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Parallelism

Special Note:

Parallelism actually has two different functions in GD&T depending which reference feature is called out. The normal form or Surface Parallelism is a tolerance that controls parallelism between two surfaces or features. The surface form is controlled similar to flatness with two parallel planes acting as its tolerance zone. Axis Parallelism is a tolerance that controls how parallel a specific parts central axis needs to be to a datum plane or axis. The axis form is controlled by a cylinder around a theoretical perfectly parallel axis. Parallelism is most commonly called out as surface parallelism. However, be sure to pay attention if it is referencing a central axis because it is different! We will only discuss surface parallelism on this page but be sure to check out our page on Perpendicularity to see how an axis is controlled with GD&T.

GD&T Symbol: Parallelism Symbol

Relative to Datum: Yes

MMC or LMC applicable: Yes

GD&T Drawing Callout:

Parallelism Drawing Callout

Description:

Parallelism is a fairly common symbol that describes a parallel orientation of one referenced feature to a datum surface or line. It can reference a 2D line referenced to another element, but more commonly it relates the orientation of one surface plane parallel to another datum plane in a 3-Dimensional tolerance zone. The tolerance indirectly controls the 0° angle between the parts by controlling where the surface can lie based on the datum. See the tolerance zone below for more details.

Note: Parallelism does not control the angle of the referenced feature, but only creates an envelope in which the feature must lie.

It is important to determine what the reference feature is (surface or axis) and then what is acting as the datum (surface or axis) to determine how the parallelism is to be controlled.

GD&T Tolerance Zone:

Two parallel planes or lines which are oriented parallel to the datum feature or surface. All points that are on the referenced feature must in the tolerance zone.

Remember: Parallelism does not directly control the angle of the referenced surface; it controls the envelope (like flatness) where the surface needs to be. The goal is to ensure all points are within a specified tolerance distance away from their corresponding datum points.

Parallelism Tolerance Zone

Gauging / Measurement:

Parallelism is quite simple to measure. Like flatness, a gauge is run across the reference surface or feature. However unlike flatness, the part is constrained against a granite block or flat plane that acts as the datum surface where it is measured.

Parallelism Gauging

Relation to Other GD&T Symbols:

Surface Parallelism

Parallelism is a specific form of angularity only at 0°/180° instead of a called out angle. All the profiles of orientation and are used in the exact same way. All of the orientation symbols (angularity, perpendicularity, and parallelism) all call out the particular feature envelope referenced to a datum.

The Parallel Symbol is also closely related to flatness when referenced/measured surface is flat. When you call out parallelism, flatness is implied (you are measuring a surface variation between two parallel planes = flatness) However the biggest difference is parallelism is measured with respect to a datum, ensuring both the datum and reference feature are always parallel.

When Used:

Whenever two surfaces or features need to work in sync with each other and constant distance must be maintained, parallelism is effective. Whenever you have a part that must always fit nicely between two planes that need to reference each other, it comes in handy. Even though surface parallelism seems to ensure that a flat surface is mating with another flat surface, it can also be applied to two sides of a hole or cylinder to avoid a taper. Any part with two critical flat surfaces such as gears, would call out parallelism.

Parallelism Example:

A gear has to maintain constant axial load on both faces. To ensure even contact one side of the gear is held parallel to the other side. To do this without parallelism, the gear width would have to be tightly controlled, which could be very difficult to do.

Parallelism Example 1

Ensuring even surfaces without GD&T

With parallelism you can open up the dimension of the gear and control the faces without rejecting good gears.

Parallelism Example 2

Controlling two faces with GD&T parallelism callout.

Final Notes:

Combination of Orientation and Form:

Parallelism is very common in its surface form. When dealing with any flat surfaces, flatness may be called out, but parallelism is usually more critical, since the relation of surfaces in an assembly is more important.

Max Material Condition with Axis:

Straightness, Axis Angularity, Axis Parallelism and Axis Perpendicularity can all be called out and controlled with a gauge in maximum material condition. However only perpendicularity and straightness are used commonly. Please see our page on Maximum Material Condition for more information.

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GDT Symbol cylindricity
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Cylindricity

GD&T Symbol:symbol_cylindricity

Relative to Datum: No

MMC or LMC applicable: No

Drawing Callout:

cylindricity drawing callout

Description:

The Cylindricity symbol is used to describe how close an object conforms to a true cylinder. Cylindricity is a 3-Dimensional tolerance that controls the overall form of a cylindrical feature to ensure that it is round enough and straight enough along its axis. Cylindricity is independent of any datum feature the tolerance needs to be less than the diameter dimensional tolerance of the part. Cylindricity essentially forms a perfect cylindrical boundary around the object that the entire 3-Dimensional part must lie in.

GD&T Tolerance Zone:

Two concentric cylinders that run the entire length of the feature – one inner and one outer, in which all the points on the entire surface of the cylindrical feature must fall into. The entire length of the called out feature would be controlled.

cylindricityTolerance Zone

 

 

Gauging / Measurement:

Cylindricity is measured by constraining a part on its axis, and rotating it around while a height gauge records the variation of the surface in several locations along the length. The height gauge must have total variation less than the tolerance amount.

Relation to Other GD&T Symbols:

Cylindricity is a merger of circularity and surface straightness. It is the 3-Dimensional version of circularity along an entire cylinder length. While circularity only is concerned with individual measurements around the surface in one circle, cylindricity takes into account how straight the axial portion of the cylinder is. Thinking of stack of coins, cylindricity would measure to make sure that the entire stack is straight up and that every coin is round. Circularity would only be measurements of the roundness of the individual coins.

When Used:

Cylindricity is a fairly common callout for shafts, pins and any critical cylindrical element. When a part needs to be both round and straight along its axis, such as a sliding shaft, or a dynamic locating pin, cylindricity is usually called out. You will see this GD&T symbol very often in automotive drawings and mechanical systems.

Example:

If you had a bushing that was to be pressed into a housing, the bushing would take the form of the housing bore when inserted. To ensure that the bushing maintains its round shape, and wears evenly along its surface, the housing bore needs to be very cylindrical. To do this without GD&T you would need very tight dimensions on the diameter of the bore, which may be very hard to control when being machined (and expensive)

cylindricity example 1Cylindricity example 1: Controlling cylindricity without GD&T Symbol

cylindricity example 2 Controlling the circularity and the straightness of the bore with cylindricity.

This GD&T control allows the diameter tolerances of the part to be opened up much larger, and better controls the entire length of the bore. You can now accept a much broader range of hole sizes as long as the cylindricity is met.

Final Notes:

Statistical Tolerances:

Because cylindricity specifies the form of the surface, it must be considered when calculating a statistical tolerance stack. For example if you have a part with a diameter and cylindricity callout, you must input both into your statistical stack since the cylindricity can contribute to a large part envelope than just the diameter tolerance alone. There are different theories on doing this and how to implement it; however it can make a slight impact on skewing the results higher. Normal tolerance stacks do not require this since due to the envelope principal; the maximum radial envelop cannot exceed your maximum diameter tolerance due to rule #1 of GD&T.

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GD&T perpendicularity symbol
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Perpendicularity

Special Note:

Perpendicularity in GD&T can mean two very different things depending which reference feature is called out. The normal form or Surface Perpendicularity is a tolerance that controls Perpendicularity between two 90° surfaces, or features. Surface Perpendicularity is controlled with two parallel planes acting as its tolerance zone. Axis Perpendicularity is a tolerance that controls how perpendicular a specific axis needs to be to a datum. Axis Perpendicularity is controlled by a cylinder around a theoretical perfectly parallel axis. Pay close attention if a hole or pin is referenced since axis perpendicularity is commonly called out on these features.

GD&T Symbol:  GD&T perpendicularity symbol

Relative to Datum: Yes

MMC or LMC applicable: Yes

GD&T Drawing Callout:

Surface Perpendicularity:

Perpendicularity-surface drawing callout

Axis Perpendicularity:

Perpendicularity axis drawing callout

Description:

Surface:

Perpendicularity is a fairly common symbol that requires the referenced surface or line to be perpendicular or 90° from a datum surface or line. Perpendicularity can reference a 2D line, but more commonly it describes the orientation of one surface plane perpendicular to another datum plane. The tolerance of the perpendicularity callout indirectly controls the 90° angle between the parts by controlling the location where the surfaces have to lie. See the tolerance zone below for more details.

Note: Perpendicularity does not control the angle of the referenced feature –the tolerance is in distance units. (mm/in)

Axis:

Axis control can also be called out for Perpendicularity and is one of the more common forms of axes call outs. When it is referenced for a circular feature, the feature control frame will contain the diameter (Ø) symbol. Axis Perpendicularity can be applied to a positive feature (pin/boss) or to a negative feature (a hole). When Perpendicularity is referenced for axial control of a feature, the symbol now specifies a cylindrical boundary where the axis of the referenced feature must lie. This cylindrical boundary is formed by taking a line that is directly perpendicular to the datum feature. When this version of Perpendicularity is called out it is to be used with maximum material condition to enable easy gauging of the part. See example 2 below for how these particular parts are gauged.

GD&T Tolerance Zone:

Surface:

Two parallel planes or lines which are oriented perpendicular to the datum feature or surface. The planes are held perpendicular to the datum, but only ensure that the entire feature falls into the tolerance zone.

Remember: Perpendicularity does not directly control the angle of the referenced surface; it controls the envelope (like flatness) where the surface needs to be.

Perpendicularity surface tolerance zone

Axis:

A cylinder surrounding a referenced theoretical axis which is directly perpendicular to the datum feature. The tolerance zone is the diameter of this symbol in which the central axis of the measured feature must lie.

Perpendicularity axis tolerance zone

Gauging / Measurement:

Surface:

Perpendicularity is measured using a height gauge, similar to flatness, however the gauge (or part) is locked to a 90° datum to measure how perpendicular the surface is. The entire surface has to be measured if it is a flat feature.

 Perpendicularity Surface Gauging

Axis:

To ensure that a part or feature is axially perpendicular, Maximum material condition is most often called out on axis perpendicularity to allow easy measurement with a gauge. This allows it to be designed for either a negative (hole) or positive (pin) feature and can take into account a bonus tolerance.*

Gauge size for an internal feature (like a hole):

Gauge Ø (pin gauge)= Min Ø of hole (MMC) – Perpendicularity Tolerance

Gauge size for an external feature (like a pin):

Gauge Ø (hole gauge) = Max Ø of pin (MMC) + Perpendicularity Tolerance

Perpendicularity Axis Gauging

See Example #2 below for a good example Axis Perpendicularity using MMC.

*Note on Bonus Tolerance:

When a functional gauge is used for Perpendicularity, any difference the actual feature size is from the maximum material condition would be a bonus tolerance. The goal of a maximum material condition callout is to ensure that when the part is in its worst tolerances, the orientation and size of the hole/pin will always assemble together. This means that if you make a pin smaller, you make more bonus tolerance for yourself. This bonus can be added to the GD&T tolerance and would widen the perpendicularity tolerance.

Bonus Tolerance = Difference between MMC & Actual condition (See Example 2 Below)

Confused yet? No worries! For more detail on see the sections on Maximum Material Condition.

Relation to Other GD&T Symbols:

Surface:

Perpendicularity is a specific form of Angularity at 90°. All of the orientation symbols (Angularity, Parallelism, and Perpendicularity) all call out the particular feature envelope referenced to a datum.

The Perpendicular Symbol is also closely related to flatness when referenced/measured surface is a surface plane. When you call out Perpendicularity, flatness is implied (you are measuring a surface variation between two parallel planes = Flatness) Perpendicularity is always measured with respect to a datum, where flatness is not.

Axis:

Perpendicularity is closely related to all the other orientation GD&T symbols when called on an axis. The tolerance zone now refers to the uniformity and cylindrical envelope of a central axis. Perpendicularity and Parallelism can be called out on holes and cylindrical pins, often with MMC added.

When Used:

Surface:

Whenever two surfaces needing a constant 90° angle, Perpendicularity is effective. Flange bearings and critical square edges usually reference it. Perpendicularity is also commonly called out on the corners of cylinders where the flat bottom must be perpendicular with the curved sides.

Axis:

Perpendicularity is very commonly called out on the center axis of a hole. Almost always, your hole needs to be perpendicular to the surface it is drilled into. When this is the case, it is called out alongside MMC to ensure that if a pin or bolt needs to be inserted into this hole, the part can enter the whole perpendicular at and always fit in. See example 2 for this explanation.

Surface Perpendicularity Example:

The edge of a stopping block for a rail must form a 90° to ensure proper mating contact takes place. The base of the block is will be our datum and the face where the stopping block makes contact is our referenced surface. To ensure that this face is always perpendicular and flat to make good contact, you would need to both tightly control the angle and the dimensional width of the part.

 

08 Perpendicularity Example 1

Ensuring perpendicular/flat surfaces without GD&T symbol

With perpendicularity you can open up the width dimension and control the face’s angle containing the part very tightly. Your tolerance zone remains the same, but your part is now easer to control and fabricate.

 

Perpendicularity-Example-21

Controlling the perpendicularity with GD&T symbol.

Axis Perpendicularity Example with MMC:

If you have a critical hole feature that needs to remain parallel to the surface that is formed into, perpendicularity can be called out to ensure that the hole is straight. In this example a bolt hole is specified to remain perpendicular to its surface.

Perpendicularity Example 3

Perpendicularity on a hole under MMC

Without an MMC callout you would need to control just the center axis of the hole and measure for it to ensure it is at 90° to the bottom surface. However when MMC is called out on the print, you are controlling both the size and the orientation of the hole. You now can check the both tolerances using a functional gauge with the following dimensions:

Formula for a perpendicularity functional gauge:

Gauge Ø (pin gauge) = Min hole Ø – Perpendicularity Tolerance

Gauge Ø = 9.9 – 0.2 = 9.7

Perpendicularity Example 4

Hole Ø + Hole Perpendicularity > 9.7 (Pin Ø) to be in spec.

Due to the Max Material Condition callout, if you have a hole that is larger than the MMC of 9.9 you will have bonus tolerance that can be added on to your perpendicularity. (According to print Hole Ø cannot be above 10.1 though)

In the example below – The hole is at the least material condition (largest hole size) with the hole at the LMC, your bonus tolerance that can be added to the perpendicularity is calculated as follows:

Bonus Tolerance = Actual Part Size – Max Material Condition

Bonus Tolerance = 10.1 – 9.9 = 0.2

Perpendicularity Example 5

Adding this bonus tolerance to your perpendicularity means your “gauged” perpendicularity tolerance can go up to 0.4 when the part is at its largest diameter.

Final Notes:

Very Common:

Perpendicularity is very common in its surface and axis form. You will see this commonly on many mechanical engineering drawings.

Features of Size:

Perpendicularity will most likely have a MMC or LMC callout if gauge control is used in a production environment. It allows both size and orientation to be measured quickly on the line, as opposed to having to measure perpendicularity with a CMM.

Axis Controls:

Straightness, Axis Angularity, Axis Parallelism, True Position, and Axis Perpendicularity can all be called out to control a center axis. Usually when this is a case in a production environment, MMC is also called out so that a functional gauge can be used. However the only callouts with this case that you would see commonly are perpendicularity and straightness.

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GD&T Symbols Orientation angularity
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Angularity

GD&T Symbol:Angularity Symbol

Relative to Datum: Yes

MMC or LMC applicable: Yes (Uncommon)

Drawing Callout:

Angularity Drawing Callout

Description:

Angularity is the symbol that describes the specific orientation of one feature to another at a referenced angle. It can reference a 2D line referenced to another 2D element, but more commonly it relates the orientation of one surface plane relative to another datum plane in a 3-Dimensional tolerance zone.  The tolerance does not directly control the angle variation and should not be confused with an angular dimension tolerance such as ± 5°.  In fact the angle for now becomes a Basic Dimension, since it is controlled by your geometric tolerance. The tolerance indirectly controls the angle by controlling where the surface can lie based on the datum. See the tolerance zone below for more details.

Maximum material condition or axis control can also be called out for angularity although the use in design and fabrication is very uncommon since gauging a hole or pin at an angle is difficult. When angularity is called out on an axis, the tolerance zone now becomes a cylinder around the referenced axis at an angle to the datum. The page on Perpendicularity goes into this type of reference in further detail since it is more common with perpendicularity.

 

GD&T Tolerance Zone:

Two parallel planes or lines which are oriented at the specified angle in relation to a datum. All points on the referenced surface must fall into this tolerance zone.

Angularity does not directly control the angle of the referenced surface; it controls the envelope (like flatness) that the entire surface can lie.

Angularity Tolerance Zone

Gauging / Measurement:

Angularity is measured by constraining a part, usually with a sine bar, tilted to the reference angle, so that the reference surface is now parallel to the granite slab. By setting the part at an angle the flatness can now be measured across the now horizontal reference surface. The entire variation must not fall outside the tolerance zone.

Angularity Gauging

Relation to Other GD&T Symbols:

Perpendicularity and Parallelism are actually refined forms of Angularity. Perpendicularity describes angularity at 90° and parallelism describes it at 0°. All of these are profiles of orientation and are used in the exact same way. They also can be used with control of an axis under maximum material condition, although perpendicularity is usually the only one you will ever see with this callout.

Orientation GD&T Symbols are also closely related to flatness when the surfaces are is flat planes. When you call out any of the orientation symbols, flatness is implied (you are measuring a surface variation between two parallel planes = Flatness) However the biggest difference is that orientation callouts are measured with respect to a datum, where flatness is not.

When Used:

Angularity helps control any feature that is at an angle to another datum surface. Anytime you have a critical feature which mates with other part at an angle, angularity can be used to help control the angle and flatness of the mating surfaces. Many stamped parts that have bent features use angularity to ensure that the 3D surface formed by the stamping operation that is formed always is controlled and encased in a tolerance zone.

Example:

If you have a stamped part that had to hook into another part at an angle of 30 degrees, you would want to call out angularity on the “bent” feature to ensure that it is always at its proper orientation. If you did not use angularity you would have to both tighten the angle tolerance of the part and the thickness tolerance of the referenced surface.

angularity example 1

 Angularity example 1: Tightening the angle and/or the thickness are required if angularity is not called out.

angularity example 2

Angularity example 2: A simple call to angularity now ensures that the stamped surface now has both proper angle and flatness. The angle must be a basic dimension, but now allows your part thickness to open up more. (Note this drawing is unconstrained and would need additional size dimensions to be accurate.)

Remember – You are not controlling the angle with angularity – you are controlling the surface to fall within the specified dimensional tolerance in millimeters!

Final Notes to Remember:

Datum Relationship:

Since all of the orientation symbols (Angularity, Perpendicularity, and Parallelism) are referenced to a datum – essentially the tolerance is not measuring a specific surface or feature on its own. You are measuring the relationship of one feature or surface with respect to another feature. If one feature is out – both surfaces could be incorrect.

Maximum Material Condition:

Maximum material condition can also be used in a similar method of perpendicularity. Although MMC is usually for pins or holes which need to be perpendicular to a reference surface, so it is not commonly used on angularity. See Perpendicularity for more details about Gauging and Calling out MMC on an orientation symbol.

Dimensional Angularity:

As stated before: 2-Dimensional references can also be used with angularity to ensure that an angle is met around a round or complex feature. If you wanted to specify the angle of a cone for example, the angularity would apply to each line element along that cone referenced to the bottom of the cone.

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