During the Renaissance, the idea of a complex mechanical system capable of autonomous movement, a forerunner concept of our modern automobile, found its first designs and exploratory conceptualizations. In particular, it will be one of the so-called "Sienese engineers", Francesco di Giorgio, one of the first to systematically explore the mechanics of self-propelled vehicles as part of his studies of machines that will later become part of his Treatise of Architecture. Francesco di Giorgio's self-propelled machines still lack an engine and are set in motion by human power, but their mechanics are already highly sophisticated and ahead of their time. Thanks to the various manuscripts that have been preserved, his legacy in this area is still entirely available. It facilitates the understanding of the development of the projects and the attempts to design machines for practical uses, as well as the theoretical approach to engineering during the Renaissance. This comprehensive study thoroughly describes Francesco di Giorgio's systematic approach to the mechanics of self-propelled vehicles. By comparing the various projects, from the rudimentary sketches in the Taccuino to the more sophisticated designs in the later versions of the Treatise of Architecture, a clear understanding of the logical and conceptual journey that led Francesco di Giorgio to pioneer the study of motion transmission in self-propelled vehicles can be obtained.