Mechanical Advantage – the Screw

Kinderdijk, modern Archimedes' screwThis is a simple machine we’re all pretty familiar with, due to its wide usage in various applications. In fact, we might be so familiar with it, and given its definition, it’s hard to associate it with the word “machine”.

Well, technically, a machine can be anything that performs mechanical “work, therefore even something as insignificant as a screw can be one. Screw systems such as the Archimedes’ screw are the basis of many mechanical devices, including those used for moving water, grain, or even the Illustration of Archimedes' screwtransporting of fish from one tank to another. So as you can see, the concept of the screw is not limited to the little sharp pieces of galvanized metal used in carpentry or fix-it jobs. It is one of several fundamental building blocks in the world of mechanics.

Speaking from a technical reference
point, a screw is nothing but an “inclined plane” wrapped around a shank or cylinder. An inclined plane is also one of the 6 simple machines termed so by Renaissance scientists, but the distinction between the screw and the inclined plane is that the former not only spirals around a cylinder but also converts a rotational force to a linear one.

Inclined plane

Let’s first define an inclined plane. Just imagine a straight line with the 2 endpoints at different heights and you have yourself an inclined plane. In practical terms, think of a wheelchair ramp beside a staircase. The wheelchair ramp climbs to the same height as the stairs but probably has to start from further back.

So the further back the ramp goes, the higher the mechanical advantage. The mechanical advantage of the inclined plane is the length of the slope divided by the height of the slope – MA=slope length/slope height.


So the thread that’s wrapped around a screw is in essence, an inclined plane, gradually climbing up the screw shaft. The mechanical advantage for the screw is calculated by MA=πdm/l where dm equals the mean or average diameter of the screw thread, and l equals the lead of the screw thread.

*You should know that the actual mechanical advantage of a screw system is more than the above equation, due to the mechanical advantage of the driver or similar device turning it.

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