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Many models are built under the theory that variation is normally distributed along a vector with the range equal to ±3σ (long-term Cpk equal to 1.0). To accommodate these models, a GD&T Deviation Method known as "Root Square Sum (RSS)" is used in 3DCS. With this mode, multiple tolerances applied to a single feature are RSSed* so that the feature may vary the full range of each callout while maintaining a normal distribution along a vector.

This RSS method treats the callouts as subsets of each other. For example, consider a pin with a parallelism callout and a position callout. Since controlling location controls orientation as well, the position callout is the higher-level callout or overall callout of the two callouts. As the orientation of the pin is controlled within the location of the pin, the parallelism callout is the lower level or subset callout.

Each input in 3DCS only impacts a type of variation: location, orientation, or form. For example, if only a position callout is applied to a pin, only the location of the pin will vary while its orientation and form remain perfect. This convention was chosen as most features will either be a single source of variation or not contribute to the outputs at all.  To add orientation variation to the pin a separate orientation callout must be added. If the orientation callout is added then the location range of the position will be internally adjusted such that the RSS of the location and orientation is equal to the total range defined by the position callout. This calculated range will be applied to the pin as location variation. Every callout is independently applied and only controls one type of variation. For example, the orientation range specified on the pin will only rotate the pin's axis around the middle of the pin and the calculated location range will only change the location of the pin. Therefore, the center of the pin only varies from the calculated location range and the ends vary from both ranges.

Typically on a drawing, there may only be a location callout (such as surface profile or position). If this is the case, it may be necessary to add an orientation or a form callout that is some percentage of the location callout's range. Otherwise, in the model there will be no orientation of form variation for that feature, only location.

With that being said, it is not always necessary (or wanted) to add orientation and form callouts to location callouts. Notice in the last example that adding an orientation callout reduced the variation of the center of the pin. If the pin is used in a move, the amount of variation it will contribute will probably decrease without user intent. One exception to this rule is if the projected axis or plane of the feature is important, e.g., the feature acts as a lever, the orientation callout should be defined.  The other exception to this rule is if the relative variation of points** on a feature is being measured. In that case, the form callout should be defined.

Since the points of a feature only represent the actual part within 3DCS, the number of points representing a feature should not affect the variation of the feature. Therefore form ranges are applied independently at each point on a feature, even though the variation of the feature affects the definition of the tolerance zone. Since a feature may have a vast number of points the defined range is applied at each point to allow for infinite points.

The RSS method will only work correctly if the input variation is normally distributed along a vector. This requires Normal distributions for one-dimensional callouts and RightSkew distributions for two-dimensional callouts (these are the default settings within 3DCS). Therefore, caution should be used if changing any of the default distributions as it is possible the combination of location, orientation, and form callouts on one surface may actually exceed the allowable boundary.

 

*RSS: to take the square root of the sum of squared values. In this document, RSS is used to refer to finding any value in a RSS equation.

**Points: unless otherwise specified, includes all mesh nodes and all feature points on a feature.