Datum Reference Frames

Datum Reference Frames (cross-cutting/tolerancing/datum-reference-frames)

Use when the task is the datum system of a GD&T scheme: establishing the datum reference frame from the datum precedence, the degrees of freedom each datum constrains, the datum feature simulators, the material condition modifiers on datum feature references, and the feature control frame callout. This leaf defines the reference frame; position tolerance zone math lives in position-tolerance-calc and worst-case stackup lives in tolerance-stackup.

Domain quick reference

• A datum reference frame is the coordinate system established from the datum features of a part, taken in precedence order: the primary datum establishes the frame first, the secondary datum locates the frame in the next direction, and the tertiary datum finishes the location. The 3-2-1 rule is the common pattern: the primary datum constrains three degrees of freedom, the secondary two, the tertiary one.
• Six degrees of freedom exist: three translations (tx, ty, tz) and three rotations (rx, ry, rz).
• Datum feature simulators: a planar surface is simulated by a plane (three point contact), a cylindrical surface (hole, pin, shaft) by its axis, a spherical surface by a point.
• A plane constrains one translation (along its normal) and two rotations (tilting about the in-plane axes). An axis constrains two translations (perpendicular to the axis) and two rotations. A point constrains three translations.
• In a frame, each datum constrains only the degrees of freedom not already constrained by the earlier datums, so swapping the primary and secondary datums changes the constraint table.
• Material condition modifiers on datum feature references set the simulator boundary: RMB (regardless of material boundary) fixes the simulator with zero datum shift; MMB (maximum material boundary) allows datum shift equal to the departure of the actual mating size from the MMB size; LMB (least material boundary) allows datum shift equal to the departure from the LMB size. For a hole the MMB size is the smallest hole and the LMB size the largest; for a pin the MMB size is the largest pin and the LMB size the smallest.
• The feature control frame is the drawing callout: the geometric characteristic symbol, the tolerance value with an optional diameter symbol and material condition modifier, then the datum feature references with their modifiers, e.g. position symbol, diameter 0.5 at MMC, datums A, B at MMB, C.

Workflow

1. Collect the datum feature references from the drawing callout in precedence order: primary, secondary, tertiary. For each, record the feature type (plane, axis, point), the orientation (x, y, z) and any material condition modifier.
2. Parse and validate the precedence with parse_datum_precedence.
3. Build the reference frame with datum_reference_frame: read the simulators and the constrained degrees of freedom table from the result.
4. Read the unconstrained degrees of freedom: a fully located frame leaves none; a free rotation about a primary axis is a normal result, not an error.
5. Apply the material condition modifier with datum_shift to get the datum shift available from each datum feature reference.
6. Build the callout with feature_control_frame and report the frame definition, the constraint table, the datum shifts, and the frame string.

Datum system model

Degrees of freedom by simulator

Precedence arithmetic

Each datum contributes its own degree of freedom set minus everything already constrained. Example, the 3-2-1 block:

1. Primary plane with normal z: {tz, rx, ry}, three constrained.
2. Secondary plane with normal x: own set {tx, ry, rz} minus the primary leaves {tx, rz}, two constrained.
3. Tertiary plane with normal y: own set {ty, rx, rz} minus both leaves {ty}, one constrained.

Total six constrained, the frame is fully located. An axis primary along z with two perpendicular planes leaves the rotation about the axis free: that degree of freedom is reported unconstrained.

Material condition model

The modifier on a datum feature reference sets the simulator boundary and the datum shift available:

Feature control frame string

Format: symbol | tolerance segment | datum references. The tolerance segment is the optional diameter symbol, the tolerance value, and the optional material condition modifier (M, L, S). Datum references are uppercase letters with an optional MMB or LMB suffix. Example: position symbol, diameter 0.5 at MMC, datum A, datum B at MMB, datum C renders as the symbol, the segment diameter-0.5-M, then A, B-M, C.

Worked example

Mounting bracket: datum A is the base face (plane, normal z), datum B is the side face (plane, normal x), datum C is the locating hole (axis, z, referenced at MMB). The hole pattern uses a position tolerance of 0.5 diameter at MMC.

1. parse_datum_precedence returns A (plane, z, rmb), B (plane, x, rmb), C (axis, z, mmb).
2. datum_reference_frame: A constrains tz, rx, ry (3); B constrains tx, rz (2); C constrains ty (1). Total six, nothing unconstrained.
3. The locating hole measures 10.2 actual mating size against the 10.0 MMB size: datum_shift("mmb", "hole", 10.0, 10.2) gives 0.2 datum shift for datum C.
4. feature_control_frame("position", 0.5, ("A", "B", {"letter": "C", "modifier": "mmb"}), "mmc") renders the frame string: position symbol, diameter 0.5 at MMC, datums A, B, C at MMB.

Pitfalls

• Confusing the datum system with the tolerance zone: the reference frame defines where the coordinate system is and what each datum locks; the position zone diameter and the stackup are separate leaves (position-tolerance-calc, tolerance-stackup).
• Ignoring precedence: the secondary datum constrains only what the primary left free; reporting its full own set double counts degrees of freedom.
• Treating an unconstrained rotation as an error: an axis primary legitimately leaves the rotation about the axis free until a tertiary feature locks it.
• Reversing the MMB direction: a hole gains datum shift as it grows past the MMB size, a pin as it shrinks below it.
• Forgetting the material condition modifier on the datum feature reference: RMB is the default, MMB and LMB change both the boundary and the available shift.
• Writing the callout without the diameter symbol for cylindrical zones: position, concentricity, symmetry, and cylindricity zones are diameters.

Behavior contract (gate 3)

The precedence parsing, simulator mapping, degree of freedom table, material condition shift, and feature control frame string logic is exercised by the gate 3 contract test: scripts/test_datum_reference_frames.py against scripts/datum_reference_frames_logic.py (stdlib unittest, offline). Run: python3 scripts/test_datum_reference_frames.py

Compliance

• Standards referenced, not reproduced: ASME Y14.5 is proprietary and sold (ASME); the datum precedence method, the degree of freedom model, the material condition boundary rules, and the feature control frame format are common GD&T methodology, name and paraphrase only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false (reference-only listing).