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This thesis aims to improve the computational methodology proposed by Fuentes et al. (2018) for the design of face-milled spiral bevel gear drives in order to get closer to the objective gear tooth surfaces and provide the desired meshing and contact conditions. In the existing computational methodology, all machine-tool settings, excluding velocity ratio, are treated as constants, whereas in this work, the machine-tool settings will be computed by polynomial functions up to the fourth degree of the cradle angle, approach commonly known as Universal Motion Concept (UMC). The proposed approach assumes a predefined geometry for the wheel member of the gear set and therefore the basic machine-tool settings for its production are considered as known. The computational approach involves computing the corresponding conjugated pinion to the wheel that generates the desired shape and maximum level of the function of transmission errors. Then, the surface deviations necessary to achieve the desired contact path and extension of the contact pattern are computed. These deviations allow the objective pinion geometry to be determined. Then, the machine-tool settings for the closest machinable pinion tooth surfaces have to be found in the first step, and with them the coefficients for the ap-plication of the Universal Motion Concept (UMC) has to be found in a second step. These steps will be based on the formulation of a nonlinear bound-constrained optimization problem aimed at minimizing deviations between the closest machinable surfaces and the desired ones. The proposed methodology will be demonstrated through numerical examples, showcasing its practical application and efficacy.