Mechanical engineering was the discipline of applying the principles of engineering, physics, mathematics, and materials science for the design, construction and operation of machinery.
In 1957, Jack planned to study mechanical engineering at college. (ENT: "Carbon Creek")
In 2373, Miles O'Brien commended Nog for his excellent grasp of mechanical engineering, which the Ferengi explained with his people's talent with figures. (DS9: "The Ascent")