Strict discrete-component arithmetic
3D Center of Mass (Center of Gravity in Uniform Gravity)
Compute the mass-weighted mean position of any number of discrete components. Every row must supply a positive mass and x, y, z coordinates in one common frame.
Mass-weighted position
Coordinate units are the length unit entered; mass moments are mass-unit × length-unit.
Discrete component equation
The NASA Glenn center-of-gravity explanation defines the location through the weighted distribution of weight. In an approximately uniform gravitational field, weight is proportional to mass, so this discrete mass-weighted equation gives the center of gravity used in ordinary engineering arithmetic.
What this coordinate does not establish
A center coordinate alone is not a stability, lifting, rigging or machine-safety approval. A real assessment also needs the support polygon or suspension geometry, force direction, attachment points, load path, acceleration and dynamic effects, structural and equipment capacities, uncertainty, and the applicable procedure. OSHA 29 CFR 1926.1404, for example, requires the center of gravity to be identified when needed for stability and requires measures against dangerous unintended movement when information is insufficient.
Do not infer “safe to lift” from this output. Lifting and rigging require a qualified plan and the governing equipment, site and legal requirements.
