Biomechanics in orthodontics obeys several fundamental laws, amalgamating physics and biology. This article on Equivalent Forces & Moment of Force Rotation is the fourth 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
Equivalent Forces & Moment of Force Rotation
Having introduced the core fundamentals of force in orthodontic biomechanics, predicting tooth movements from forces will be analysed. This article analyses forces and moments experienced by the Centre of Resistance (CR) of that tooth when applying force to any point of a tooth.
Understanding the forces the CR experiences results in an understanding of how the tooth will move. A key challenge in orthodontics is that the point of application is distant from the tooth CR. This distance means corresponding forces must be applied to create an equivalent force to generate the intended effect. This is the principle of equivalence, and it must be understood to produce accurate movements.
Therefore, to create an equivalent force so perfect translation of a tooth can be generated, counter forces must be generated where the applied force vector does not pass through the tooth CR. In this example, a 100g force to the lingual is applied 10mm from CR. This means a moment of 1000gmm is created at the CR (F = Md, see Moment of Force article). For translation, a counter moment of force must be created to counteract the rotational forces created.
Applying the concept of equivalence in brackets requires several steps where, firstly, a force needs to be applied at a point (the bracket) of application distant from the CR, maintaining a force and direction, then secondly, the possible moment of the system needs to be added. The advantages of clear aligners are that the point of application is far more dynamic given clear aligners cover the entire tooth crown and forces (and counterforces) can be applied at any point with small changes at each step by simply changing the aligner. However, forces required for complex movements, such as translational movements for large space closures and large rotations, are difficult to achieve with aligners due to the greater stress relaxation of plastic as compared to metal. Given the increased points of applications for the delivery of smaller forces using plastic as compared to larger forces applied to a smaller area of tooth with metal, it is prudent to say Clear Aligners are just as successful as metal braces for correcting mild and some moderate malocclusions. In some cases, clear aligners may be a more rapid and efficient solution as when compared to traditional braces to fix simple orthodontic discrepancies. Fixed appliances are still desired for more complex malocclusions.
An example of equivalence of forces required when closing a central diastema.
1. How NOT to do it: Single forces
The result of applying a single force at the distal surface will not be aesthetically acceptable. The force system will result in the teeth tipping mesially, creating a gingival black triangle.
2. Required forces: Equivalence
The necessary forces must result in the transference of forces from the point of application to the CR. This is achieved by applying a force to direct the tooth’s intended movement, combined with a moment of force to counter the uncontrolled tipping that will be generated.
Clear aligners use attachments to apply the required equivalent forces. These attachments are called medio-distal root movement (optimised) attachments.
Moment of Force Ratio
The moment to force ratio (M/F) is the ratio of the moment (produced by a force, a couple, or both of them) to the force applied to a specific part of a tooth.
It can be used to describe the M/F at the CR or at the point of application of force.
For translation of teeth where an equivalence of force must be applied, combining a force and a counter couple force, the M/F between the CR and the point of application is zero. This is because the moment of force is neutralised by the moment of a couple.
Moment of Couple to Moment of Force Ratio
With the combination of moments of couples and moments of forces, it is important to understand the relationship of Mc/Mf. Couples are essential in both fixed and clear aligner mechanics.
The ratio between the moment produced by the force applied to move a tooth (MF) and the counterbalancing moment produced by the couple used to control root position (MC) determines the type of tooth movement.
With no Mc (Mc/Mf = 0), the tooth rotates around the CR (Pure Tipping).
As the moment-to-force ratio increase (0<Mc/Mf<1), the Centre of Rotation (CRot) (see article 5) is displaced further and further away from the CR, producing what is called controlled tipping.
When Mc/Mf=1, the CRot is displaced to infinity and bodily movement (translation) occurs.
If Mc/Mf>1 the CRot is displaced incisally and the root apex will move more than the crown, producing Root Torque
Summary
As we don’t have direct access to the CRot and our application of forces are limited to the crown of the tooth generally, the relationship between moment of forces and counter moments will determine the type of tooth movement observed. The balance between moments created by forces and couples relates to the movement of the tooth.
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 Centre of Rotation.
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