Biomechanics in orthodontics obeys several fundamental laws, amalgamating physics and biology. This article on Moment of Force is the third in a series of five articles covering the fundamentals of biomechanics in orthodontics. It will enable you to better understand the physics and biological responses governing tooth movement.

Understanding the principles of biomechanics in orthodontics is essential to controlling the outcome of tooth treatment, and confidently managing your patients’ cases. While it is possible for a dentist beginning in the field of orthodontics to lean on a technician’s skill to develop a clear aligner treatment plan for basic cases, as a professional is important to understanding how to control orthodontic outcomes and to lead the development of treatment planning, particularly when attempting to correct complex malocclusions such a cross bite. For more on the complexity of treating cross bites, read this __article__.

Each article in this series covers the following key principles for biomechanics:

The orthodontic force

Centre of resistance

Moments of force and couples

Equivalent forces

Centre of rotation

**Moment of Force and Couples**

The rotational impact of a force is known as the moment of force (M) which is mathematically defined as the force (F) times the perpendicular separation between the force and the Centre of Resistance (D) (See Article 2 [__LINK__]) (M = F x D). Stated differently, the moment of force (M) depends on its magnitude (F) and the perpendicular separation (D) between it and the pivot. Therefore, the twisting impact increases as the perpendicular distance increases (moment).

Moment = Force x Distance

The Moment is the term used to describe the turning effect of a force on an object’s pivot, otherwise known as the Centre of Resistance (CR). The Moment is generally depicted as a turning arrow in the direction of the tooth’s movement.

The next two points on how to generate Moments are possibly the most important concepts in orthodontics, so take notes!

**1. Moment of Force**

Applying a force at different points from the tooth’s CR changes the Moment of Force. For example, where a lingual force of 50 grams is applied 10mm from the CR, both a distal direction and clockwise moment of 500gmm (M=FxD) will be generated. However, reduce the distance from the CR to 50mm, and the Moment decreases to 250gmm.

This is called the “Moment of Force” which clearly depends on the:

Amount of force applied (Magnitude);

Direction; and

Point of Application.

Note, the Magnitude applied also changes the distal force, but this will be covered in a later article.

**2. Pure Moment / Moment of a Couple**

An alternative moment consists in the application of two parallel forces of equal magnitude and in opposite directions. In this instance, the tooth rotates around its CR. This is called a pure moment or a moment of a couple.

For example, two forces of 50 grams each in opposing directions, both 10mm from the CR, results in a moment of 1000 gmm (50 x (2 + 10)). Importantly for couples, it does not matter whether the opposing forces are the same distance from the Centre of Resistance as they act as vectors and result in the same outcome. That is, the point of application for couples does not change the final effect so long as the magnitude of force and direction is maintained.

To better understand this concept, it helps to imagine the CR as a bolt or screw that requires 1000gmm to rotate it. To achieve the pure moment there are different tools available, of which each apply forces at different distances from the CR. Each tool simply changes magnitudes of force required to generate the same moment.

The same applies to orthodontics, meaning the couple torque force application can be anywhere on the tooth. Applying the moment of the couple anywhere on the tooth results in the same movement on the CR.

**Appliances to Apply Forces**

All appliances must follow the same laws of physics and biology. The appliance used moves teeth by the application of a force, whether a single point application force (finger spring on URA), a group of forces (multiplanar attachments on teeth for aligner treatments), a couple (bracket mechanics), or a combination.

Where an application of a single force is displaced from the CR a moment is created, rotating the tooth. Where rotation is not desired, rather a translation movement is necessary, a force can be applied through the CR or counter forces can be applied to offset the rotation around the CR. With clear aligners it is possible to apply forces over the entire area of crown or direct it at a particular point(s) making simple translation movements achievable. While the same effect can be achieved with traditional fixed braces it can be mechanically more complex as the forces must be managed at the point of application, limited to where the bracket is fixed.

**Summary**

Applying a force a distance away from the centre of resistance of a tooth causes a moment (rotational force on the tooth). A couple is useful in orthodontics as it provides pure rotational movement. Predicable tooth movements depend on the delicate balance between moment of couple and moment of force ratios as we will learn in more detail in the next article.

Dental professionals interested in gaining a greater understanding of orthodontics and clear aligners are encouraged to look out for a Proligner Introduction to Clear Aligners Course near you or join the course online via live streaming: __Education__.

Look out for our next article in the Biomechanics in Orthodontics series covering __Equivalent Forces__.

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