KEVOS® MAKEOS · Mechanics
Combined Centre of Gravity
Where is the centre of gravity of these combined masses?
Total mass and centre of gravity (X, Y, Z) of up to five masses at known positions, for lifting, transport and machine layout.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Mass 1 | ||
| Mass | kg | Mass of item 1 (0 if not used), from weighing or CAD. |
| X position of its CG | mm | X coordinate of item 1’s own centre of gravity from a common datum. |
| Y position of its CG | mm | Y coordinate of item 1’s centre of gravity. |
| Z position of its CG | mm | Z coordinate of item 1’s centre of gravity. |
| Mass 2 | ||
| Mass | kg | Mass of item 2 (0 if not used), from weighing or CAD. |
| X position of its CG | mm | X coordinate of item 2’s own centre of gravity from a common datum. |
| Y position of its CG | mm | Y coordinate of item 2’s centre of gravity. |
| Z position of its CG | mm | Z coordinate of item 2’s centre of gravity. |
| Mass 3 | ||
| Mass | kg | Mass of item 3 (0 if not used), from weighing or CAD. |
| X position of its CG | mm | X coordinate of item 3’s own centre of gravity from a common datum. |
| Y position of its CG | mm | Y coordinate of item 3’s centre of gravity. |
| Z position of its CG | mm | Z coordinate of item 3’s centre of gravity. |
| Mass 4 | ||
| Mass | kg | Mass of item 4 (0 if not used), from weighing or CAD. |
| X position of its CG | mm | X coordinate of item 4’s own centre of gravity from a common datum. |
| Y position of its CG | mm | Y coordinate of item 4’s centre of gravity. |
| Z position of its CG | mm | Z coordinate of item 4’s centre of gravity. |
| Mass 5 | ||
| Mass | kg | Mass of item 5 (0 if not used), from weighing or CAD. |
| X position of its CG | mm | X coordinate of item 5’s own centre of gravity from a common datum. |
| Y position of its CG | mm | Y coordinate of item 5’s centre of gravity. |
| Z position of its CG | mm | Z coordinate of item 5’s centre of gravity. |
Method and formulas
- Total mass M = Σ mᵢ.
- X̄ = Σ(mᵢ xᵢ) ÷ M, and similarly for Y and Z.
- Example: the default items total 195 kg with the centre of gravity at X 153.85, Y 46.154, Z 61.538 mm.
Limitations
- Each item’s own centre of gravity must be known; estimated item CGs limit the accuracy.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find lifting points for an assembly or skid
- Check tipping stability of a machine
- Locate the CG of a fixture with work
Who it is for
- Design engineers
- Lifting planners
- Machine builders
What you get
- Total mass
- Combined centre of gravity X, Y, Z
Interpreting the result
- Place lifting points so the hook is directly above the combined centre of gravity.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 221–227. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
