Justificación teórica del modelado matemático cinemático de un robot manipulador de cuatro grados de libertad

Abstract

In the context of mathematical application, the modeling of physical systems is an interest topic as well as a challenge for both, students and teachers; thus, the aim of the current research was to describe in detail the theoretical justification of the mathematical kinematic modeling of a robot which manipulates four degrees of freedom. The methodology of the current research had a qualitative approach and used a documental design, since the information about the problem to be studied was gathered from reliable bibliographic sources such as scientific papers and books. In addition, the most important characteristics of the research like definitions and the analytical obtention of equations were detailed. Through the use of these methodological aspects, it was possible to obtain a referential document on the kinematic and mathematical model, its main result evidences three chapters: The first one has to do with the description of the system which specifies the components and structure of the robot, predefining a configuration for a four degree of freedom robot with rotational joints; in the second one, the geometric model proposes the equations of each referential system; regarding its joints, the third one has to do with the cinematic model which analytically describes the spatial trajectory of the robot as a time function and particularly the relationship existing between the position and orientation of the end of the robot with the angular values of the joints. This material will be used as an alternative instrument for the teaching and learning of a mathematical application; thus, it is concluded that by means of this referential document, it is possible to contribute to the development of work in this area and to their mathematical contextualization