Innovación en el diseño de mecanismos de cuatro barras (MCB): aplicación integrada de desigualdades de Hlawka-Grashoff junto a controladores tipo PID con MatLab

Abstract

Introduction: This research carries out an applied and exploratory study of four-bar mechanisms (FBM), focusing on geometric constraints for an advanced analysis that facilitates the understanding of design, construction and kinematics, aimed at practical applications in engineering and education. Problem: Traditionally, FBM design has been based on the theory of mechanisms and machines, without incorporating advanced geometric mathematical constraints such as the Hlawka inequality. This omission limits the ability to comprehensively optimize these systems for specific applications. Objective: Develop software in Matlab that integrates mathematical criteria based on the Hlawka and Grashof inequalities, also applying the Lagrangian for kinematic analysis and PI, PD and PID controllers for system dynamics using FBM. Methodology: An integrated approach that combines geometric, kinematic and control analysis was used for FBM, developing an algorithm based on the Hlawka inequality. It was complemented by the creation of software in Matlab that adjusts drivers according to Grashof's law. Validation was performed using graphical comparisons and mean absolute error (MAE) analysis with a relevant case study. Results: This project highlights the potential of an innovative mathematical approach in the design of four-bar mechanisms (FBM), significantly enriching their practical and training application. Furthermore, it sets an important precedent for future research, proposing new avenues of study and exploration in advanced kinematics and mechatronic design, thus paving the way for innovative developments in fields related to engineering and technical education. Conclusion: This project establishes a baseline for applications of FBM synthesis in control implementations, and brings the user closer to the manipulation of parameters and variables through software that guarantees the understanding of the phenomenon for the design and construction of devices. Originality: This study introduces a novel approach by integrating Hlawka inequality into FBM design, establishing a pioneering framework for future research and technological development. Limitations: Restrictions of the study arose from the paucity of specific comparative data available, underscoring the need for future research for further evaluation.