SIMPLE MACHINES / SCREW

How does a screw turn a small hand force into a large axial force?

Compare screw lead, handle radius, required torque and hand force.

ORIGINAL IDEAL EXAMPLE

500 N load
3.97887 N effort

One turn moves the hand through a circle while the load advances by the screw lead. In the ideal model, those two motions exchange equal work.

Conceptual schematic; use the model below for parameter-linked geometry.

screw.napkin / editable

XZ / UNDEFORMED GEOMETRYFITTED TO VIEW

Screw shaft selected · related inputs are marked.

hand force3.98 N✓ passes

BASELINE INPUTS

load500 Nlead5 mm212handleRadius100 mm50200

CALCULATED

torque0.39789 N*m

effort3.9789 N

mechanicalAdvantage125.66

handleLength200 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Screw: convert handle rotation into axial travel
# Scope: Ideal frictionless screw; lead is axial advance per full revolution. Shaft and handle are schematic, without thread geometry or self-locking behavior.
load = 500 N
lead = 5 mm in 2..12
handleRadius = 100 mm in 50..200
torque := load * lead / (2*pi) [N*m]
effort := torque / handleRadius [N]
mechanicalAdvantage := 2*pi*handleRadius / lead
handleLength := 2*handleRadius [mm]
part shaft "Screw shaft": cylinder 8 mm, 100 mm
part handle "Handle": box handleLength, 10 mm, 10 mm at 0 mm, 0 mm, 60 mm
check hand force: effort <= 5 N
scenario coarser lead: lead = 10 mm

Calculated from your source · not saved

Baseline · Baseline

hand force3.98 N ✓ passes

coarser lead · coarser lead

hand force7.96 N × fails

Calculated from the same .napkin source. Edits preview a temporary study and are not saved.

How the model works

One turn moves the hand through a circle while the load advances by the screw lead. In the ideal model, those two motions exchange equal work.

torque = load × lead / (2π); effort = torque / handleRadius

Try the alternative

A finer lead reduces torque and hand force but requires more turns. Lead is advance per revolution; it equals pitch only for a single-start thread.

Choose a scenario, change an input, then inspect the equations and force check in Source.

Assumptions and limits

Thread and collar friction, efficiency, self-locking, buckling and thread strength are omitted. The drawing is a schematic shaft and handle without modeled threads.