Pulley & Wheel-Axle
Compute mechanical advantage and required effort for wheel-axle, n movable-pulley systems and differential (chain) hoist.
Inputs
Formula
Wheel-axle MA=R/r; n pulleys MA=2n; differential MA=2R/(R−r); F = W/MA
Fundamentals
Pulleys use rope and wheels to redirect and scale force — a simple but effective mechanical advantage device.
An ideal block-and-tackle gains force by $1/n$ where $n$ is the number of rope segments supporting the load (travel grows by $n$). A single fixed pulley only redirects.
History
Belt drives lifted water since antiquity; leather belts (19th c.), then V-belts and timing belts (20th c.) enabled distant, cushioned transmission.
Engineering applications
Used for distant power transmission and speed reduction in farm machinery, fans, compressors and machine-tool spindles.
Glossary
| Mech. advantage | Output/input force ratio = supported rope segments. |
| Fixed pulley | Anchored axle, only changes pull direction. |
| Movable pulley | Moves with load, halves the required force. |
How to use
- Fill in Mechanism, Large radius R, Small radius r, Load W, Pulley count n in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Mechanical adv. MA, Effort F in the results area.
Formula notesPulley system mechanical advantage = number of rope segments n supporting load; ideal pull F = W / n.
Formula · Worked Example · Knowledge
Formula
Wheel-axle $MA=R/r$; $n$ movable pulleys $MA=2n$; differential $MA=2R/(R-r)$; effort $F=W/MA$.
Worked Example
Wheel-axle R=200, r=50 → MA=4; lift W=1000 N needs F=250 N.
Key Points
- Higher MA saves force but costs distance.
- More movable pulleys → more advantage.
- Differential hoist MA is set by the radius difference.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Mechanism | mode | wheel | |
| Large radius R (mm) | R | mm | 200 |
| Small radius r (mm) | r | mm | 50 |
| Load W (N) | W | N | 1000 |
| Pulley count n | n | 3 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Mechanical adv. MA | MA | |
| Effort F | F | N |
Applications
- Linkage and cam kinematics design
- Pulley mechanical-advantage study
- Engine valve-train and crank analysis
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: Wheel-axle MA=R/r; n pulleys MA=2n; differential MA=2R/(R−r); F = W/MA
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Linkage and cam kinematics design