This paper aims to show the design process of a mechanical transmission system proposed by Universidad Santo Tomás for the Baja SAE competition following the standards defined by SAE normative. In this way, different CAD models and their respective calculus are presented from conceptual to detail design for each system, providing the base of the paper's objective. This paper describes SAE normative rules, the design specifications, alternative solutions, calculus, and results from validations using the finite element method and the topological optimization with ANSYS software. Finally, a mechanical design is proposed considering all the requirements for each component and following the competition rules.