Screw Thread Mechanical Advantage

Question:

I would like to know the IMA,ideal mechanical advantage for screw threads

Answer:

The ideal mechanical advantage is the ratio of the force applied to the load over the force applied to the machine, neglecting any losses to friction. This may be expressed also as the ratio of the distance moved by the effort over the distance moved by the resistance. These two ratios will be equal in the absence of friction.

If we look at the screw as a simple machine the distance moved by the resistance is going to be the pitch of the thread times the number of turns of the screw, where the pitch is the distance advanced in a single turn. The distance moved by the effort will depend on the radius from the axis of the screw to the point where the effort is applied. If the screw is turned by a screwdriver whose handle is 2 cm in diameter, the radius of the effort is going to be 1 cm so the distance of the effort will be 2*pi*1cm per turn of the screw. If the screw is turned by a wrench where the force is applied 10 cm from the axis of the screw, then the distance of the effort will be 2*pi*10 cm per turn. With this in mind we can express the ideal mechanical advantage of the screw as 2*pi*r/p where r is the radius at which the effort is applied and p is the pitch of the thread.

You could plug any consistent units into this relationship, r in centimeters and p in centimeters per thread, r in inches and p in inches per thread or any other unit of length as long as you use the same units for radius and pitch.

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.

JDJ