Screw Jack Mechanical Advantage
Screw Jack Mechanical Advantage
A screw jack multiplies a modest hand force at the end of a long handle into a much larger lifting force at the screw, by converting the handle's circular sweep into a small linear advance of the screw for every full turn. The ratio between how far the hand travels around the handle circle and how far the load actually rises defines the jack's theoretical mechanical advantage.A finer screw thread (smaller lead) gives a larger mechanical advantage for the same handle length, letting a person lift heavy loads with modest hand force — but this comes at the direct cost of needing many more turns to raise the load any given height, and real-world screw jacks lose a further, often substantial fraction of this theoretical advantage to thread friction, which is what separately determines whether the jack is self-locking (holds the load without back-driving) once the handle is released.
The theoretical mechanical advantage of a screw jack is MA = 2·pi·R_h/L_lead, the handle's circular travel distance per turn divided by the screw's linear advance per turn. where R_h is the handle length (radius of the hand's circular path), L_lead is the screw lead (linear advance per turn), and MA is the resulting theoretical mechanical advantage.
Inputs
R_h := 0.3 m=300 mm
L_lead := 5 mm=5 mm
Comparing the circumference the hand travels in one full turn of the handle with the small linear distance the screw advances in that same turn gives the theoretical ratio between input force and output lifting force.
MA := 2·pi·R_h/L_lead=376.99
Results
A theoretical mechanical advantage of about 377 here means, ignoring friction, a hand force of roughly 27 N could theoretically lift a 10 kN load — an enormous multiplication that illustrates why screw jacks can lift vehicles and heavy machinery with modest hand effort. In practice, thread friction consumes a significant share of this theoretical advantage (real efficiency is often only 20–40% for a standard square or Acme thread jack), so the actual force needed at the handle is noticeably higher than this ideal number suggests — but that same friction is also what typically makes the jack self-locking, safely holding the load in place without the handle needing to be restrained. This makes mechanical advantage alone an incomplete design check; the actual required handle force and self-locking behavior both need the thread friction angle included as well.
Assumptions & limitations
- Theoretical (frictionless) mechanical advantage only — actual required force is higher due to thread friction.
- Single-start screw thread assumed, where lead equals thread pitch (multi-start threads have a larger lead).
- Handle length is measured to the point of applied hand force, assumed perpendicular to the handle at that point.
- Self-locking behavior depends on the thread friction angle, a separate consideration not evaluated by this ratio.