The Accuracy of Bed Implant Processing with the Aid of Drill Templates. - A Mathematical Depiction of the Tolerance Limits -Introduction:In the process of planning and drill templates, the drilling of the implant takes place after putting the templates on the teeth with guidance of titanium sleeves that are inserted into the templates in the desired positions of the implant. The maximum tolerance limits that naturally appear on the tip of the drill after guided drilling over template anchored titanium sleeves are to be determined with assistance of a simple mathematical model.Materials and Methods:Three basic processes (process 2: illustration 1a and chart 2, process 3: illustration 1b and chart 3) that occur individually or combined are to be differentiated from the deviation of the drilling to the desired drilling direction. The maximum drilling deviation in the area of the drill tip when drilling with a 2 mm preparatory twist drill (firm Nobel Biocare) up to 13 mm mark of length is calculated for two types of sleeves: sleeves along the lines of Yildrim (firm Nobel Biocare), and steco-titanium sleeves (firm Steco System Technology).Results:The maximum deviation at the drill tip is calculated as follows:Process 1(with parallel shifting of the drill):the maximum drill deviation is equivalent to the tolerance limit between drill and sleeve (a).Process 2(tilting of the drill to the level of the upper edge of the sleeve, illustration 1a, chart 2):for the angle (angle divergence of the drill to the sleeve axle during rotation and translation) as follows:see b).The drill deviations at the drill tip in the X and Y axles can be deduced from this as follows:See c) and d).dB: drill diameter, dH: sleeve diameter, LB: drill length, LH: sleeve lengthProcess 3(during torsion of the fixture, illustration 1b, chart 3):The following angle divergences for the drill result by torsion of the sleeve fixture:See e), f) and g).Conclusion:The maximum horizontal deviations when tilting the drill (illustration1a, chart 2) and when twisting the joint sleeve to tooth (illustration 1b, chart 3) are between 0,2 and 0,4 mm. The deviation of the drill when twisting can be neglected while doing so. The horizontal deviation when moving the drill parallel (process 1) corresponds to the tolerance limit between the drill and sleeve and lies maximum between 0,19 mm (Yildrim sleeve) and 0,4 mm (steco sleeve). A better coordination of the workpieces drill-sleeve is called for considering the fact that with further suportless drilling, or else like with the steco sleeve partly guided drilling, additional tolerance limits appear and then lie clearly above 0,5 mm. Keywords: implant, drill template, guidet drilling, tolerance, implant position