Screw (simple Machine) - Frictionless Mechanical Advantage

Frictionless Mechanical Advantage

The mechanical advantage MA of a screw is defined as the ratio of axial output force F_out applied by the shaft on a load to the rotational force F_in applied to the rim of the shaft to turn it. For a screw with no friction (also called an ideal screw), from conservation of energy the work done on the screw by the input force turning it is equal to the work done by the screw on the load force:

Work is equal to the force multiplied by the distance it acts, so the work done in one complete turn of the screw is and the work done on the load is . So the mechanical advantage is equal to the distance ratio:

It can be seen that the mechanical advantage of a screw depends on its lead, . The smaller the distance between its threads, the larger the mechanical advantage, and the larger the force the screw can exert for a given applied force. However most actual screws have large amounts of friction and their machanical advantage is less than given by the above equation.