engineering fundamentals Spring Introduction
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Hooke's Law
Springs are fundamental mechanical components which form the basis of many mechanical systems. A spring can be defined to be an elastic member which exerts a resisting force when its shape is changed. Most springs are assumed linear and obey the Hooke's Law,

where F is the resisting force, D is the displacement, and the k is the spring constant.

For a non-linear spring, the resisting force is not linearly proportional to its displacement. Non-linear springs are not covered in depth here.

Basic Spring Types
Springs are of several types, the most plentiful of which are shown as follows,

Circular cross section springs are shown. If space is limited, such as with automotive valve springs, square cross section springs can be considered. If space is extremely limited and the load is high, Belleville washer springs can be considered. These springs are illustrated below,

Leaf springs, which are illustrated below in a typical wheeled-vehicle application, can be designed to have progressive spring rates. This "non-linear spring constant" is useful for vehicles which must operate with widely varying loads, such as trucks.

History of Springs
Like most other fundamental mechanisms, metal springs have existed since the Bronze Age. Even before metals, wood was used as a flexible structural member in archery bows and military catapults. Precision springs first became a necessity during the Renaissance with the advent of accurate timepieces. The fourteenth century saw the development of precise clocks which revolutionized celestial navigation. World exploration and conquest by the European colonial powers continued to provide an impetus to the clockmakers' science and art. Firearms were another area that pushed spring development.

The eighteenth century dawn of the industrial revolution raised the need for large, accurate, and inexpensive springs. Whereas clockmakers' springs were often hand-made, now springs needed to be mass-produced from music wire and the like. Manufacturing methodologies were developed so that today springs are ubiquitous. Computer-controlled wire and sheet metal bending machines now allow custom springs to be tooled within weeks, although the throughput is not as high as that for dedicated machinery.

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