KEVOS® MAKEOS · Power Transmission
Crossed Belt and Three-Pulley Belt Length
How long is the belt for this crossed drive or for a belt around three pulleys?
Belt length for a crossed (reversing) two-pulley drive, with the open-belt length for comparison, or for a belt wrapped around the outside of three pulleys at given positions, with wrap angles.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Drive | choice | Crossed two-pulley drive, or open belt around three pulleys (pulley 1 at the origin). |
| Pulley 1 diameter | mm | Pitch diameter of pulley 1. |
| Pulley 2 diameter | mm | Pitch diameter of pulley 2. |
| Pulley 3 diameter (three-pulley) | mm | Pitch diameter of pulley 3 (three-pulley drive). |
| Centre distance (crossed) | mm | Centre distance of the crossed drive. |
| Pulley positions (three-pulley) | ||
| Pulley 2 X | mm | X position of pulley 2 centre (pulley 1 is at 0, 0). |
| Pulley 2 Y | mm | Y position of pulley 2 centre. |
| Pulley 3 X | mm | X position of pulley 3 centre. |
| Pulley 3 Y | mm | Y position of pulley 3 centre. |
Method and formulas
- Crossed: L = 2√(C² − ((D + d)/2)²) + (D + d)/2 × (π + 2 arcsin((D + d) ÷ 2C)).
- Three pulleys: tangent length between pulleys i and j = √(dᵢⱼ² − (rᵢ − rⱼ)²); the belt’s outward normal on each span is found from cos(angle) = (rᵢ − rⱼ) ÷ dᵢⱼ.
- Arc on each pulley = radius × wrap angle between its incoming and outgoing spans; L = Σ spans + Σ arcs.
- Example: the default three-pulley drive needs a 1,810.5 mm belt.
Limitations
- Pitch-line lengths; the belt maker’s length designation (inside or outside) may differ.
- All three pulleys must be on the outside of the belt loop (no back-bent idler).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Order belts for reversing drives
- Find belt length around an idler or third pulley
- Check wrap on each pulley
Who it is for
- Design engineers
- Maintenance engineers
What you get
- Belt length
- Wrap angle on each pulley
- Open-belt length (crossed drive comparison)
Interpreting the result
- Keep at least about 120° of wrap on the driving pulley.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2473–2490. Topic reference; no source tables or recommended settings are reproduced.
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