The Spiral Inclined Plane
A screw is fundamentally an inclined plane wrapped around a central cylindrical core. When a turning force (torque) is applied, the screw converts rotational motion into linear motion, creating an enormous force multiplier.
The mechanical advantage depends on two critical factors: the radius of the tool used to turn the screw (like a screwdriver handle or a long wrench) and the pitch of the screw (the linear distance between two adjacent threads). A smaller pitch means more mechanical advantage, but requires many more turns to advance the screw.
Massive Force Multiplication
Screws are unique because they easily provide the highest mechanical advantage of all simple machines.
- Jackscrews: Used to lift entire houses off their foundations or lift heavy aircraft for maintenance.
- Vises: A bench vise uses a thick screw to clamp down on materials with thousands of pounds of crushing force using only a simple hand-turned handle.
- Propellers: Airplane and boat propellers act like screws twisting their way through fluid mediums.
The Formula
Example Calculation
Imagine you are using a wrench with a $20 , ext{cm}$ handle ($r = 20$) to turn a thick bolt that has a thread pitch of $0.2 , ext{cm}$ ($p = 0.2$).
- Calculate Circumference: $2 \cdot \pi \cdot 20 \approx 125.66 , ext{cm}$.
- Divide by Pitch: $125.66 / 0.2 = 628.3$.
The mechanical advantage is over $628$! A tiny $10 , ext{N}$ force applied to the wrench handle translates into over $6000 , ext{N}$ of clamping force on the bolted joint.