Relative friction minimization in fixed orthodontic bracket appliances

The biomechanical and mathematical analysis of friction on an arch wire/bracket combination and the wire supports has demonstrated that there is an optimal relationship, i.e. minimal friction forces, between the bracket width and the distance between the adjacent brackets on the neighboring teeth. With this optimal situation, less force will develop for a given deflection of the arch wire. This, in turn, will lead to fewer frictional effects when the friction forces are assumed to be proportional to the concentrated perpendicular forces on the arch wire. As long as the contacting surface can be regarded as a point, Coulomb's law of friction can be applied in its simplest form. Relative friction minimization can thereby be qualitatively and quantitatively obtained by linear theory for any specified angulation, wire properties and coefficients of friction. Literature stating that narrow brackets will lead to less friction for specified angulation cannot be confirmed according to the presented analysis. The other extreme statement 'Use the widest bracket possible' also cannot be used in principle. Since the analysis shows a mathematical relationship between most of the relevant design variables of an arch wire/bracket combination and the magnitude of friction forces, empirical results can be sorted and ranked by their physical figures instead of by statistical distribution. In addition, it is possible to make recommendations about the appropriate bracket sizes for various cases. The dependences of the coefficients of friction themselves on material, surface roughness, lubrication, etc. are not investigated here. These factors are also very relevant, especially in reduction of the absolute magnitude of frictional forces, but this problem is left to tribologists.