Dataset/fbd_dataset_3000/README.md

GRIP Free Body Diagram Dataset 3000

Current version: free-body-diagram-2.0.0; the initial build is preserved under archive/v1/. V2 stores explicit physical_frame, rendered_frame, and question_frame_policy declarations. All 750 wrong_diagram items explicitly separate drawn-arrow judgments from physically correct calculations in both Levels 3 and 4.

Level 3 answer formatting uses structured tie groups and accepts any ordering within a tied group. The maximum tie-group-size distribution is: size 1 for 1,624 items, size 2 for 1,001, size 3 for 125, and size 4 for 250; thus fully tied four-force rankings occur in 250/3,000 items and do not dominate the dataset. PNG validation recovers the count and direction of every shown arrow in all 3,000 images.

1. Dataset overview

This is the third Physical/Mechanical Reasoning category in GRIP, following gear trains and physical stability. It contains 3,000 deterministic free-body-diagram images and 15,000 questions covering force identification, vector comparison, equilibrium, Newton’s second law, physical error/omission detection, and counterfactual force analysis.

The wrong_diagram preset parallels the global-consistency skill in impossible_object_dataset_3000, but applies it to mechanics rather than pure geometry. Images are synthetic and generated from exact physics parameters with random.Random(image_index).

2. Visual scenarios and presets

Six scenario types are balanced at 500 images each:

• block on an incline;
• hanging mass;
• Atwood machine;
• block pushed against a wall;
• mass in an elevator;
• car on a banked curve.

Four presets are balanced at 750 images each: equilibrium, accelerating, missing_force, and wrong_diagram. Every record separates the complete physically correct forces list from shown_forces, the exact list rendered in the PNG. Missing and wrong diagrams therefore never overwrite the physical source of truth.

Force directions use 0° = right and 90° = up. Arrow lengths share one per-image Newton-to-pixel scale and are exactly proportional to shown magnitude. Weight, normal, friction, tension, applied force, and drag have fixed visual encodings on an off-white #FDFAF4 background.

3. Five-level question structure

1. Simple Description: count rendered force arrows.
2. Basic Relational: identify a force’s arrow label; missing-force items also identify the omitted force.
3. Comparative/Structural: rank shown magnitudes, check shown vertical balance, and judge physical equilibrium.
4. Compound Reasoning: compute physical net force plus a scenario-specific derived quantity; wrong-diagram items also identify and explain the invalid arrow.
5. Extrapolative/Counterfactual: recompute direction after removing a force, or test whether an incline block would slip at 40°.

The original design contained ten question points: arrow count, downward-force identification, magnitude ranking, net force, friction/tension identification, vertical balance, equilibrium, removed-force direction, scenario-derived calculation, and incline-angle counterfactual. They were condensed respectively into Levels 1; 2; 3; 4; and 5 so the dataset follows GRIP’s unified five-level rubric without discarding those reasoning checks.

4. Physics and ground truth

Per-scenario solvers implement:

• incline decomposition using mg sin(theta), mg cos(theta), applied force, and friction;
• hanging-mass tension from T = m(g-a);
• Atwood tension T = 2 m1 m2 g / (m1+m2);
• wall normal equal to horizontal applied force and friction constrained by mu*N;
• elevator support force N = m(g+a);
• banked-curve radial/vertical resolution, including the direction of required friction.

Each annotation stores physical parameters, correct forces, shown forces, physical and shown net vectors, acceleration, equilibrium, missing-force identity, wrong-force details, scenario-specific derived quantities, and five ground-truth questions.

5. Numeric-tolerance schema

Level 4 introduces GRIP’s first structured real-valued grading declaration:

{"type":"numeric_tolerance","tolerance_percent":2}

This is private scoring metadata stored in annotations.jsonl and answer_key.csv. It is absent from public question_set.csv. The prompt asks for the physical values, while downstream scoring may accept answers within 2% of independently recomputed ground truth.

6. Independent validation and files

validate_fbd_dataset.py has independent per-scenario equations and does not import generation-time solvers. It recomputes every true force, reconstructs each controlled missing/wrong variant, vector-sums net force, re-derives acceleration and all five answers, verifies that omissions are physically required and wrong arrows genuinely invalid, checks exact 500/750 scenario/preset balance, validates public/private CSV separation, and probes every rendered arrow’s color, direction, and proportional length directly in the saved PNG.

Files:

• images/fbd_0001.png through images/fbd_3000.png
• annotations.jsonl
• dataset_final.csv and dataset_final.jsonl
• public question_set.csv
• private answer_key.csv
• validation_report.txt, generation_stats.json, stats.md
• contact_sheet.png, review_sheet.png, and sample_test/

Commands:

python generate_fbd_dataset.py
python flatten_annotations.py
python validate_fbd_dataset.py
python make_artifacts.py
python -m pytest tests -q
python generate_fbd_dataset.py --sample

7. Known limitations

• Only six scenario families are represented.
• Forces are limited to weight, normal, friction, tension, applied force, and optional drag vocabulary.
• Diagrams use idealized point-mass/rigid-body introductory mechanics rather than deformation, torque, or fluid dynamics.
• Banked-curve equilibrium scenes represent a parked body; moving banked-curve scenes correctly retain centripetal acceleration.
• Real-valued Level 4 answers require 2% tolerance rather than exact-string grading.
• Missing and wrong diagrams are deliberately diagnostic and should not be treated as measurements of naturally occurring diagram error frequency.

Supplementary open-ended questions

Version free-body-diagram-6.0.0 replaces the supplementary free-response set with the exact approved domain template or scene-specific variant in OPEN_QUESTION_SPEC.md. It includes 3000 eligible items and excludes 0 under {}. Every prompt uses visible evidence, asks for justification, and ends with a confidence score from 0 to 1.

• open_questions.csv is public and contains exactly question_id,image,prompt.
• open_answer_key.csv is answer-key-side and contains separate partial-credit fields, an exhaustive acceptance_set, deterministic targets, and machine-readable tolerances for every numeric field.
• open_annotations.jsonl is answer-key-side and adds the complete derivation and scoring declaration.
• open_validation_metrics.json contains full target and answer distributions, constant-answer baselines, prompt/schema checks, independent metadata derivation results, and exhaustive PNG recovery results.

Scored fields at or above 60% after template revision: {}. Targeted fields: drawn_magnitude_ranking. Do not provide open_answer_key.csv, open_annotations.jsonl, or the closed-set annotations.jsonl to a model under evaluation because they expose answer-side scene metadata.