How to Calculate Mechanical Advantage Screws

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A screw is a simple machine that works as a modified inclined plane. You can think of the thread of the screw as an inclined plane wrapped around the shaft of the screw. The slope of the screw is the distance for one complete rotation while the height of the inclined plane is the distance between the threads, known as pitch. The relationship between the pitch and circumference of the screw gives the mechanical advantage.

TL;DR (Too Long; Didn't Read)

The mechanical advantage of a screw is the circumference of the shaft divided by the thread pitch.

    Measure the pitch of the screw. The pitch is the distance between the threads; you can determine this number by measuring the number of threads per inch (or centimeter) on the screw, then divide one by the number of threads:

    \text{pitch}=\frac{1}{\text{number of threads per inch or cm}

    For example, if a screw has eight threads per inch, the pitch is 1/8. Note: to measure small objects such as screws accurately, a vernier calipers can be a big help.

    Calculate the circumference of the screw shaft by measuring the diameter of the screw and multiplying by pi. For example, if a screw has a diameter of 0.25 inches, then the circumference of the screw is 0.79 inches.

    Calculate the mechanical advantage of the screw by dividing the circumference of the screw by the pitch of the screw. Using the previous examples, a screw with a pitch of 1/8 and a circumference of 0.79 inches would produce a mechanical advantage of 6.3.

    Things You'll Need

    • Ruler
    • Screw

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