How is a screw an inclined plane?
Wrap a long thin triangle round a pencil and its sloping edge traces a helix — that helix is the thread. The rise of the triangle is the pitch, the distance the screw advances in one full turn, and its base is the circumference of the cylinder. A screw is simply an inclined plane rolled up, which is why it obeys the same distance-for-force trade. The difference is that the effort travels round a circle rather than along a straight slope, letting an enormous ratio fit into a very small space.
How do you calculate the mechanical advantage of a screw?
Divide the circumference swept by the handle by the thread pitch. A jack with a 200 mm lever arm sweeps 2π times 200, about 1,257 mm, in one turn while advancing a 3 mm pitch — an ideal mechanical advantage of roughly 419. That is how one person lifts a car. The figure is theoretical, though: screw threads are so inefficient that the real advantage is typically a quarter of it or less, and any serious calculation has to allow for that.
Why are screws so inefficient?
Because a large area of thread slides against a large area of nut under heavy load, and nearly all of that contact is sliding rather than rolling. Typical efficiency runs from about 15 to 30 percent for a plain square or trapezoidal thread. The waste turns out to be a feature rather than a fault: it is what makes a screw self-locking, so a jack holds a car up instead of unwinding the moment you let go. Ball screws reach 90 percent efficiency and are correspondingly unsafe as a jack — they back-drive.
What is thread pitch and how does it affect the tool?
Pitch is the distance from one thread crest to the next, and therefore how far the screw travels per turn. A fine pitch gives a very large mechanical advantage and precise control but takes many turns to move anywhere — right for a micrometer or a vice. A coarse pitch moves fast with less force per turn, which suits a woodscrew you want driven quickly. Choosing between them is choosing where on the force-versus-distance curve you want to sit.
Where are screws used as machines rather than fasteners?
Car jacks, bench vices, G-clamps, workshop presses, piano stools, adjustable feet on appliances, micrometers, corkscrews, and the leadscrew driving the carriage of a lathe. Archimedes' screw for raising water is the same geometry used in reverse. In each case the screw is not holding two things together but converting rotation into a slow, powerful, precisely controlled linear movement.