Betancourt Synthesis for Three-Position Problem in Mechanism Design

Between the late 18th century and the early 19th century, the Spanish engineer Agustín de Betancourt y Molina (1758–1824) left an indelible mark on the field of kinematic design of mechanisms through two groundbreaking contributions to the formulation and resolution of trajectory synthesis problems, particularly within the realm of steam engine design. These pivotal contributions are encapsulated in two distinct works: the “Mémoire sur une machine à vapeur à double effet,” presented at the French Académie Royale des Sciences in 1789, and the collaborative effort “Essai sur la composition des machines,” co-authored with José Maria de Lanz y Zaldívar (1764–1839) published in Paris in 1808. The here-in proposed comprehensive examination delves into the intricacies, advancements, limitations, and nuances of both of Betancourt’s seminal works. Today, with accessible and thoroughly studied documentation at our disposal, it is evident that these contributions represent the earliest formulations and resolutions of what would later evolve into the synthesis of a four-bar linkage, wherein the coupler point exhibits approximately rectilinear motion with three points of precision.