# Screw Jacks

## Screw jacks and effort force

A screw jack is a mechanical device that can increase the magnitude of an effort force.

The effort force for a screw jack when neglecting friction can be expressed as

F = (Q p) / (2 π R) (1)

where

F = effort force at the end of the arm or handle (lb, N)

Q = weight or load (lb, N)

p = pitch - distance or lead of thread in one turn (in, m)

R = lever-arm radius (in, m)

The torque acting on the screw can be calculated as

*T = F R (2)*

*where *

*T = torque (lb in, Nm)*

### Example - Screw jack without friction

If the load on a screw jack is *50000 lb*, the lever-arm is * 20 inches* and the pitch equals *1/8 inches* - the effort force can be estimated to

F = ((50000 lb) (1/8 in)) / (2 π (20 in))

= 49.8 lb

The torque acting on the screw can be calculated

T = (49.8 lb) (20 in)

= 995 lb in

= 82.9 lb ft

### Example - Metric Screw Lift

A M24 metric screw with pitch 3 mm is used in a mechanical screw lift with load *225 kN*. The lever arm is *0.5 m*. The effort force required can be calculated as

F = ((225000 N) (0.003 m)) / (2 π (0.5 m))

= 215 N

The torque acting on the screw can be calculated

T = (215 N) (0.5 m)

= 107 Nm

### Screw Jack Calculator - without Friction - Imperial Units

Calculate torque and effort force acting on the lever arm.

*load (lb)*

* pitch - distance or lead of thread in one turn (in)*

* lever arm (in)*

### Screw Jack Calculator - without Friction - Metric Units

Calculate torque and effort force acting on the lever arm.

*load (N)*

* pitch - distance or lead of thread in one turn (m)*

* lever arm (m)*

**Note** the difference between mass and weight!

### Screw Jack with Friction

For motion in the **same direction** as the load (load assist the screw jack), the effort force can expressed as

F = Q ( (2 π μ r - p) / (2 π r + μ p) ) (r / R) (2)

where

r = pitch radius of screw (in)

For motion in the **opposite direction** as the load (load resists the screw jack), the effort force can expressed as

F = Q ( (2 π μ r + p) / (2 π r - μ p) ) (r / R) (3)