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This screw mechanical advantage calculator determines the theoretical mechanical advantage of a screw from its diameter and the linear distance the screw travels in one complete revolution of the screw shaft (screw lead). It can also determine the axial distance a screw shaft moves when it is rotated through a known angle.

You are watching: Ideal mechanical advantage of a screw

Example: Calculate the ideal mechanical advantage of a screw with a 4-centimeter lever if its thread lead is 5 mm.


To calculate, enter the values and tap or click the Calculate button. To calculate the mechanical advantage, enter only the screw lead and its handle radius (see picture). Enter the angle of rotation if you want to calculate the distance the screw moves.



A book press (also called dab press, dabpress, hard press, and screw press) used in bookbinding consists of a press screw, which moves an upper platen up and down against a fixed bottom platen. The upper platen evenly distributes the pressure from the screw.

Definitions and Formulas

A screw is often considered a separate kind of a simple machine. However, a screw is really a kind of another simple machine — inclined plane, the thread of which is actually a narrow inclined plane wrapped around a cylinder, and the screw pitch is like an angle of an inclined plane. The screw is such an important kind of inclined plane that it was set aside as a new category of simple machines.

A screw converts rotational motion to linear motion or a rotational force (torque) into a linear force. A screw is one of the six classical simple machines defined by Renaissance scientists and its examples can be found everywhere: screws and bolts are used to hold parts together or they may be used for lifting heavy objects (water screw) and to tighten various parts (vise or clamp). A drill bit is actually a screw with deep grooves that carry pieces of the material being drilled from the hole to the surface. A screw can be found in a water faucet, at the end of light bulbs, and even in biology (DNA and various plants, for example, spirogyra). As with all simple machines, screws help make work easier to do.



A filamentous green alga Spirogyra with its characteristic helical arrangement of chloroplasts in the cells under ×10 magnification

The most common screw consists of a cylindrical shaft with helical grooves and ridges called threads that are made around the outside surface of the screw shaft. If a screw is rotated inside a fixed object, it moves along its axis relative to this object. On the other hand, if a rotating screw is stationary the nut can linearly move on its shaft. This design is used in lead screws in various machines to translate turning motion into linear motion. For example, lead screws driven with stepper motors are used in DVD and floppy disc drives.



Single-start thread screws are the most common; they have one continuous thread running along the screw body

Screws can have single-start or multi-start threads. A single-start thread means there is only one ridge wrapped around the screw shaft. Each time a screw makes a full turn, it moves axially by the width of one ridge.

A multi-start thread consists of two or more threads that are intertwined and running parallel to one another. A double-start screw has two ridges wrapped around the screw shaft and when a screw rotates one turn, it moves axially by the width of two ridges.



Double-start (twin-start) thread screws have two threads running along the cylindrical body; they have a larger lead in comparison with single-start thread screws and consequently, they can be inserted or removed twice as fast as screws with a single-start thread.

Single-start threads are used for heavy loads because they provide a greater mechanical advantage and multi-start threads provide quick movement for only a small angular movement of the screw.



The triple-start thread on this bottle ensures that more contact surface is engaged in a single thread rotation. The cap will screw on in a quick turn and at the same time, instead of one thread, there will be three threads fully engaged to securely hold the cap in place.

The mechanical advantage of a screw depends on its thread lead, which is the linear distance the screw travels along its axis during one revolution (360°). Any screw thread can also be characterized by its pitch, which is the distance between the two adjacent crests of the thread. For a single-start thread, its lead and pitch are the same. However, for a two-start thread, its lead is two times larger than its pitch P and for a thread with n starts, its lead L is given by

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The ideal (frictionless) mechanical advantage MA of a screw is defined as the ratio of axial load force Fload applied by the screw shaft on the load to the rotational effort force Feffort applied to the rim or handle of the shaft:

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Because of conservation of energy, for an ideal screw with no friction, the work done on the screw Weffort by the effort force is equal to the work done by the screw on the load Wload:

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A lead screw in an electric linear actuator of an optical disc drive is used to move the pickup head with the laser, its lens, and photodiodes for detecting the light reflected from the disc surface

Because work is the product of force and displacement, for one complete turn of the screw (360°) the work Weffort is determined as

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where R is the radius of the screw rim. On the other hand, the work done by the screw on the load during one turn of the screw is defined as

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where l is the lead of the screw defined above. After the substitution and rearranging, we get

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or

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Therefore, the ideal mechanical advantage of a screw is equal

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This formula is used in our calculator. As we can see from it, the mechanical advantage of a screw depends on its lead. That is, the smaller the distance between its threads, the larger the mechanical advantage. Of course, we are talking about the ideal mechanical advantage and real screws provide a mechanical advantage that is smaller than given by the equation above.

The actual mechanical advantage of a screw is determined as

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where 0 ≤ η ≤ 1 is the efficiency.


In an adjustable wrench (adjustable spanner), a worm screw is used to adjust the position of a movable jaw; it drives the movable jaw with sufficient mechanical advantage necessary to accomplish tight clamping of nuts and bolts. 1 — fixed jaw, 2 — adjustable jaw, 3 — worm screw, 4 — handle
Mechanics

This online unit converter allows quick and accurate conversion between many units of measure, from one system to another. The Unit Conversion page provides a solution for engineers, translators, and for anyone whose activities require working with quantities measured in different units.

See more: Are You Supposed To Wear Underwear With Compression Shorts, Two Types Of Compression Shorts


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