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This paper presents a semi-automated design algorithm for computing straight bevel gear involute profiles. The proposed formulation is based on the Tredgold approximation method. It allows the design of a pair of bevel gears with any desired number of teeth and relative axes inclination angles by implementing additive manufacturing technology. A specific case study is discussed to calculate the profiles of two straight bevel gears of a biomedical application. Namely, this paper illustrates the design of the bevel gears for a new laparoscopic robotic system, EasyLap, under development with a grant from POR Calabria 2014−2020 Fesr-Fse. A meshing analysis is carried out to identify potential design errors. Moreover, finite element-based tooth contact analysis is fulfilled for determining the vibrational performances of the conjugate tooth profiles throughout a whole meshing cycle. Simulation results and a built prototype are reported to show the engineering feasibility and effectiveness of the proposed design approach.