Geometric Dimensioning and Tolerancing: Why ?
Geometric Dimensioning and Tolerancing (GDT) is a method for precisely defining the geometry of mechanical parts. It introduces tools which allow mechanical designers, fabricators, and inspectors to effectively communicate complex geometrical descriptions which are not otherwise able to be described in a defined language.
Figure 1.1

A good example of why GDT is needed is the automobile stamped chassis shown in Figure 1.1. The rear quarter panel must fit snugly in order to allow spot welds and in this competitive business, cosmetic appearance and noise abatement are critical. Without GDT, geometric description of this assembly is difficult if not impossible. Computer modelling of these complex surfaces continues to increase the complexity of interface shapes.
Illustrated in Figure 1.2 is an imprecise sand-cast sewer termination fitting. Its hole pattern must mate with the corresponding pattern of the equally imprecise mating pipe. Flatness is also an issue with these rough-surfaced parts. Inspectors must be able to pass as many parts as possible without sacrificing fit. Tens of thousands of the parts are produced. GDT allows fabricators, inspectors, and assemblers to match covers with equally imprecise pipes.
Figure 1.2

Geometric Dimensioning and Tolerancing is a vast language of which there are many facets. However, what is commonly used is a small subset of the total. This subset is based on concepts which MUST be learned in order to progress further. Without a solid understanding of these fundamentals, one cannot gain a firm grasp of later topics. We will present the most essential (and often misinterpreted) topics in a step-by-step fashion, starting with a simple two-dimensional case. After the 2D case has been understood, the full three-dimensional geometry will be described. We also include common areas of confusion and a reference section, but at this point the primary objective is to explain the fundamentals. Please select "2D DATUMS" from the menu bar to the left to continue.

History of Geometric Dimensioning and Tolerancing

Geometric Dimensioning and Tolerancing symbols have been in use since at least the turn of the century. GDT was especially important during the Second World War in relation to extremely high volume production of Liberty Ships, aircraft, and ground vehicles. The automotive industry, with its high volumes, has also benefited from GDT. The computer industry, in particular mass storage manufacturers, have used GDT extensively to increase their yields of high-volume and low-margin hard disk drives. However, as with most engineering and scientific methodologies, GDT was not rigorously established and documented until later in the twentieth century. The American National Standards Institute publication in 1982 of ANSI Y14.5M-1982 was a turning point in the rigorous, unambiguous standardization of the methodology.

GD&T

GD&T (per ASME Y14.5M-1994) is an international language that is used on engineering drawings to accurately describe the size, form, orientation, and location of part features. It is also a design-dimensioning philosophy that encourages designers to define a part based on how it functions in the final product or assembly.
GD&T is an exact language that enables design engineers to "say what they mean" on a drawing, thus improving product designs and lowering cost. Process engineers and manufacturing use the language to interpret the design intent and to determine the best manufacturing approach. Quality control and inspection use the GD&T language to determine proper set-up and part verification.
By providing company-wide uniformity in the drawing specifications and interpretation, GD&T reduces controversy, guesswork, and assumptions throughout the design, manufacturing and inspection process.
• Create clear, concise drawings
• Improve product design
• Create drawings that reduce controversy, guesswork, and assumptions throughout the manufacturing process
• Effectively communicate or interpret design requirements for suppliers and manufacturing
However, because GD&T is such a precise language, it involves a great many symbols and terms. Here is a list of some of the topics involved in geometric dimensioning and tolerancing fundamentals and a short definition of each.

Actual Local Size - The value of any individual distance at any cross section of a feature of size.
Actual Mating Envelope of an External Feature of Size - A similar perfect feature counterpart of the smallest size that can be circumscribed about the feature so that it just contacts the surfaces at the highest points.
Actual Mating Envelope of an Internal Feature of Size - A similar perfect feature counterpart of the largest size that can be inscribed within the feature so that it just contacts the surfaces at their highest points.

All-Around Symbol - A circle placed on the bend of the leader line of a profile control

Angularity - The condition of a surface, centerplane or axis being exactly at a specified angle...

Angularity Control - A geometric tolerance that limits the amount a surface, axis, or centerplane is permitted to vary from its specified angle.
ASME Y14.5M-1994 - The national standard for dimensioning and tolerancing in the United States. ASME stands for American Society of Mechanical Engineers. The Y14.5 is the standard number. "M" is to indicate the standard is metric, and 1994 is the date the standard was officially approved.
Axis Theory - The axis (or centerplane) of a feature of size must be within the tolerance zone.
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Basic Dimension - A numerical value used to describe the theoretically exact size, true profile, orientation, or location of a feature or datum target.

Between Symbol - A double ended arrow that indicates the tolerance zone extends to include multiple surfaces

Bi-Directional Control - Where the location of a hole is controlled to a different tolerance value in two directions.
Bilateral Tolerance - A tolerance that allows the dimension to vary in both the plus and minus directions.
Bonus Tolerance - An additional tolerance for a geometric control. Whenever a geometric tolerance is applied to a feature of size, and it contains an MMC (or LMC) modifier in the tolerance portion of the feature control frame, a bonus tolerance is permissible.
Boundary - The word "BOUNDARY" is placed beneath the feature control frames to invoke a boundary control.
Cartoon Gage - A sketch of a functional gage. A cartoon gage defines the same part limits that a functional gage would, but it does not represent the actual gage construction of a functional gage.

Circularity - A condition where all points of a surface of revolution, at any section perpendicular to a common axis, are equidistant from that axis.

Circularity Control - A geometric tolerance that limits the amount of circularity on a part surface.
Circular Runout - A composite control that affects the form, orientation, and location of circular elements of a part feature relative to a datum axis.
Circular Runout Control - A geometric tolerance that limits the amount of circular runout of a part surface.
Coaxial Datum Features - When coaxial diameters are used to establish a datum axis.
Coaxial Diameters - Two (or more) diameters that are shown on the drawing as being on the same centerline (axis).

Composite Control - Controls the form, location, and orientation of a part feature simultaneously (in a single gage reading).
 Concentricity - The condition where the median points of all diametrically opposed elements of a cylinder (or a surface of revolution) are congruent with the axis of a datum feature.
Concentricity Control - A geometric tolerance that limits the concentricity error of a part feature.

Controlled Radius - A radius with no flats or reversals allowed. The symbol for a controlled radius is "CR."

Coordinate Tolerancing - A dimensioning system where a part feature is located (or defined) by means of rectangular dimensions with given tolerances.
Coplanar Datum Features - Two or more datum features that are on the same plane.
Coplanar Surfaces - Two or more surfaces that are on the same plane.
Cylindrical Feature of Size - Contains one feature: the cylindrical surface.

Cylindricity - A condition of a surface of revolution in which all points of the surface are equidistant from a common axis.

Cylindricity Control - A geometric tolerance that limits the amount of cylindricity error permitted on a part surface.
Datum - A theoretically exact plane, point or axis from which a dimensional measurement is made.

Datum Feature - A part feature that contacts a datum.

Datum Feature Simulator - The inspection equipment (or gage surfaces) used to establish a datum.
Datum Reference Frame - A set of three mutually perpendicular datum planes.
Datum Shift - The allowable movement, or looseness, between the part datum feature and the gage.
Datum System - A set of symbols and rules that communicate to the drawing user how dimensional measurements are to be made.

Datum Target - A symbol that describes the shape, size, and location of gage elements that are used to establish datum planes or axes.

Dimension - A numerical value expressed in appropriate units of measure and used to define the size, location, orientation, form, or other geometric characteristics of a part.
Engineering Drawing - A document that communicates a precise description of a part. This description consists of pictures, words, numbers, and symbols.
Equal Bilateral Tolerance - A tolerance where the allowable variation from the nominal value is the same in both directions.
Feature - A general term applied to a physical portion of a part, such as a surface, hole, or slot.

Feature Control Frame - A rectangular box that is divided into compartments within which the geometric characteristic symbol, tolerance value, modifiers, and datum references are placed.

Feature of Size - One cylindrical or spherical surface, or a set of two opposed elements or opposed parallel surfaces, associated with a size dimension.
Feature of Size Dimension - A dimension that is associated with a feature of size.
Fixed Fastener Assembly - Where the fastener is held in place (restrained) into one of the components of the assembly.
Fixed Fastener Formula - H = F + 2T or T =
Where:
T = position tolerance diameter
H = MMC of the clearance hole
F = MMC of the fastener

Flatness - The condition of a surface having all of its elements in one plane

Flatness Control - A geometric tolerance that limits the amount of flatness error a surface is allowed.
Floating Fastener Assembly - Where two (or more) components are held together with fasteners (such as bolts and nuts), and both components have clearance holes for the fasteners.
Floating Fastener Formula - T = H - F
Where:
T = position tolerance diameter (for each part)
H = MMC of the clearance hole
F= MMC of the fastener
Functional Dimensioning - A dimensioning philosophy that defines a part based on how it functions in the final product.
Functional Gage - A gage that verifies functional requirements of part features as defined by the geometric tolerances.
Fundamental Dimensioning Rules - A set of general rules defined by ASME for dimensioning and interpreting drawings.
Geometric Characteristic Symbols (14) - The symbols are divided into five categories: form, profile, orientation, location, and runout.
Geometric Dimensioning and Tolerancing (GD&T) - A set of fourteen symbols used in the language of GD&T. It consists of well-defined of symbols, rules, definitions and conventions, used on engineering drawings to accurately describe a part. GD&T is a precise mathematical language that can be used to describe the size, form, orientation, and location of part features. GD&T is also a design philosophy on how to design and dimension parts.
Go Gage - A gage that is intended to fit into (for an internal feature of size) or fit over (for an external feature of size) the feature of size.
Great Myth of GD&T - The misconception that geometric tolerancing raises product costs.
Implied Basic 90° Angles -A 90° basic angle applies where centerlines of features in a pattern (or surfaces shown at right angles on a drawing) are located and defined by basic dimensions, and no angle is specified.
Implied Basic Zero Dimension - Where a centerline or centerplane of a feature of size is shown in line with a datum axis or centerplane, the distance between the centerlines or centerplanes is an implied basic zero.
Implied Datum - An assumed plane, axis, or point from which a dimensional measurement is made.
Inclined Datum Feature - A datum feature that is at an angle other than 90o, relative to the other datum features.
Inner Boundary (IB) - A worst-case boundary generated by the smallest feature of size minus the stated geometric tolerance (and any additional tolerance, if applicable).
International Standards Organization (ISO) - The organization that published an associated series of standards on dimensioning and tolerancing.

Least Material Condition - The condition in which a feature of size contains the least amount of material everywhere within the stated limits of size.

Limit Tolerance - When a dimension has its high and low limits stated. In a limit tolerance, the high value is placed on top, and the low value is placed on the bottom.

Maximum Material Condition - The condition in which a feature of size contains the maximum amount of material everywhere within the stated limits of size

Median Point - The mid-point of a two-point measurement.
Modifiers (8) - Communicate additional information about the drawing or tolerancing of a part.
Multiple Single-Segment Profile Control - When two or more profile controls are tolerancing a surface relative to different datums.
Multiple Single-Segment Tolerance of Position Control - When two (or more) single segment tolerance of position callouts are used to define the location, spacing, and orientation of a pattern of feature of size.
No-Go Gage - A gage that is not intended to fit into or over a feature of size. A No-Go gage is made to the LMC limit of the feature of size.
Non-Feature of Size Dimension - A dimension that is not associated with a feature of size.
Outer Boundary (OB) - A worst-case boundary generated by the largest feature of size plus the stated geometric tolerance (and any additional tolerance, if applicable).

Parallelism - The condition that results when a surface, axis or centerplane is exactly parallel to a datum.

Parallelism Control - A geometric tolerance that limits the amount a surface, axis, or centerplane is permitted to vary from being parallel to the datum

Perpendicularity - The condition that results when a surface, axis, or centerplane is exactly 90° to a datum.

Perpendicularity Control - A geometric tolerance that limits the amount a surface, axis, or centerplane is permitted to vary from being perpendicular to the datum.
Planar Datum - The true geometric counterpart of a planar datum feature.
Planar Feature of Size - A feature of size that contains two features: the two parallel plane surfaces.
Plus-minus Tolerance - The nominal or target value of the dimension is given first, followed by a plus-minus expression of a tolerance.
Primary Datum - The first datum plane that the part contacts in a dimensional measurement.
Profile- The outline of a part feature in a given plane.
Profile Control - A geometric tolerance that specifies a uniform boundary along the true profile that the elements of the surface must lie within.

 Profile of a Line Control - A geometric tolerance that limits the amount of error for line elements relative to their true profile.

 Profile of a Surface Control - A geometric tolerance that limits the amount of error a surface can have relative to its true profile.

 Projected Tolerance Zone - A tolerance zone that is projected above the part surface.

 Radius - A straight line extending from the center of an arc or circle to its surface.

Regardless of Feature Size - The term that indicates a geometric tolerance applies at any increment of size of the feature, within its size tolerance.
Rule #1 - Where only a tolerance of size is specified, the limits of size of an individual feature prescribe the extent to which variations in its form--as well as in its size--are allowed.
Rule #2 - RFS applies, with respect to the individual tolerance, datum reference, or both, where no modifying symbol is specified.
Secondary Datum - The second datum plane that the part contacts in a dimensional measurement
Simulated Datum - The plane (or axis) established by the datum feature simulator.
Simultaneous Engineering - A process where design is a result of input from marketing, engineering, manufacturing, inspection, assembly, and service.
Special-Case Feature of Size Datum - When a feature of size datum feature is referenced at MMC, but simulated in the gage at a boundary other than MMC.
 Straightness (Axis or Centerplane) - The condition where an axis is a straight line (or, in the case of a centerplane, each line element is a straight line).
Straightness of a Line Element - The condition where each line element (or axis or centerplane) is a straight line.
Straightness Control (Feature of Size) - A geometric tolerance that, when applied to a feature of size, limits the amount of straightness error allowed in the axis or centerplane.
Straightness Control (Surface) - A geometric tolerance that, when directed to a surface, limits the amount of straightness error allowed in each surface line element.
 Symmetry - The condition where the median points of all opposed elements of two or more feature surfaces are congruent with the axis or centerplane of a datum feature.
Symmetry Control - A geometric tolerance that limits the symmetry error of a part feature.
Tertiary Datum - The third datum plane that the part contacts in a dimensional measurement.
3-2-1 Rule - Defines the minimum number of points of contact required for a part datum feature with its primary, secondary, and tertiary datum planes.
Tolerance - The total amount that features of the part are permitted to vary from the specified dimension.

Tolerance Analysis Chart - A means of graphically displaying the limits of a part as defined by the print specifications
Tolerance of Position Control - A geometric tolerance that defines the location tolerance of a feature of size from its true position.
Tolerance Stack - A calculation used to find the extreme max. or min. distance on a part

Total Runout - A composite control affecting the form, orientation, and location of all surface elements of a diameter (or surface) relative to a datum axis.

Total Runout Control - A geometric tolerance that limits the amount of total runout of a surface.
True Geometric Counterpart - The theoretical perfect boundary or best fit tangent plane of a specified datum feature.
True Position - The theoretically exact location of a feature of size as defined by basic dimensions.
True Profile - The exact profile of a part feature as described by basic dimensions.
Unequal Bilateral Tolerance - A tolerance where the allowable variation is from the target value, and the variation is not the same in both directions.
Unilateral Tolerance - A tolerance where the allowable variation from the target value is all in one direction and zero in the other direction.
Variable Gage - A gage capable of providing a numerical reading of a part parameter.
Virtual Condition (VC) - A worst-case boundary generated by the collective effects of a feature of size specified at MMC or at LMC and the geometric tolerance for that material condition.
Virtual Condition Boundary Theory - A theoretical boundary limits the location of the surfaces of a feature of size.
Worst-case Boundary (WCB) - A general term to refer to the extreme boundary of a feature of size that is the worst-case for assembly. Depending upon the part dimensioning, a worst-case boundary can be a virtual condition, inner boundary, or outer boundary.
Zero Tolerance at MMC - A method of tolerancing part features that includes the tolerance geometric value with the feature of size tolerance and states a zero at MMC in the feature control frame