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.

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universe works. My name is James D. Jones. If I can be of more help,
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JDJ