KEVOS® MAKEOS · Mechanics
Three-Leg Sling Load Share (3D Leg Geometry, Tensions, Angles)
For a three-leg sling to lift points that are not symmetric, how is the load shared between the legs, how long is each leg, and is any leg overloaded or too steep?
Check of a three-leg bridle with the hook directly above the load’s centre of gravity and the lift points at any positions: leg lengths and angles from vertical from the point coordinates (as the cylindrical and spherical coordinates tool), and the tension in each leg by solving the three equilibrium equations of the hook (as the simultaneous equations tool), checked for slack legs, the leg working load limit and the largest angle from vertical.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load (with rigging below the hook) | kN | Weight of the load and everything below the hook. |
| Lift points from the hook (z negative below) | ||
| Point 1 x | mm | Horizontal x position of lift point 1 from the hook, which sits directly above the centre of gravity. |
| Point 1 y | mm | Horizontal y position of lift point 1. |
| Point 1 z | mm | Vertical position of lift point 1 (negative: below the hook). |
| Point 2 x | mm | x of lift point 2. |
| Point 2 y | mm | y of lift point 2. |
| Point 2 z | mm | z of lift point 2. |
| Point 3 x | mm | x of lift point 3. |
| Point 3 y | mm | y of lift point 3. |
| Point 3 z | mm | z of lift point 3. |
| Limits | ||
| Working load limit of each leg | kN | Working load limit of each leg at the angle used. |
| Largest leg angle from vertical | ° | Steepest leg angle from vertical your rigging rules allow. |
Method and formulas
- Leg length = distance from the hook to each lift point; angle from vertical from the spherical coordinates of the point (as the cylindrical and spherical coordinates tool).
- Hook equilibrium: Σ Tᵢ uᵢ = (0, 0, −W) with uᵢ the unit vector along each leg, solved as three simultaneous equations (as the simultaneous equations tool).
- A negative tension means that leg goes slack: the centre of gravity lies outside the triangle of lift points.
- Example: the legs carry 12.806, 12.667 and 12.667 kN at 38.66°, 37.864° and 37.864° from vertical.
Limitations
- Hook directly over the centre of gravity and rigid legs of the lengths given; stretch and hook shift redistribute load.
- Three legs only: a four-leg bridle is statically indeterminate and is usually rated on two legs.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Plan a lift with three uneven lift points
- Check which leg of a bridle carries most
- Find leg lengths for a level lift
Who it is for
- Riggers
- Lifting supervisors
- Lifting engineers
What you get
- Leg lengths and angles from vertical
- Tension in each leg
- Checks for slack, overload and angle
Interpreting the result
- The leg nearest the centre of gravity and the steepest legs carry most: shorten or re-position to even them out.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 43–45, 122–127, 153–163. Topic reference; no source tables or recommended settings are reproduced.
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Open the Three-Leg Sling Load Share (3D Leg Geometry, Tensions, Angles) calculator
