3. Anchorage point definition and coordinate systems

Every restraint-system geometry decision ultimately reduces to a set of coordinates. Before a single belt span can be routed, before a retractor can be positioned, and before any lap-belt angle can be evaluated, the engineer must fix where each anchorage sits in a frame that everyone on the program agrees on. This chapter establishes the reference frames used in seatbelt anchorage work, explains how SAE J1100 formalizes vehicle dimensions, and shows how to parameterize anchorage points so that geometry can be driven, checked, and optimized rather than hand-placed.

Vehicle Reference Frames

Automotive geometry is defined against a small family of right-handed Cartesian frames. The most fundamental is the vehicle coordinate system, whose origin is conventionally placed at the intersection of the vehicle centerline, the front axle centerline, and the ground plane (or a designated design ground). The axes follow the SAE convention:

• X — longitudinal, positive toward the rear of the vehicle.
• Y — lateral, positive toward the right side of the vehicle (from the driver's seated perspective).
• Z — vertical, positive upward.

This sign convention matters enormously. A common error is assuming X is positive forward; under SAE practice it points rearward, so a point 400 mm behind the front axle has X = +400. Mixing conventions between CAD, CAE, and test data is one of the most persistent sources of anchorage mislocation. Always confirm the convention at the start of a program and document it.

Two derived frames appear constantly in restraint work. The seating reference point (S&R or "R-point") frame is a local frame whose origin is the manufacturer-designated hip point of a specific seating position, with axes parallel to the vehicle frame. The H-point is the measured hip point from a physical or digital HPM (H-point machine); the R-point is the design intent, and the two should be reconciled during development. Anchorage locations are frequently expressed relative to the R-point because belt geometry is fundamentally a relationship between the occupant's hip/shoulder and the anchorages, not between the anchorages and the ground.

SAE J1100 and Dimensional Nomenclature

SAE J1100 (Motor Vehicle Dimensions) provides the standardized vocabulary and measurement procedures that let a seatbelt anchorage be communicated unambiguously across OEMs and suppliers. Rather than inventing local names, engineers reference J1100 codes. The codes most relevant to restraint geometry include:

J1100 also defines the measurement conditions — occupant posture, seat position, and the reference planes — so that a reported L31 value means the same thing in a supplier's CAD model and in a physical audit. When you parameterize anchorages, adopt these codes as your variable names. A model that reports "L31 = (X, Y, Z)" is immediately legible to any restraint engineer; a model that reports "anchor_A" is not.

Geometric Parameterization for Restraint Systems

Parameterization converts a cloud of coordinates into a small set of meaningful, constrained variables. For a three-point belt, the essential parameters are the four anchorage points (shoulder/D-ring, outboard lap, inboard lap/buckle, and retractor) plus the webbing path between them. A practical parameterization expresses each point in the R-point frame and then derives the angles that govern performance:

• Lap-belt angle — the angle of the lap belt in side view relative to horizontal, typically targeted within a range that keeps the belt on the pelvis rather than the abdomen.
• Shoulder-belt angle — the angle of the shoulder belt relative to horizontal, which influences chest loading and the tendency to slip off the shoulder.
• Wrap angle at the D-ring — the angle through which the webbing turns, affecting friction and retraction.
• Span lengths — the straight-line distances between anchorages, which set webbing take-up and retractor stroke.

These derived quantities are what the optimization actually targets. The anchorage coordinates are the design variables; the angles and spans are the responses. Keeping this separation explicit is what makes load-path optimization tractable.

From Coordinates to a Checkable Model

The value of a clean parameterization is that it can be checked automatically. A typical workflow defines the anchorage points as named parameters, computes the derived angles and spans, and compares them against requirement bands. The following pseudo-configuration shows the structure; it is a template, not a validated model:

# Anchorage definition in R-point frame (mm)
R_point_vehicle = (1200, -380, 520)

anchors = {
  "L31_shoulder": (X=-150, Y=-330, Z=+430),
  "L33_lap_out":  (-220, -180, -220),
  "L34_lap_in":   (-180,  +60, -200),
  "L38_retractor":(-260, -200, -260),
}

# Derived checks
lap_angle_side = atan2(dZ_L33, dX_L33)      # target band, e.g. 30..55 deg
shoulder_angle = atan2(dZ_L31, dX_L31)      # target band, e.g. 20..40 deg
lap_span       = norm(L33 - L34)            # target band, e.g. 300..420 mm

When a check fails, the failure is traceable to a specific coordinate, not to a vague "belt looks wrong." That traceability is the entire point of parameterization.

Visualizing the Anchorage Geometry

The diagram below shows the four anchorage points of a three-point belt expressed in the R-point frame, with the derived lap and shoulder angles and the webbing path. It is the mental model that the parameterization encodes.

With the frame fixed, the J1100 codes adopted as variable names, and the derived angles and spans computed from the anchorage coordinates, the restraint geometry becomes a checkable, optimizable model. The next step — using these parameters to evaluate and improve the load path — depends entirely on the discipline established here: one frame, one convention, one set of names.