BIZOMAT 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.
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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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
Mass 1
What this means: Mass
- What it is
- The mass of this item in the assembly, from weighing or the CAD model. Items left at zero are not included.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 10000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same mass unit for every item; the result is a mass-weighted average.
What this means: X position of its CG
- What it is
- The X coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use one datum and one set of axis directions for every item; a coordinate on the other side of the datum is negative.
What this means: Y position of its CG
- What it is
- The Y coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign of the coordinate; mixing directions moves the combined centre of gravity.
What this means: Z position of its CG
- What it is
- The Z coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If Z is height, measure all items from the same base level.
Mass 2
What this means: Mass
- What it is
- The mass of this item in the assembly, from weighing or the CAD model. Items left at zero are not included.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 10000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same mass unit for every item; the result is a mass-weighted average.
What this means: X position of its CG
- What it is
- The X coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use one datum and one set of axis directions for every item; a coordinate on the other side of the datum is negative.
What this means: Y position of its CG
- What it is
- The Y coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign of the coordinate; mixing directions moves the combined centre of gravity.
What this means: Z position of its CG
- What it is
- The Z coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If Z is height, measure all items from the same base level.
Mass 3
What this means: Mass
- What it is
- The mass of this item in the assembly, from weighing or the CAD model. Items left at zero are not included.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 10000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same mass unit for every item; the result is a mass-weighted average.
What this means: X position of its CG
- What it is
- The X coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use one datum and one set of axis directions for every item; a coordinate on the other side of the datum is negative.
What this means: Y position of its CG
- What it is
- The Y coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign of the coordinate; mixing directions moves the combined centre of gravity.
What this means: Z position of its CG
- What it is
- The Z coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If Z is height, measure all items from the same base level.
Mass 4
What this means: Mass
- What it is
- The mass of this item in the assembly, from weighing or the CAD model. Items left at zero are not included.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 10000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same mass unit for every item; the result is a mass-weighted average.
What this means: X position of its CG
- What it is
- The X coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use one datum and one set of axis directions for every item; a coordinate on the other side of the datum is negative.
What this means: Y position of its CG
- What it is
- The Y coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign of the coordinate; mixing directions moves the combined centre of gravity.
What this means: Z position of its CG
- What it is
- The Z coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If Z is height, measure all items from the same base level.
Mass 5
What this means: Mass
- What it is
- The mass of this item in the assembly, from weighing or the CAD model. Items left at zero are not included.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 10000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same mass unit for every item; the result is a mass-weighted average.
What this means: X position of its CG
- What it is
- The X coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use one datum and one set of axis directions for every item; a coordinate on the other side of the datum is negative.
What this means: Y position of its CG
- What it is
- The Y coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign of the coordinate; mixing directions moves the combined centre of gravity.
What this means: Z position of its CG
- What it is
- The Z coordinate of this item’s own centre of gravity, measured from the datum shared by all items.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If Z is height, measure all items from the same base level.
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.
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