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The effects of third-order torque and self - Saint Louis University

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CHAPTER 2: REVIEW OF THE LITERATURE<br />

Classical Friction<br />

In the orthodontic literature, friction was discussed<br />

as early as 1960 when Stoner 1 warned <strong>of</strong> the difficulty in<br />

determining the amount <strong>of</strong> force to be applied to a tooth<br />

because <strong>of</strong> the role <strong>of</strong> frictional resistance. Our current<br />

underst<strong>and</strong>ing <strong>of</strong> friction impairing tooth movement is based<br />

largely on long-st<strong>and</strong>ing theories, not directly related to<br />

orthodontics, by Leonardo Da Vinci, Guillaume Amontons, <strong>and</strong><br />

Charles-Augustin Coulomb. Although Da Vinci’s work was not<br />

published until the other investigators had carried out<br />

friction experiments, he left behind the earliest known<br />

studies on the subject in a collection <strong>of</strong> journals in which<br />

he detailed his research. 2 Collectively, these scientists<br />

are credited with establishing the classical laws <strong>of</strong><br />

friction, or the Amontons-Coulomb laws, which state the<br />

following: 1. Frictional force is proportional to normal<br />

force; 2. Frictional force is independent <strong>of</strong> contact-area;<br />

3. Frictional force is independent <strong>of</strong> sliding velocity. 2,3<br />

Friction is defined as the resistance to motion<br />

when one object moves or tends to move tangentially<br />

relative to another object. 4 <strong>The</strong> total contact-force<br />

3

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