Planar Force Balance Workbench

How to use Planar Force Balance Workbench

Sum horizontal/vertical forces and counterclockwise moments about the entered reference, solve independent unknown directions and verify every equilibrium equation.

1. Use the example as the schema; replace its labels and entered model assumptions.
2. Sum horizontal/vertical forces and counterclockwise moments about the entered reference, solve independent unknown directions and verify every equilibrium equation.
3. Calculate, inspect the complete witnesses and limitations, then copy or download the JSON report.

Good to know

• 0–100 known forces, 0–100 free couples and up to 3 unknown forces. Inputs are decimal strings in meters, newtons and N·m, each magnitude at most 1 billion. Unknown directions must have exact squared length 1.
• Resultant mode requires an empty unknowns array; balance mode requires 1–3 independent unknown columns. Singular, underdetermined and inconsistent systems fail explicitly. Approximate direction cosines that do not square to exactly 1 are outside this exact subset. No contact/tension admissibility, structural design or safety verdict.
• Local calculation with no upload, input persistence or outside lookup. Model JSON is limited to 30,000 characters and 10,000 values. Decimal quantities are strings with up to six places; count fields use plain JSON integers. Exact fractions are capped at 8,192 bits. The complete JSON output is limited to 1,000,000 characters; approximate numbers preserve their stored values. Unsupported states fail explicitly.