Assembly Support

This document explains how assemblies (hierarchical structures) are represented in STEP files.

1. Hierarchy Mechanism

In STEP, parent-child relationships and their associated transformation (placement) information are described separately.

• NEXT_ASSEMBLY_USAGE_OCCURRENCE (NAUO): The central entity that logically connects a parent part to a child part.
• ITEM_DEFINED_TRANSFORMATION: The coordinate transformation matrix (rotation and translation).

2. External References

When dealing with large assemblies, there are two common management methods:

Method	Characteristics	Compatibility Risks
Monolithic	All data is packed into a single file.	File size can become massive, sometimes leading to loading failures.
External Reference	Geometry data is stored in separate files and referenced via paths.	Relative paths may break, or the receiver may not support reference resolution.

3. Mathematical Details of Transformation

Assembly placement information is typically described in one of two ways:

A. Transformation Matrix (ITEM_DEFINED_TRANSFORMATION)

Describes the transformation from the parent coordinate system to the child coordinate system as a direct matrix (or a 3x3 matrix and a translation vector).

• Application Order: If $P_{child}$ is the local coordinate of the child part and $M$ is the transformation matrix, the position in the parent coordinate system $P_{parent}$ is usually $P_{parent}=M\times P_{child}$.
• Note: While formulated in the STEP standard, some CAD kernels may require the matrix to be transposed.

B. Definition via Axis Placement (AXIS2_PLACEMENT_3D)

Uses REPRESENTATION_RELATIONSHIP_WITH_TRANSFORMATION to specify the origin in the parent (From) and the target placement for the child (To) using AXIS2_PLACEMENT_3D.

• Pros: More intuitive than numerical matrices and tends to have higher interoperability between CAD systems.

4. Implementation Notes

• Transformation Reversal: The order of matrix application (Parent to Child vs. Child to Parent) is defined in the standard, but some implementations may read them in reverse.
• Unit Propagation: If a parent assembly is in mm and a child part is in inches, units must be converted before applying the transformation matrix.

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📚 Next Steps

• PMI Support - Definition of dimensions and tolerances.

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