Solid Bench

Parts

Part

Mass properties

Method

Units are mm, g and g/cm³. Each part is a parametric primitive whose volume, area, center of mass and inertia tensor come from closed-form formulas, then are rotated (R·I·Rᵀ) and combined with the parallel-axis theorem. Sketched parts get exact profile moments (Green's theorem) times the extrude depth, or Pappus's theorems for revolves. Joined and cut bodies add and subtract those moments, minus the overlap. Imported STL, 3MF and OBJ meshes are integrated triangle by triangle (divergence theorem) and must be watertight. All of it is checked against textbook answers.

Limits: no 3D edge fillets yet; radii come from sketches. A Join or Cut that only partly overlaps a body gets its overlap from the mesh (about 0.1 % on curved faces); overlaps that are all-or-nothing stay exact. Overlapping parts are counted twice. Hidden parts are left out of mass properties and STL export. The bounding box comes from the display mesh. Densities are nominal handbook values.